Packing

2112 cases · 9 beaten · 497 reproduced · 1606 behind

Pack n unit items (circles, or regular polygons, tans, dominoes and L's allowed to rotate) in the smallest container: circle, triangle, square, pentagon, hexagon, octagon, tan, domino, or the L (a 2x2 square with one corner unit square removed; the page lists its long side). Validated with exact decimal predicates and no overlap tolerance; the beaten circle-in-L cases were also checked in exact rational arithmetic by two independently written checkers.

Beaten (9)

Circles in an L, n = 44

15.270195484 vs listed 15.27022+
margin +2.45e-05 (0.000%)

Found by Tej Stead in June 2026.

figure · coordinates

Circles in an L, n = 45

15.431836747 vs listed 15.43636+
margin +4.52e-03 (0.029%)

Found by Tej Stead in June 2026.

figure · coordinates

Circles in an L, n = 46

15.709648886 vs listed 15.71083+
margin +1.18e-03 (0.008%)

Found by Jonathan Viquerat in September 2026.

figure · coordinates

Hexagons in a domino, n = 5

3.248710331 vs listed 3.24871+
margin +9.75e-07 (0.000%)

Found by Jonathan Viquerat in April 2026.

figure · coordinates

Hexagons in a domino, n = 23

6.190597806 vs listed 6.25797+
margin +6.74e-02 (1.077%)

Found by Jonathan Viquerat in September 2026.

figure · coordinates

L's in a triangle, n = 29

16.248807784 vs listed 16.39862+
margin +1.50e-01 (0.914%)

Found by Aapo Lipponen in July 2026.

figure · coordinates

L's in a triangle, n = 30

16.387913898 vs listed 16.46648+
margin +7.86e-02 (0.477%)

Found by Aapo Lipponen in July 2026.

figure · coordinates

Tans in an L, n = 5

0.999915808 vs listed 1
margin +8.42e-05 (0.008%)

figure · coordinates

Triangles in a hexagon, n = 50

2.999355618 vs listed 3
margin +6.44e-04 (0.021%)

figure · coordinates

All cases

showing cases

Problem	n	Listed on the page	Our certified value	Margin	Margin %	Status	Listed by
Circles in a circle	2	r = 2	2.000000001	−8.00e-10	-0.000	reproduced
Circles in a circle	3	r = 1 + 2 / √3 = 2.154+	2.154700539	−8.62e-10	-0.000	reproduced
Circles in a circle	4	r = 1 + √2 = 2.414+	2.414213563	−9.66e-10	-0.000	reproduced
Circles in a circle	12	r = 4.029+	4.029601932	−6.02e-04	-0.015	reproduced	Found by Kravitz in 1967.
Circles in a circle	14	r = 4.328+	4.328428557	−4.29e-04	-0.010	reproduced	Found by Goldberg in 1971.
Circles in a circle	15	r = 4.521+	4.521356967	−3.57e-04	-0.008	reproduced	Found by Kravitz in 1967.
Circles in a circle	16	r = 4.615+	4.615425597	−4.26e-04	-0.009	reproduced	Found by Goldberg in 1971.
Circles in a circle	17	r = 4.792+	4.792033750	−3.38e-05	-0.001	reproduced	Found by Reis in 1975.
Circles in a circle	18	r = 1 + √2 + √6 = 4.863+	4.863703307	−1.95e-09	-0.000	reproduced	Found by Kravitz in 1967.
Circles in a circle	20	r = 5.122+	5.122320739	−3.21e-04	-0.006	reproduced	Found by Goldberg in 1971.
Circles in a hexagon	2	s = 1 + 2/√3 = 2.154+	2.154700539	−8.62e-10	-0.000	reproduced
Circles in a hexagon	3	s = 4/√3 = 2.309+	2.309401078	−9.24e-10	-0.000	reproduced
Circles in a hexagon	4	s = 2/√3 + 4/√7 = 2.666+	2.666558431	−1.07e-09	-0.000	reproduced	Found by Shahriar Manzoor in April 2002.
Circles in a hexagon	5	s = 2.999+	2.999355401	−3.55e-04	-0.012	reproduced	Found by Erich Friedman in 1999.
Circles in a hexagon	6	s = 2 + 2/√3 = 3.154+	3.154700540	−1.26e-09	-0.000	reproduced
Circles in a hexagon	7	s = 2 + 2/√3 = 3.154+	3.154700540	−1.26e-09	-0.000	reproduced
Circles in a hexagon	8	s = 3.709+	3.709400096	−4.00e-04	-0.011	reproduced	Found by David W. Cantrell in July 2002.
Circles in a hexagon	9	s = 20/7 + 2/√3 = 4.011+	4.011843397	−1.60e-09	-0.000	reproduced	Found by David W. Cantrell in July 2002.
Circles in a hexagon	10	s = 4.119+	4.119357181	−3.57e-04	-0.009	reproduced	Found by David W. Cantrell in July 2002.
Circles in a hexagon	11	s = 2 + 4/√3 = 4.309+	4.309401078	−1.72e-09	-0.000	reproduced	Found by Erich Friedman in 1999.
Circles in a hexagon	12	s = 2 + 4/√3 = 4.309+	4.309401078	−1.72e-09	-0.000	reproduced	Found by Erich Friedman in 1999.
Circles in a hexagon	13	s = 8/√3 = 4.618+	4.618802155	−1.85e-09	-0.000	reproduced	Found by Erich Friedman in 1999.
Circles in a hexagon	14	s = 2 + 2/√3 + 4/√7 = 4.666+	4.666558432	−1.87e-09	-0.000	reproduced	Found by David W. Cantrell in July 2002.
Circles in a hexagon	15	s = 4.961+	4.961321279	−3.21e-04	-0.006	reproduced	Found by David W. Cantrell in January 2006.
Circles in a hexagon	16	s = 4.999+	4.999355401	−3.55e-04	-0.007	reproduced	Found by David W. Cantrell in July 2002.
Circles in a hexagon	17	s = 5.133+	5.133119426	−1.19e-04	-0.002	reproduced	Found by David W. Cantrell in January 2006.
Circles in a hexagon	18	s = 4 + 2/√3 = 5.154+	5.154700540	−1.55e-09	-0.000	reproduced
Circles in a hexagon	19	s = 4 + 2/√3 = 5.154+	5.154700540	−1.55e-09	-0.000	reproduced
Circles in a hexagon	20	s = 5.676+	5.676887318	−8.87e-04	-0.016	reproduced	Found by David W. Cantrell in July 2012.
Circles in a hexagon	21	s = 5.709+	5.709400097	−4.00e-04	-0.007	reproduced	Found by David W. Cantrell in July 2012.
Circles in a hexagon	22	s = 5.952+	5.951749794	+2.50e-04	0.004	reproduced	Found by David W. Cantrell in July 2012.
Circles in a hexagon	23	s = 34/7 + 2/√3 = 6.011+	6.011843397	−1.80e-09	-0.000	reproduced	Found by David W. Cantrell in July 2012.
Circles in a hexagon	24	s = 6.117+	6.117620861	−6.21e-04	-0.010	reproduced	Found by Rob Pratt in March 2020.
Circles in a pentagon	2	s = 2tan(36°) + √5 - 1 s = 2.689+	2.689153035	−1.53e-04	-0.006	reproduced
Circles in a pentagon	3	s = 3.015+	3.015862479	−8.62e-04	-0.029	reproduced	Found by George Sicherman in July 2012.
Circles in a pentagon	4	s = 3.314+	3.314449566	−4.50e-04	-0.014	reproduced	Found by George Sicherman in July 2012.
Circles in a pentagon	5	s = 2tan(36°) + 2 s = 3.453+	3.453085057	−8.51e-05	-0.002	reproduced
Circles in a pentagon	6	s = 2tan(36°) + 4sin(36°) s = 3.804+	3.804226067	−2.26e-04	-0.006	reproduced
Circles in a pentagon	7	s = 4.236+	4.236120738	−1.21e-04	-0.003	reproduced	Found by George Sicherman in July 2012.
Circles in a pentagon	8	s = 4.564+	4.564580947	−5.81e-04	-0.013	reproduced	Found by George Sicherman in July 2012.
Circles in a pentagon	9	s = 4.825+	4.825026360	−2.64e-05	-0.001	reproduced	Found by George Sicherman in July 2012.
Circles in a pentagon	10	s = 5.095+	5.095192535	−1.93e-04	-0.004	reproduced	Found by George Sicherman in July 2012.
Circles in a pentagon	11	s = 5.240+	5.240278496	−2.78e-04	-0.005	reproduced	Found by David W. Cantrell in July 2012.
Circles in a pentagon	12	s = 5.407+	5.407790091	−7.90e-04	-0.015	reproduced	Found by George Sicherman in July 2012.
Circles in a pentagon	13	s = 5.651+	5.651781418	−7.81e-04	-0.014	reproduced	Found by George Sicherman in July 2012.
Circles in a pentagon	14	s = 5.808+	5.808533027	−5.33e-04	-0.009	reproduced	Found by George Sicherman in July 2012.
Circles in a pentagon	15	s = 5.945+	5.945158606	−1.59e-04	-0.003	reproduced	Found by George Sicherman in July 2012.
Circles in a pentagon	16	s = 6.129+	6.129607483	−6.07e-04	-0.010	reproduced	Found by George Sicherman in July 2012.
Circles in a pentagon	17	s = 6.419+	6.419436755	−4.37e-04	-0.007	reproduced	Found by David W. Cantrell in July 2012.
Circles in a pentagon	18	s = 6.586+	6.586813631	−8.14e-04	-0.012	reproduced	Found by David W. Cantrell in July 2012.
Circles in a pentagon	19	s = 6.777+	6.777892052	−8.92e-04	-0.013	reproduced	Found by David W. Cantrell in July 2012.
Circles in a pentagon	20	s = 6.944+	6.944556888	−5.57e-04	-0.008	reproduced	Found by David W. Cantrell in July 2012.
Circles in a pentagon	21	s = 7.107+	7.107266889	−2.67e-04	-0.004	reproduced	Found by David W. Cantrell in July 2012.
Circles in a pentagon	22	s = 7.271+	7.271271706	−2.72e-04	-0.004	reproduced	Found by David W. Cantrell in July 2012.
Circles in a pentagon	23	s = 7.397+	7.397090335	−9.03e-05	-0.001	reproduced	Found by David W. Cantrell in July 2012.
Circles in a pentagon	24	s = 7.534+	7.534389921	−3.90e-04	-0.005	reproduced	Found by David W. Cantrell in July 2012.
Circles in a square	2	s = 2 + √2 = 3.414+	3.414213564	−1.37e-09	-0.000	reproduced
Circles in a square	3	s = 2 + 1/√2 + √6/2 = 3.931+	3.931851654	−1.57e-09	-0.000	reproduced
Circles in a square	4	s = 4	4.000000002	−1.60e-09	-0.000	reproduced
Circles in a square	5	s = 2 + 2√2 = 4.828+	4.828427127	−1.93e-09	-0.000	reproduced
Circles in a tan	8	s = 2 + 3√2 + √6 = 8.692+	8.692130433	−3.48e-09	-0.000	reproduced	Found by Hans Melissen in 1997.
Circles in a tan	9	s = 2 + 5√2 = 9.071+	9.071067815	−3.63e-09	-0.000	reproduced
Circles in a tan	10	s = 8 + √2 = 9.414+	9.414213566	−3.77e-09	-0.000	reproduced
Circles in a tan	11	s = 5 + √(2/3) + 3√2 = 10.059+	10.059137272	−4.02e-09	-0.000	reproduced	Found by David W. Cantrell in June 2005.
Circles in a tan	12	s = 10.422+	10.422815211	−8.15e-04	-0.008	reproduced	Found by David W. Cantrell in June 2005.
Circles in a tan	13	s = 10.798+	10.798666393	−6.66e-04	-0.006	reproduced	Found by Hans Melissen in 1997.
Circles in a tan	14	s = 2 + 3√2 + 2√6 = 11.141+	11.141620177	−4.46e-09	-0.000	reproduced	Found by Erich Friedman in April 2005.
Circles in a tan	15	s = 10 + √2 = 11.414+	11.414213565	−3.02e-09	-0.000	reproduced
Circles in a tan	16	s = 11.892+	11.891982511	+1.75e-05	0.000	reproduced	Found by David W. Cantrell in January 2006.
Circles in a tan	17	s = 12.155+	12.155914064	−9.14e-04	-0.008	reproduced	Found by David W. Cantrell in January 2006.
Circles in a tan	18	s = 12.542+	12.542719624	−7.20e-04	-0.006	reproduced	Found by Eckard Specht in April 2009.
Circles in a tan	19	s = 12.798+	12.798666392	−6.66e-04	-0.005	reproduced	Found by David W. Cantrell in January 2006.
Circles in a tan	20	s = 13.092+	13.092605393	−6.05e-04	-0.005	reproduced	Found by Maurizio Morandi in December 2008.
Circles in a tan	21	s = 12 + √2 = 13.414+	13.414213566	−3.72e-09	-0.000	reproduced
Circles in a triangle	2	s = 2 + 2√3 = 5.464+	5.464101617	−2.19e-09	-0.000	reproduced
Circles in a triangle	3	s = 2 + 2√3 = 5.464+	5.464101617	−2.19e-09	-0.000	reproduced
Circles in a triangle	13	s = 4 + 2√6/3 + 10√3/3 = 11.406+	11.406495858	−4.56e-09	-0.000	reproduced	Found by Melissen in 1993.
Circles in a triangle	14	s = 8 + 2√3 = 11.464+	11.464101620	−4.59e-09	-0.000	reproduced	Found by Erdős/Oler in 1961.
Circles in an L	2	s = 4	4.000000002	−1.60e-09	-0.000	reproduced
Circles in an L	3	s = 4	4.000000002	−1.60e-09	-0.000	reproduced
Circles in an L	4	s = 5.304+	5.304812895	−8.13e-04	-0.015	reproduced	Found by Erich Friedman in June 2005.
Circles in an L	5	s = 5.780+	5.780892895	−8.93e-04	-0.015	reproduced	Found by David W. Cantrell in June 2005.
Circles in an L	6	s = 6.416+	6.416500412	−5.00e-04	-0.008	reproduced	Found by David W. Cantrell in June 2005.
Circles in an L	7	s = 6.787+	6.787322146	−3.22e-04	-0.005	reproduced	Found by David W. Cantrell in June 2005.
Circles in an L	8	s = 7.116+	7.116251345	−2.51e-04	-0.004	reproduced	Found by Erich Friedman in June 2005.
Circles in an L	9	s = 4 + 12/√13 = 7.328+	7.328201180	−2.93e-09	-0.000	reproduced	Found by Erich Friedman in June 2005.
Circles in an L	10	s = 7.628+	7.628290963	−2.91e-04	-0.004	reproduced	Found by Erich Friedman in June 2005.
Circles in an L	11	s = 4 + √2 + √6 = 7.863+	7.863703308	−3.15e-09	-0.000	reproduced	Found by David W. Cantrell in January 2006.
Circles in an L	12	s = 8	8.000000003	−3.20e-09	-0.000	reproduced
Circles in an L	13	s = 8.812+	8.812490023	−4.90e-04	-0.006	reproduced	Found by David W. Cantrell in January 2006.
Circles in an L	14	s = 9.085+	9.085893323	−8.93e-04	-0.010	reproduced	Found by David W. Cantrell in January 2006.
Circles in an L	15	s = 9.412+	9.412649498	−6.49e-04	-0.007	reproduced	Found by David W. Cantrell in January 2006.
Circles in an L	16	s = 9.635+	9.635745974	−7.46e-04	-0.008	reproduced	Found by David W. Cantrell in January 2006.
Circles in an L	17	s = 10.00425+	10.004253590	−3.59e-06	-0.000	reproduced	Found by Tej Stead in June 2026.
Circles in an L	18	s = 10.27388+	10.273885059	−5.06e-06	-0.000	reproduced	Found by Tej Stead in June 2026.
Circles in an L	19	s = 10.46489+	10.464896647	−6.65e-06	-0.000	reproduced	Found by Tej Stead in June 2026.
Circles in an L	20	s = 10.61664+	10.616645072	−5.07e-06	-0.000	reproduced	Found by Tej Stead in June 2026.
Circles in an L	21	s = 10.82564+	10.825649498	−9.50e-06	-0.000	reproduced	Found by Tej Stead in June 2026.
Circles in an L	22	s = 10.89927+	10.899275670	−5.67e-06	-0.000	reproduced	Found by Tej Stead in June 2026.
Circles in an L	23	s = 11.21781+	11.217812413	−2.41e-06	-0.000	reproduced	Found by Tej Stead in June 2026.
Circles in an L	24	s = 11.41224+	11.412241305	−1.30e-06	-0.000	reproduced	Found by Tej Stead in June 2026.
Circles in an L	25	s = 11.71270+	11.712699601	+3.99e-07	0.000	reproduced	Found by Tej Stead in June 2026.
Circles in an L	26	s = 11.86038+	11.860386699	−6.70e-06	-0.000	reproduced	Found by Tej Stead in June 2026.
Circles in an L	27	s = 12	12.000000003	−3.28e-09	-0.000	reproduced
Circles in an L	28	s = 12.49680+	12.496806465	−6.46e-06	-0.000	reproduced	Found by Tej Stead in June 2026.
Circles in an L	29	s = 12.67553+	12.675529689	+3.11e-07	0.000	reproduced	Found by Tej Stead in June 2026.
Circles in an L	30	s = 12.94284+	12.942845261	−5.26e-06	-0.000	reproduced	Found by Tej Stead in June 2026.
Circles in an L	31	s = 13.12408+	13.124080708	−7.08e-07	-0.000	reproduced	Found by Tej Stead in June 2026.
Circles in an L	32	s = 13.30282+	13.302823642	−3.64e-06	-0.000	reproduced	Found by Tej Stead in June 2026.
Circles in an L	33	s = 13.52754+	13.527544221	−4.22e-06	-0.000	reproduced	Found by Jonathan Viquerat in September 2026.
Circles in an L	34	s = 13.72415+	13.724157861	−7.86e-06	-0.000	reproduced	Found by Tej Stead in June 2026.
Circles in an L	35	s = 13.86770+	13.867708776	−8.78e-06	-0.000	reproduced	Found by Leo Strijbos in August 2026.
Circles in an L	36	s = 14.01152+	14.011527575	−7.58e-06	-0.000	reproduced	Found by Tej Stead in June 2026.
Circles in an L	37	s = 14.10954+	14.109546337	−6.34e-06	-0.000	reproduced	Found by Tej Stead in June 2026.
Circles in an L	38	s = 14.23736+	14.237364434	−4.43e-06	-0.000	reproduced	Found by Tej Stead in June 2026.
Circles in an L	39	s = 14.30561+	14.305616537	−6.54e-06	-0.000	reproduced	Found by Tej Stead in June 2026.
Circles in an L	40	s = 14.54974+	14.549742882	−2.88e-06	-0.000	reproduced	Found by Tej Stead in June 2026.
Circles in an L	41	s = 14.69163+	14.691635123	−5.12e-06	-0.000	reproduced	Found by Tej Stead in June 2026.
Circles in an L	42	s = 14.90788+	14.907881852	−1.85e-06	-0.000	reproduced	Found by Tej Stead in June 2026.
Circles in an L	43	s = 15.06571+	15.065713308	−3.31e-06	-0.000	reproduced	Found by Tej Stead in June 2026.
Circles in an L	44	s = 15.27022+	15.270195484	+2.45e-05	0.000	beaten	Found by Tej Stead in June 2026.
Circles in an L	45	s = 15.43636+	15.431836747	+4.52e-03	0.029	beaten	Found by Tej Stead in June 2026.
Circles in an L	46	s = 15.71083+	15.709648886	+1.18e-03	0.008	beaten	Found by Jonathan Viquerat in September 2026.
Circles in an L	47	s = 15.85935+	15.859349870	+1.30e-07	0.000	reproduced	Found by Jonathan Viquerat in September 2026.
Circles in an L	48	s = 15.98311+	15.983106863	+3.14e-06	0.000	reproduced	Found by Tej Stead in June 2026.
Circles in an L	49	s = 16.13179+	16.131792995	−3.00e-06	-0.000	reproduced	Found by Leo Strijbos in August 2026.
Circles in an L	50	s = 16.30078+	16.300776166	+3.83e-06	0.000	reproduced	Found by Jonathan Viquerat in September 2026.
Dominoes in a circle	2	r = √2 = 1.41421+	1.414213572	−9.53e-09	-0.000	reproduced
Dominoes in a circle	3	r = √13/2 = 1.80277+	1.802775664	−2.59e-08	-0.000	reproduced
Dominoes in a circle	4	r = 1.97949+	1.979495622	−5.62e-06	-0.000	reproduced	Found by Jonathan Viquerat in May 2026
Dominoes in a circle	5	r = 2.18039+	2.180565951	−1.76e-04	-0.008	behind	Found by Jonathan Viquerat in May 2026.
Dominoes in a circle	6	r = √5 = 2.23606+	2.355851455	−1.20e-01	-5.357	behind
Dominoes in a circle	7	r = 2.51459+	2.515370505	−7.81e-04	-0.031	behind	Found by Jonathan Viquerat in May 2026.
Dominoes in a circle	8	r = 2.65851+	2.771078931	−1.13e-01	-4.234	behind	Found by Jonathan Viquerat in May 2026.
Dominoes in a circle	9	r = 2.76860+	2.786397797	−1.78e-02	-0.643	behind	Found by Jonathan Viquerat in May 2026.
Dominoes in a circle	10	r = 2.93560+	2.968276694	−3.27e-02	-1.113	behind	Found by Jonathan Viquerat in August 2026.
Dominoes in a circle	11	r = 3.08701+	3.261265256	−1.74e-01	-5.645	behind	Found by Jonathan Viquerat in August 2026.
Dominoes in a circle	12	r = √10 = 3.16227+	3.354102043	−1.92e-01	-6.066	behind	Found by Maurizio Morandi in May 2026.
Dominoes in a circle	13	r = 3.27852+	3.411424403	−1.33e-01	-4.054	behind	Found by Jonathan Viquerat in May 2026.
Dominoes in a circle	14	r = 3.37689+	3.629240510	−2.52e-01	-7.473	behind	Found by Jonathan Viquerat in May 2026.
Dominoes in a circle	15	r = 3.48515+	3.649879165	−1.65e-01	-4.727	behind	Found by Jonathan Viquerat in May 2026.
Dominoes in a circle	16	r = √13 = 3.60555+	3.786572973	−1.81e-01	-5.021	behind	Found by Jonathan Viquerat in May 2026.
Dominoes in a circle	17	r = √53/2 = 3.64005+	3.750656366	−1.11e-01	-3.038	behind	Found by Maurizio Morandi in May 2026.
Dominoes in a circle	18	r = 3.78121+	4.132510889	−3.51e-01	-9.291	behind	Found by Jonathan Viquerat in May 2026.
Dominoes in a circle	19	r = 3.85867+	4.217066296	−3.58e-01	-9.288	behind	Found by Jonathan Viquerat in August 2026.
Dominoes in a circle	20	r = 3.99407+	4.189908554	−1.96e-01	-4.903	behind	Found by Jonathan Viquerat in May 2026.
Dominoes in a circle	21	r = 4.09448+	4.383777682	−2.89e-01	-7.066	behind	Found by Jonathan Viquerat in August 2026.
Dominoes in a circle	22	r = 4.17546+	4.445780882	−2.70e-01	-6.474	behind	Found by Jonathan Viquerat in August 2026.
Dominoes in a circle	23	r = 4.25369+	4.517920953	−2.64e-01	-6.212	behind	Found by Jonathan Viquerat in May 2026.
Dominoes in a circle	24	r = 4.27200+	4.605259437	−3.33e-01	-7.801	behind	Found by Jonathan Viquerat in August 2026.
Dominoes in a circle	25	r = 4.40723+	4.712585593	−3.05e-01	-6.929	behind	Found by Jonathan Viquerat in August 2026.
Dominoes in a domino	2	s = (2+√2)/√3 = 1.971+	1.971197120	−8.55e-10	-0.000	reproduced	Found by Erich Friedman in April 2026.
Dominoes in a domino	3	s = 2	2.000000001	−8.00e-10	-0.000	reproduced
Dominoes in a domino	4	s = 2	2.000000001	−8.00e-10	-0.000	reproduced
Dominoes in a domino	5	s = 5/2 = 2.5	2.500000038	−3.77e-08	-0.000	reproduced
Dominoes in a domino	6	s = 2.916+	3.000000056	−8.40e-02	-2.881	behind	Found by Erich Friedman in April 2026.
Dominoes in a domino	7	s = 3	3.000000051	−5.09e-08	-0.000	reproduced
Dominoes in a domino	8	s = 3	3.000000058	−5.83e-08	-0.000	reproduced
Dominoes in a domino	9	s = 3	3.000000056	−5.58e-08	-0.000	reproduced
Dominoes in a domino	10	s = 7/2 = 3.5	3.500399378	−3.99e-04	-0.011	reproduced
Dominoes in a domino	11	s = (5+√41)/3 = 3.801+	4.000000084	−1.99e-01	-5.234	behind	Found by Maurizio Morandi in April 2026.
Dominoes in a domino	12	s = 5/2+√2 = 3.914+	4.000000080	−8.58e-02	-2.192	behind	Found by Maurizio Morandi in April 2026.
Dominoes in a domino	13	s = 4	4.000000002	−1.60e-09	-0.000	reproduced	Inherited published construction at n=14; not a newly discovered record
Dominoes in a domino	14	s = 4	4.000000002	−1.60e-09	-0.000	reproduced
Dominoes in a domino	15	s = 4	4.000000076	−7.64e-08	-0.000	reproduced
Dominoes in a domino	16	s = 4	4.000000076	−7.56e-08	-0.000	reproduced
Dominoes in a domino	17	s = 9/2 = 4.5	4.504410611	−4.41e-03	-0.098	reproduced
Dominoes in a domino	18	s = 9/2 = 4.5	4.550237521	−5.02e-02	-1.116	reproduced
Dominoes in a domino	19	s = 3(5+√2)/4 = 4.81066+	5.006748390	−1.96e-01	-4.076	behind	Found by Maurizio Morandi in June 2026.
Dominoes in a domino	20	s = 4.95714+	5.000028388	−4.29e-02	-0.865	behind	Found by Maurizio Morandi in June 2026.
Dominoes in a domino	21	s = 5	5.000034280	−3.43e-05	-0.001	behind
Dominoes in a domino	22	s = 5	5.000332101	−3.32e-04	-0.007	behind
Dominoes in a domino	23	s = 5	5.001294930	−1.29e-03	-0.026	behind
Dominoes in a domino	24	s = 5	5.002345650	−2.35e-03	-0.047	behind
Dominoes in a domino	25	s = 5	5.386125347	−3.86e-01	-7.723	behind
Dominoes in a hexagon	2	s = 2/3^(1/4) = 1.51967+	1.519671385	−1.37e-08	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Dominoes in a hexagon	3	s = √2(3)^(1/4) = 1.86120+	1.861209750	−3.19e-08	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Dominoes in a hexagon	4	s = 1+2/√3 = 2.15470+	2.154700584	−4.58e-08	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Dominoes in a hexagon	5	s = 4/√3 = 2.30940+	2.309401130	−5.35e-08	-0.000	reproduced
Dominoes in a hexagon	6	s = 1+5√3/6 = 2.44337+	2.484192219	−4.08e-02	-1.671	behind	Found by Jonathan Viquerat in May 2026.
Dominoes in a hexagon	7	s = 2.63126+	2.728312746	−9.71e-02	-3.688	behind	Found by Aapo Lipponen in July 2026.
Dominoes in a hexagon	8	s = 2.85220+	2.925149823	−7.29e-02	-2.558	behind	Found by Jonathan Viquerat in May 2026.
Dominoes in a hexagon	9	s = 2.93631+	3.008565343	−7.23e-02	-2.461	behind	Found by Jonathan Viquerat in May 2026.
Dominoes in a hexagon	10	s = 3.20593+	3.256366576	−5.04e-02	-1.573	behind	Found by Aapo Lipponen in July 2026.
Dominoes in a hexagon	11	s = 3.33391+	3.464101684	−1.30e-01	-3.905	behind	Found by Luke Kaiser in September 2026.
Dominoes in a hexagon	12	s = 3.44304+	3.601273566	−1.58e-01	-4.596	behind	Found by Luke Kaiser in September 2026.
Dominoes in a hexagon	13	s = 3.52702+	3.670637486	−1.44e-01	-4.072	behind	Found by Jonathan Viquerat in May 2026.
Dominoes in a hexagon	14	s = 3.65080+	3.729108393	−7.83e-02	-2.145	behind	Found by Luke Kaiser in September 2026.
Dominoes in a hexagon	15	s = 2(12)^(1/4) = 3.72241+	3.839768564	−1.17e-01	-3.153	behind	Found by Maurizio Morandi in July 2026.
Dominoes in a hexagon	16	s = 3.87030+	4.136723692	−2.66e-01	-6.884	behind	Found by Luke Kaiser in September 2026.
Dominoes in a hexagon	17	s = 4.00242+	4.457212454	−4.55e-01	-11.363	behind	Found by Luke Kaiser in September 2026.
Dominoes in a hexagon	18	s = 2+7√3/6 = 4.02072+	4.491089836	−4.70e-01	-11.698	behind	Found by Maurizio Morandi in July 2026.
Dominoes in a hexagon	19	s = 4.19677+	4.628932373	−4.32e-01	-10.297	behind	Found by Jonathan Viquerat in May 2026.
Dominoes in a hexagon	20	s = 4.35104+	4.628167247	−2.77e-01	-6.369	behind	Found by Luke Kaiser in September 2026.
Dominoes in a hexagon	21	s = 4.43949+	4.634177126	−1.95e-01	-4.385	behind	Found by Luke Kaiser in September 2026.
Dominoes in a hexagon	22	s = 4.54229+	4.768194748	−2.26e-01	-4.973	behind	Found by Luke Kaiser in September 2026.
Dominoes in a hexagon	23	s = 2+3√3/2 = 4.59807+	4.831566310	−2.33e-01	-5.078	behind	Found by Maurizio Morandi in July 2026.
Dominoes in a hexagon	24	s = 2+3√3/2 = 4.59807+	4.698458445	−1.00e-01	-2.183	behind	Found by Maurizio Morandi in July 2026.
Dominoes in a hexagon	25	s = 3+√3 = 4.73205+	4.851100258	−1.19e-01	-2.516	behind	Found by Maurizio Morandi in July 2026.
Dominoes in a hexagon	26	s = 4+√3/2 = 4.86602+	5.088196055	−2.22e-01	-4.566	behind	Found by Maurizio Morandi in July 2026.
Dominoes in a hexagon	27	s = 4.95289+	5.334327147	−3.81e-01	-7.701	behind	Found by Jonathan Viquerat in September 2026.
Dominoes in a hexagon	28	s = 5.07598+	5.381169643	−3.05e-01	-6.012	behind	Found by Luke Kaiser in September 2026.
Dominoes in a hexagon	29	s = 2+11√3/6 = 5.17542+	5.538719287	−3.63e-01	-7.020	behind	Found by Maurizio Morandi in July 2026.
Dominoes in a hexagon	30	s = 2+11√3/6 = 5.17542+	5.425542479	−2.50e-01	-4.833	behind	Found by Maurizio Morandi in July 2026.
Dominoes in a pentagon	2	s = 1.86166+	1.861668577	−8.58e-06	-0.000	reproduced	Found by Aapo Lipponen in July 2026.
Dominoes in a pentagon	3	s = 2.31933+	2.319335606	−5.61e-06	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Dominoes in a pentagon	4	s = 2.58859+	2.588595825	−5.83e-06	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Dominoes in a pentagon	5	s = 2.80725+	2.807256341	−6.34e-06	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Dominoes in a pentagon	6	s = 2.98883+	2.988831868	−1.87e-06	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Dominoes in a pentagon	7	s = 3.24589+	3.348544121	−1.03e-01	-3.163	behind	Found by Jonathan Viquerat in May 2026.
Dominoes in a pentagon	8	s = 3.49269+	3.625397741	−1.33e-01	-3.800	behind	Found by Jonathan Viquerat in May 2026.
Dominoes in a pentagon	9	s = 3.65963+	3.724506393	−6.49e-02	-1.773	behind	Found by Jonathan Viquerat in May 2026.
Dominoes in a pentagon	10	s = 3.82264+	4.012541325	−1.90e-01	-4.968	behind	Found by Jonathan Viquerat in May 2026.
Dominoes in a pentagon	11	s = 3.94761+	4.235426770	−2.88e-01	-7.291	behind	Found by Jonathan Viquerat in May 2026.
Dominoes in a pentagon	12	s = 4.13414+	4.420234203	−2.86e-01	-6.920	behind	Found by Jonathan Viquerat in August 2026.
Dominoes in a pentagon	13	s = 4.26767+	4.380532304	−1.13e-01	-2.645	behind	Found by Jonathan Viquerat in May 2026.
Dominoes in a pentagon	14	s = 4.50050+	4.589929776	−8.94e-02	-1.987	behind	Found by Jonathan Viquerat in May 2026.
Dominoes in a pentagon	15	s = 4.59464+	4.938689230	−3.44e-01	-7.488	behind	Found by Jonathan Viquerat in August 2026.
Dominoes in a pentagon	16	s = 4.73238+	4.865180017	−1.33e-01	-2.806	behind	Found by Luke Kaiser in September 2026.
Dominoes in a pentagon	17	s = 4.84579+	5.404585024	−5.59e-01	-11.532	behind	Found by Jonathan Viquerat in August 2026.
Dominoes in a pentagon	18	s = 4+√((5+√5)/8) = 4.95105+	5.417264114	−4.66e-01	-9.416	behind	Found by Maurizio Morandi in August 2026.
Dominoes in a pentagon	19	s = 5.16530+	5.610794929	−4.45e-01	-8.625	behind	Found by Luke Kaiser in September 2026.
Dominoes in a pentagon	20	s = 5.26425+	5.682735273	−4.18e-01	-7.950	behind	Found by Jonathan Viquerat in August 2026.
Dominoes in a pentagon	21	s = 5.40180+	5.772848849	−3.71e-01	-6.869	behind	Found by Jonathan Viquerat in August 2026.
Dominoes in a pentagon	22	s = 5.53463+	5.658094139	−1.23e-01	-2.231	behind	Found by Luke Kaiser in September 2026.
Dominoes in a pentagon	23	s = 5.63467+	5.899713376	−2.65e-01	-4.704	behind	Found by Luke Kaiser in September 2026.
Dominoes in a pentagon	24	s = 5.70796+	5.883083232	−1.75e-01	-3.068	behind	Found by Jonathan Viquerat in August 2026.
Dominoes in a pentagon	25	s = 5.84981+	5.991777780	−1.42e-01	-2.427	behind	Found by Jonathan Viquerat in August 2026.
Dominoes in a pentagon	26	s = 5.94561+	6.425751084	−4.80e-01	-8.076	behind	Found by Jonathan Viquerat in August 2026.
Dominoes in a pentagon	27	s = 6.03477+	6.279659485	−2.45e-01	-4.058	behind	Found by Jonathan Viquerat in August 2026.
Dominoes in a pentagon	28	s = 6.19946+	6.458944272	−2.59e-01	-4.186	behind	Found by Jonathan Viquerat in August 2026.
Dominoes in a pentagon	29	s = 6.27249+	6.748334999	−4.76e-01	-7.586	behind	Found by Jonathan Viquerat in August 2026.
Dominoes in a pentagon	30	s = 6.36194+	6.811864942	−4.50e-01	-7.072	behind	Found by Jonathan Viquerat in August 2026.
Dominoes in a square	2	s = 2	2.000000001	−8.00e-10	-0.000	reproduced
Dominoes in a square	4	s = 3	3.000000001	−1.20e-09	-0.000	reproduced
Dominoes in a square	6	s = 4	4.000000002	−1.60e-09	-0.000	reproduced
Dominoes in a square	7	s = 4	4.000000020	−1.98e-08	-0.000	reproduced
Dominoes in a square	8	s = 4	4.000000076	−7.56e-08	-0.000	reproduced
Dominoes in a square	9	s = 4.86784+	4.939418233	−7.16e-02	-1.470	behind	Found by Aapo Lipponen in July 2026.
Dominoes in a square	10	s = 5	5.002532217	−2.53e-03	-0.051	behind
Dominoes in a square	11	s = 5	5.000013050	−1.31e-05	-0.000	behind
Dominoes in a square	12	s = 5	6.000041841	−1.0000	-20.001	behind
Dominoes in a square	13	s = 5+1/√2 = 5.70710+	6.000000124	−2.93e-01	-5.132	behind	Found by Jonathan Viquerat in May 2026.
Dominoes in a square	14	s = 3+2√2 = 5.82842+	6.000026094	−1.72e-01	-2.944	behind	Found by Maurizio Morandi in June 2026.
Dominoes in a square	15	s = 6	6.000011444	−1.14e-05	-0.000	behind
Dominoes in a square	16	s = 6	6.000413722	−4.14e-04	-0.007	behind
Dominoes in a square	17	s = 6	6.015695797	−1.57e-02	-0.262	behind
Dominoes in a square	18	s = 6	6.000039003	−3.90e-05	-0.001	behind
Dominoes in a square	19	s = 47/7 = 6.71428+	7.005509629	−2.91e-01	-4.337	behind	Found by Maurizio Morandi in June 2026.
Dominoes in a square	20	s = 11/2+√2 = 6.91421+	7.001648960	−8.74e-02	-1.265	behind	Found by Maurizio Morandi in August 2026.
Dominoes in a square	21	s = 7	7.023071376	−2.31e-02	-0.330	behind
Dominoes in a square	22	s = 7	8.002727369	−1.0027	-14.325	behind
Dominoes in a square	23	s = 7	8.012743313	−1.0127	-14.468	behind
Dominoes in a square	24	s = 7	8.016026579	−1.0160	-14.515	behind
Dominoes in a square	25	s = 7+1/√2 = 7.70710+	8.005276147	−2.98e-01	-3.869	behind	Found by Maurizio Morandi in August 2026.
Dominoes in a square	26	s = 5+2√2 = 7.82842+	8.003907263	−1.75e-01	-2.242	behind	Found by Maurizio Morandi in August 2026.
Dominoes in a square	27	s = 8	8.013833447	−1.38e-02	-0.173	behind
Dominoes in a square	28	s = 8	8.007879951	−7.88e-03	-0.098	behind
Dominoes in a square	29	s = 8	8.000782244	−7.82e-04	-0.010	behind
Dominoes in a square	30	s = 8	8.033610843	−3.36e-02	-0.420	behind
Dominoes in a square	31	s = 8	8.020187413	−2.02e-02	-0.252	behind
Dominoes in a square	32	s = 8	8.075638221	−7.56e-02	-0.945	behind
Dominoes in a tan	2	s = 1+2√2 = 3.82842+	3.828427141	−1.61e-08	-0.000	reproduced
Dominoes in a tan	3	s = 3√2 = 4.24264+	4.242640689	−1.70e-09	-0.000	reproduced
Dominoes in a tan	4	s = 2+2√2 = 4.82842+	4.949747487	−1.21e-01	-2.513	behind	Found by Erich Friedman in May 2026
Dominoes in a tan	5	s = 1+3√2 = 5.24264+	5.242640722	−3.44e-08	-0.000	reproduced	Found by Erich Friedman in May 2026.
Dominoes in a tan	6	s = 4√2 = 5.65685+	5.828427237	−1.72e-01	-3.033	behind
Dominoes in a tan	7	s = 2+3√2 = 6.24264+	6.242640808	−1.21e-07	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Dominoes in a tan	8	s = 5+√2 = 6.41421+	6.618741797	−2.05e-01	-3.189	behind	Found by Erich Friedman in May 2026.
Dominoes in a tan	9	s = 4+2√2 = 6.82842+	7.007474369	−1.79e-01	-2.622	behind	Found by Erich Friedman in May 2026.
Dominoes in a tan	10	s = 5√2 = 7.07106+	7.414213710	−3.43e-01	-4.853	behind
Dominoes in a tan	11	s = 6+√2 = 7.41421+	7.538142665	−1.24e-01	-1.672	behind	Found by Jonathan Viquerat in May 2026.
Dominoes in a tan	12	s = 5+2√2 = 7.82842+	7.829498746	−1.07e-03	-0.014	behind	Found by Jonathan Viquerat in May 2026.
Dominoes in a tan	13	s = 8	8.333590058	−3.34e-01	-4.170	behind	Found by Erich Friedman in May 2026.
Dominoes in a tan	14	s = 4+3√2 = 8.24264+	9.088750096	−8.46e-01	-10.265	behind	Found by Maurizio Morandi in May 2026.
Dominoes in a tan	15	s = 6√2 = 8.48528+	9.078887519	−5.94e-01	-6.996	behind
Dominoes in a tan	16	s = 6+2√2 = 8.82842+	8.830299434	−1.87e-03	-0.021	behind	Found by Erich Friedman in May 2026.
Dominoes in a tan	17	s = 9	10.163959327	−1.1640	-12.933	behind	Found by Maurizio Morandi in May 2026.
Dominoes in a tan	18	s = 5+3√2 = 9.24264+	10.090449130	−8.48e-01	-9.173	behind	Found by Maurizio Morandi in May 2026.
Dominoes in a tan	19	s = 1+6√2 = 9.48528+	10.266843558	−7.82e-01	-8.240	behind	Found by Maurizio Morandi in May 2026.
Dominoes in a tan	20	s = 7+2√2 = 9.82842+	10.366945735	−5.39e-01	-5.479	behind	Found by Jonathan Viquerat in May 2026.
Dominoes in a triangle	2	s = 2+4/√3 = 4.30940+	4.309401078	−1.72e-09	-0.000	reproduced
Dominoes in a triangle	3	s = 2+4/√3 = 4.30940+	4.309401078	−1.72e-09	-0.000	reproduced
Dominoes in a triangle	4	s = 5.38188+	5.381887117	−7.12e-06	-0.000	reproduced	Found by Jonathan Viquerat in April 2026.
Dominoes in a triangle	5	s = 2+2√3 = 5.46410+	5.464101686	−7.06e-08	-0.000	reproduced	Found by Jonathan Viquerat in April 2026.
Dominoes in a triangle	6	s = 4+4/√3 = 6.30940+	6.593261133	−2.84e-01	-4.499	behind	Found by Jonathan Viquerat in April 2026.
Dominoes in a triangle	7	s = 6.61394+	6.618830469	−4.89e-03	-0.074	behind	Found by Aapo Lipponen in July 2026.
Dominoes in a triangle	8	s = 6+2/√3 = 7.15470+	7.154700687	−1.49e-07	-0.000	reproduced	Found by Jonathan Viquerat in April 2026.
Dominoes in a triangle	9	s = 5+4/√3 = 7.30940+	7.466282999	−1.57e-01	-2.146	behind	Found by Jonathan Viquerat in April 2026.
Dominoes in a triangle	10	s = 3+8/√3 = 7.61880+	7.625035401	−6.23e-03	-0.082	behind	Found by Bhavithran Ananthan in July 2026.
Dominoes in a triangle	11	s = 7+2/√3 = 8.15470+	8.679517618	−5.25e-01	-6.436	behind	Found by Jonathan Viquerat in April 2026.
Dominoes in a triangle	12	s = 6+4/√3 = 8.30940+	8.619012732	−3.10e-01	-3.726	behind	Found by Jonathan Viquerat in April 2026.
Dominoes in a triangle	13	s = 4+8/√3 = 8.61880+	9.487565296	−8.69e-01	-10.080	behind	Found by Bhavithran Ananthan in July 2026.
Dominoes in a triangle	14	s = 3+10/√3 = 8.77350+	9.961718046	−1.1882	-13.543	behind	Found by Maurizio Morandi in April 2026.
Dominoes in a triangle	15	s = 7+4/√3 = 9.30940+	9.871832021	−5.62e-01	-6.042	behind	Found by Jonathan Viquerat in April 2026.
Dominoes in a triangle	16	s = 6+2√3 = 9.46410+	10.344730559	−8.81e-01	-9.305	behind	Found by Maurizio Morandi in April 2026.
Dominoes in a triangle	17	s = 4+10/√3 = 9.77350+	11.195183463	−1.4217	-14.546	behind	Found by Jonathan Viquerat in April 2026.
Dominoes in a triangle	18	s = 3+4√3 = 9.92820+	10.966075871	−1.0379	-10.454	behind	Found by Jonathan Viquerat in April 2026.
Dominoes in a triangle	19	s = 8+4/√3 = 10.30940+	10.625339912	−3.16e-01	-3.065	behind	Found by Jonathan Viquerat in April 2026.
Dominoes in a triangle	20	s = 7+2√3 = 10.46410+	11.417483716	−9.53e-01	-9.111	behind	Found by Maurizio Morandi in April 2026.
Dominoes in a triangle	21	s = 2+5√3 = 10.66025+	11.313705159	−6.53e-01	-6.130	behind	Found by Maurizio Morandi in April 2026.
Dominoes in a triangle	22	s = 4(1+√3) = 10.92820+	12.001026659	−1.0728	-9.817	behind	Found by Maurizio Morandi in April 2026.
Dominoes in a triangle	23	s = 10+2/√3 = 11.15470+	11.779578399	−6.25e-01	-5.602	behind	Found by Maurizio Morandi in April 2026.
Dominoes in a triangle	24	s = 9+4/√3 = 11.30940+	12.092425330	−7.83e-01	-6.924	behind	Found by Maurizio Morandi in April 2026.
Dominoes in a triangle	25	s = 7+8/√3 = 11.61880+	12.545206751	−9.26e-01	-7.973	behind	Found by Maurizio Morandi in June 2026.
Dominoes in a triangle	26	s = 11.79418+	12.949747813	−1.1556	-9.798	behind	Found by Aapo Lipponen in July 2026.
Dominoes in a triangle	27	s = 4+14/√3 = 12.08290+	12.822649464	−7.40e-01	-6.122	behind	Found by Maurizio Morandi in June 2026.
Dominoes in an L	2	s = 3/2 = 1.5	1.500000013	−1.31e-08	-0.000	reproduced
Dominoes in an L	3	s = (6+√2)/4 = 1.853+	1.853553424	−3.36e-08	-0.000	reproduced	Found by Erich Friedman in April 2026.
Dominoes in an L	4	s = 2	2.000000001	−8.01e-10	-0.000	reproduced
Dominoes in an L	5	s = 2	2.000000004	−3.62e-09	-0.000	reproduced
Dominoes in an L	6	s = 2	2.000000001	−1.13e-09	-0.000	reproduced
Dominoes in an L	7	s = 5/2 = 2.5	2.502125189	−2.13e-03	-0.085	reproduced
Dominoes in an L	8	s = 5/2 = 2.5	3.000000036	−5.00e-01	-20.000	behind
Dominoes in an L	9	s = 2.87746+	2.958618060	−8.12e-02	-2.820	behind	Found by Jonathan Viquerat in June 2026.
Dominoes in an L	10	s = 3	3.013860710	−1.39e-02	-0.462	behind
Dominoes in an L	11	s = 3	3.016500442	−1.65e-02	-0.550	behind
Dominoes in an L	12	s = 3	3.091753832	−9.18e-02	-3.058	behind
Dominoes in an L	13	s = 3	3.511413699	−5.11e-01	-17.047	behind
Dominoes in an L	14	s = 3+√2/4 = 3.353+	3.812847627	−4.59e-01	-13.698	behind	Found by Maurizio Morandi in April 2026.
Dominoes in an L	15	s = 7/2 = 3.5	3.501290032	−1.29e-03	-0.037	reproduced
Dominoes in an L	16	s = 7/2 = 3.5	4.000025678	−5.00e-01	-14.286	behind
Dominoes in an L	17	s = (10+9√2)/6 = 3.787+	4.002294351	−2.14e-01	-5.659	behind	Found by Maurizio Morandi in April 2026.
Dominoes in an L	18	s = (11+6√2)/5 = 3.897+	4.005614362	−1.09e-01	-2.786	behind	Found by Maurizio Morandi in April 2026.
Dominoes in an L	19	s = 4	4.004432984	−4.43e-03	-0.111	behind
Dominoes in an L	20	s = 4	4.000443622	−4.44e-04	-0.011	behind
Dominoes in an L	21	s = 4	4.020826630	−2.08e-02	-0.521	behind
Dominoes in an L	22	s = 4	4.001824505	−1.82e-03	-0.046	behind
Dominoes in an L	23	s = 4	4.002847603	−2.85e-03	-0.071	behind
Dominoes in an L	24	s = 4	4.002843305	−2.84e-03	-0.071	behind
Dominoes in an octagon	2	s = √(4–2√2) = 1.08239+	1.082392210	−9.97e-09	-0.000	reproduced
Dominoes in an octagon	3	s = √(5–√2–√(8√2–9)) = 1.43690+	1.436905902	−2.33e-08	-0.000	reproduced	Found by Maurizio Morandi in May 2026.
Dominoes in an octagon	4	s = 1.57337+	1.573372066	−2.07e-06	-0.000	reproduced	Found by Maurizio Morandi in May 2026.
Dominoes in an octagon	5	s = 1.71644+	1.720930933	−4.49e-03	-0.262	behind	Found by Jonathan Viquerat in June 2026.
Dominoes in an octagon	6	s = √(6–√2–√(20√2–26)) = 1.75339+	1.754465126	−1.07e-03	-0.061	behind	Found by Maurizio Morandi in May 2026.
Dominoes in an octagon	7	s = 2.00516+	2.071067848	−6.59e-02	-3.287	behind	Found by Jonathan Viquerat in June 2026.
Dominoes in an octagon	8	s = 5(√2–1) = 2.07106+	2.071067868	−5.59e-08	-0.000	reproduced
Dominoes in an octagon	9	s = 2.19803+	2.287462606	−8.94e-02	-4.069	behind	Found by Jonathan Viquerat in June 2026.
Dominoes in an octagon	10	s = 2.32394+	2.508903512	−1.85e-01	-7.959	behind	Found by Jonathan Viquerat in June 2026.
Dominoes in an octagon	11	s = 2.44911+	2.490798930	−4.17e-02	-1.702	behind	Found by Jonathan Viquerat in June 2026.
Dominoes in an octagon	12	s = 6(√2–1) = 2.48528+	2.528319420	−4.30e-02	-1.732	behind
Dominoes in an octagon	13	s = 2.56556+	2.705658792	−1.40e-01	-5.461	behind	Found by Jonathan Viquerat in June 2026.
Dominoes in an octagon	14	s = 2.67740+	2.865703294	−1.88e-01	-7.033	behind	Found by Jonathan Viquerat in June 2026.
Dominoes in an octagon	15	s = 2.80446+	2.912641803	−1.08e-01	-3.857	behind	Found by Jonathan Viquerat in June 2026.
Dominoes in an octagon	16	s = 2√(5–√2–√(8√2–9)) = 2.87381+	3.098160357	−2.24e-01	-7.807	behind	Found by Maurizio Morandi in June 2026.
Dominoes in an octagon	17	s = 2.92223+	3.164660764	−2.42e-01	-8.296	behind	Found by Aapo Lipponen in July 2026.
Dominoes in an octagon	18	s = 9–17√2/4 = 2.98959+	3.234555339	−2.45e-01	-8.194	behind	Found by Maurizio Morandi in August 2026.
Dominoes in an octagon	19	s = 3.08791+	3.193679353	−1.06e-01	-3.425	behind	Found by Jonathan Viquerat in June 2026.
Dominoes in an octagon	20	s = 3.16881+	3.318460076	−1.50e-01	-4.723	behind	Found by Jonathan Viquerat in June 2026.
Dominoes in an octagon	21	s = 8(√2–1) = 3.31370+	3.455489292	−1.42e-01	-4.279	behind	Found by Maurizio Morandi in July 2026.
Dominoes in an octagon	22	s = 8(√2–1) = 3.31370+	3.468370526	−1.55e-01	-4.667	behind	Found by Maurizio Morandi in July 2026.
Dominoes in an octagon	23	s = (26–9√2)/4 = 3.31801+	3.547791491	−2.30e-01	-6.925	behind	Found by Maurizio Morandi in July 2026.
Dominoes in an octagon	24	s = 4(13–5√2)/7 = 3.38796+	3.588257025	−2.00e-01	-5.912	behind	Found by Maurizio Morandi in July 2026.
Dominoes in an octagon	25	s = 2√(6–√2–√(20√2–26)) = 3.50679+	3.726295144	−2.19e-01	-6.259	behind	Found by Maurizio Morandi in July 2026.
Dominoes in an octagon	26	s = 2√(6–√2–√(20√2–26)) = 3.50679+	3.728578015	−2.22e-01	-6.324	behind	Found by Maurizio Morandi in July 2026.
Dominoes in an octagon	27	s = 10–9/√2 = 3.63603+	3.864332291	−2.28e-01	-6.279	behind	Found by Maurizio Morandi in July 2026.
Dominoes in an octagon	28	s = 9(√2–1) = 3.72792+	3.808998788	−8.11e-02	-2.175	behind	Found by Maurizio Morandi in July 2026.
Dominoes in an octagon	29	s = 22(3–2√2) = 3.77460+	3.849043411	−7.44e-02	-1.972	behind	Found by Maurizio Morandi in July 2026.
Dominoes in an octagon	30	s = (42–19√2)/4 = 3.78248+	3.955288859	−1.73e-01	-4.569	behind	Found by Maurizio Morandi in July 2026.
Dominoes in an octagon	31	s = 3.80663+	4.088598547	−2.82e-01	-7.407	behind	Found by Aapo Lipponen in July 2026.
Hexagons in a circle	2	r = √13/2 = 1.802+	1.802775649	−1.10e-08	-0.000	reproduced
Hexagons in a circle	3	r = 2	2.000000032	−3.17e-08	-0.000	reproduced
Hexagons in a circle	4	r = (21–√145)/4 = 2.239+	2.239601380	−2.47e-08	-0.000	reproduced	Found by Maurizio Morandi in March 2026.
Hexagons in a circle	5	r = 2.471+	2.474128397	−3.13e-03	-0.127	behind	Found by Maurizio Morandi in March 2026.
Hexagons in a circle	6	r = √7 = 2.645+	2.645751339	−2.84e-08	-0.000	reproduced
Hexagons in a circle	7	r = √7 = 2.645+	2.645751349	−3.83e-08	-0.000	reproduced
Hexagons in a circle	8	r = 2.984+	2.984724774	−7.25e-04	-0.024	reproduced	Found by Maurizio Morandi in March 2026.
Hexagons in a circle	9	r = 3.301+	3.305379380	−4.38e-03	-0.133	behind	Found by Maurizio Morandi in March 2026.
Hexagons in a circle	10	r = 3.48172+	3.483073709	−1.35e-03	-0.039	behind	Found by Jake Loyd in June 2026.
Hexagons in a circle	11	r = 3.59003+	3.597900765	−7.87e-03	-0.219	behind	Found by Jake Loyd in June 2026.
Hexagons in a circle	12	r = √13 = 3.605+	3.605896383	−3.45e-04	-0.010	reproduced	Found by Maurizio Morandi in March 2026.
Hexagons in a circle	13	r = 3.82289+	3.860633247	−3.77e-02	-0.987	behind	Found by Jake Loyd in June 2026.
Hexagons in a circle	14	r = 3.87755+	3.885382759	−7.83e-03	-0.202	behind	Found by Jake Loyd in June 2026.
Hexagons in a circle	15	r = 4.08154+	4.121615704	−4.01e-02	-0.982	behind	Found by Jake Loyd in June 2026.
Hexagons in a circle	16	r = 4.13960+	4.262161965	−1.23e-01	-2.961	behind	Found by Jake Loyd in June 2026.
Hexagons in a circle	17	r = 4.30158+	4.350686807	−4.91e-02	-1.142	behind	Found by Jake Loyd in June 2026.
Hexagons in a circle	18	r = √19 = 4.35889+	4.365336597	−6.44e-03	-0.148	behind
Hexagons in a circle	19	r = √19 = 4.35889+	4.359924373	−1.03e-03	-0.024	behind
Hexagons in a circle	20	r = 4.62527+	4.846202759	−2.21e-01	-4.777	behind	Found by Jake Loyd in June 2026.
Hexagons in a circle	21	r = 4.68305+	4.685197727	−2.15e-03	-0.046	behind	Found by Jake Loyd in June 2026.
Hexagons in a circle	22	r = 4.89204+	4.934687569	−4.26e-02	-0.872	behind	Found by Jake Loyd in June 2026.
Hexagons in a circle	23	r = 4.98608+	4.988883042	−2.80e-03	-0.056	behind	Found by Jake Loyd in June 2026.
Hexagons in a circle	24	r = 5.08387+	5.194122124	−1.10e-01	-2.169	behind	Found by Jake Loyd in June 2026.
Hexagons in a circle	25	r = 5.18804+	5.220865891	−3.28e-02	-0.633	behind	Found by Haowei Lin in June 2026.
Hexagons in a circle	26	r = 5.25746+	5.299591377	−4.21e-02	-0.801	behind	Found by Haowei Lin in June 2026.
Hexagons in a circle	27	r = 5.28167+	5.326570627	−4.49e-02	-0.850	behind	Found by Haowei Lin in June 2026.
Hexagons in a domino	2	s = 1.8946+	1.894691516	−9.15e-05	-0.005	reproduced	Found by Jonathan Viquerat in April 2026.
Hexagons in a domino	3	s = 6–2√3 = 2.53589+	2.535898400	−1.55e-08	-0.000	reproduced	Found by Jonathan Viquerat in April 2026.
Hexagons in a domino	4	s = 22–11√3 = 2.94744+	2.947441134	−1.75e-08	-0.000	reproduced	Found by Jonathan Viquerat in April 2026.
Hexagons in a domino	5	s = 7(2√3–3) = 3.24871+	3.248710331	+9.75e-07	0.000	beaten	Found by Jonathan Viquerat in April 2026.
Hexagons in a domino	6	s = 21(15–2√3)/71 = 3.41202+	3.418866590	−6.84e-03	-0.200	behind	Found by Jonathan Viquerat in April 2026.
Hexagons in a domino	7	s = 3.48722+	3.488558354	−1.34e-03	-0.038	behind	Found by Bhavithran Ananthan in July 2026.
Hexagons in a domino	8	s = 3.6906+	3.690675039	−7.50e-05	-0.002	reproduced	Found by Jonathan Viquerat in April 2026.
Hexagons in a domino	9	s = (36+5√3)/11 = 4.06002+	4.060023165	−7.09e-08	-0.000	reproduced	Found by Jonathan Viquerat in April 2026.
Hexagons in a domino	10	s = 9(2√3–3) = 4.17691+	4.177928279	−1.01e-03	-0.024	behind	Found by Jonathan Viquerat in April 2026.
Hexagons in a domino	11	s = 4.5036+	4.556392537	−5.28e-02	-1.172	behind	Found by Jonathan Viquerat in April 2026.
Hexagons in a domino	12	s = 41(18–5√3)/83 = 4.6136+	4.614300600	−6.91e-04	-0.015	behind	Found by Jonathan Viquerat in April 2026.
Hexagons in a domino	13	s = 4.8137+	4.850100141	−3.64e-02	-0.756	behind	Found by Jonathan Viquerat in April 2026.
Hexagons in a domino	14	s = 25(6–√3)/22 = 4.84994+	4.850457896	−5.16e-04	-0.011	behind	Found by Jonathan Viquerat in April 2026.
Hexagons in a domino	15	s = 56(27–4√3)/227 = 4.95163+	5.010455293	−5.88e-02	-1.188	behind	Found by Jonathan Viquerat in April 2026.
Hexagons in a domino	16	s = 3√3 = 5.19615+	5.207258177	−1.11e-02	-0.214	behind
Hexagons in a domino	17	s = 3√3 = 5.19615+	5.630296993	−4.34e-01	-8.355	behind
Hexagons in a domino	18	s = 31(4–√3)/13 = 5.40818+	5.409339221	−1.15e-03	-0.021	behind	Found by Jonathan Viquerat in April 2026.
Hexagons in a domino	19	s = 5.65222+	5.922971913	−2.71e-01	-4.790	behind	Found by Jonathan Viquerat in September 2026.
Hexagons in a domino	20	s = 5.8012+	5.804448714	−3.25e-03	-0.056	behind	Found by Jonathan Viquerat in April 2026.
Hexagons in a domino	21	s = 5.85640+	6.077039658	−2.21e-01	-3.767	behind	Found by Thomas Greenleaf in June 2026.
Hexagons in a domino	22	s = 6.06943+	6.254917655	−1.85e-01	-3.056	behind	Found by Jonathan Viquerat in September 2026.
Hexagons in a domino	23	s = 6.25797+	6.190597806	+6.74e-02	1.077	beaten	Found by Jonathan Viquerat in September 2026.
Hexagons in a hexagon	2	s = 2	2.000000001	−8.00e-10	-0.000	reproduced
Hexagons in a hexagon	3	s = 2	2.000000001	−8.00e-10	-0.000	reproduced
Hexagons in a hexagon	4	s = 7/3 = 2.333+	2.333333334	−9.33e-10	-0.000	reproduced
Hexagons in a hexagon	5	s = 8/3 = 2.666+	2.666666677	−1.05e-08	-0.000	reproduced	Found by Erich Friedman in March 2015.
Hexagons in a hexagon	6	s = 5/√3 = 2.886+	2.896311904	−9.56e-03	-0.331	behind	Found by Maurizio Morandi in April 2015.
Hexagons in a hexagon	7	s = 5/√3 = 2.886+	2.886753673	−2.33e-06	-0.000	reproduced	Found by Maurizio Morandi in April 2015.
Hexagons in a hexagon	8	s = (51+5√3)/18 = 3.314+	3.314458618	−6.03e-08	-0.000	reproduced	Found by Maurizio Morandi in April 2015.
Hexagons in a hexagon	9	s = (24+5√3)/9 = 3.628+	3.628917182	−6.66e-08	-0.000	reproduced	Found by Maurizio Morandi in April 2015.
Hexagons in a hexagon	10	s = 2 + √3 = 3.732+	3.732051689	−8.81e-07	-0.000	reproduced	Found by Maurizio Morandi in April 2015.
Hexagons in a hexagon	11	s = 2+10/3√3 = 3.92450+	3.947381150	−2.29e-02	-0.583	behind	Found by Johann Schellhorn in July 2025.
Hexagons in a hexagon	12	s = 3.94164+	4.000000082	−5.84e-02	-1.481	behind	Found by Alpha Evolve in May 2025.
Hexagons in a hexagon	13	s = 4	4.014712736	−1.47e-02	-0.368	behind
Hexagons in a hexagon	14	s = 4.26899+	4.271218699	−2.23e-03	-0.052	behind	Found by Dominik Kamp in April 2026.
Hexagons in a hexagon	15	s = 4.44727+	4.519829749	−7.26e-02	-1.632	behind	Found by Alex Kravatsky et al in February 2026.
Hexagons in a hexagon	16	s = 4.52746+	4.640546365	−1.13e-01	-2.498	behind	Found by Alex Kravatsky et al in February 2026.
Hexagons in a hexagon	17	s = 4.6136+	4.619689871	−6.09e-03	-0.132	behind	Found by Alex Kravatsky et al in February 2026.
Hexagons in a hexagon	18	s = 8/√3 = 4.618+	4.619589055	−7.87e-04	-0.017	reproduced	Found by Maurizio Morandi in April 2015.
Hexagons in a hexagon	19	s = 8/√3 = 4.618+	4.619270937	−4.69e-04	-0.010	reproduced	Found by Maurizio Morandi in April 2015.
Hexagons in a hexagon	20	s = 5	5.001369118	−1.37e-03	-0.027	behind
Hexagons in a hexagon	21	s = 5	5.020405858	−2.04e-02	-0.408	behind
Hexagons in a hexagon	22	s = (39+8√3)/10 = 5.285+	5.515371047	−2.30e-01	-4.347	behind	Found by Maurizio Morandi in April 2015.
Hexagons in a hexagon	23	s = 5.39998+	5.403412893	−3.43e-03	-0.064	behind	Found by Jonathan Viquerat in June 2026.
Hexagons in a hexagon	24	s = 19√3/6 = 5.484+	5.486372533	−1.54e-03	-0.028	behind	Found by Maurizio Morandi in April 2015.
Hexagons in a hexagon	25	s = 5.62390+	5.657226878	−3.33e-02	-0.593	behind	Found by Alex Kravatsky et al in February 2026.
Hexagons in a hexagon	26	s = 5.70972+	5.811907653	−1.02e-01	-1.790	behind	Found by Alex Kravatsky et al in February 2026.
Hexagons in a hexagon	27	s = 5.71415+	5.795204125	−8.11e-02	-1.418	behind	Found by Alex Kravatsky et al in February 2026.
Hexagons in a hexagon	28	s = 5.90893+	5.919773982	−1.08e-02	-0.184	behind	Found by Alex Kravatsky et al in February 2026.
Hexagons in a hexagon	29	s = 6	6.001888785	−1.89e-03	-0.031	behind
Hexagons in a hexagon	30	s = 6	6.002234563	−2.23e-03	-0.037	behind
Hexagons in a hexagon	31	s = 6	6.001699172	−1.70e-03	-0.028	behind
Hexagons in a hexagon	32	s = 6.26088+	6.390413890	−1.30e-01	-2.069	behind	Found by Aristotle Papowitz in July 2026.
Hexagons in a hexagon	33	s = 6.26580+	6.272610959	−6.81e-03	-0.109	behind	Found by Jonathan Viquerat in September 2026.
Hexagons in a pentagon	2	s = 2.46585+	2.465852284	−2.28e-06	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Hexagons in a pentagon	3	s = 2.74282+	2.742825935	−5.93e-06	-0.000	reproduced	Found by Ethan Riddle in May 2026.
Hexagons in a pentagon	4	s = 3.01521+	3.015218981	−8.98e-06	-0.000	reproduced	Found by Bhavithran Ananthan in July 2026.
Hexagons in a pentagon	5	s = 3.21972+	3.219728524	−8.52e-06	-0.000	reproduced	Found by Aristotle Papowitz in July 2026.
Hexagons in a pentagon	6	s = 3.54952+	3.549533503	−1.35e-05	-0.000	behind	Found by Jonathan Viquerat in May 2026.
Hexagons in a pentagon	7	s = 3.79749+	3.797494365	−4.37e-06	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Hexagons in a pentagon	8	s = 4.14916+	4.149170533	−1.05e-05	-0.000	behind	Found by Bhavithran Ananthan in July 2026.
Hexagons in a pentagon	9	s = 4.34314+	4.343145221	−5.22e-06	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Hexagons in a pentagon	10	s = 4.55810+	4.560096107	−2.00e-03	-0.044	behind	Found by Jonathan Viquerat in May 2026.
Hexagons in a pentagon	11	s = 4.71959+	4.771278849	−5.17e-02	-1.095	behind	Found by Bhavithran Ananthan in July 2026.
Hexagons in a pentagon	12	s = 4.91850+	4.920964326	−2.46e-03	-0.050	behind	Found by Jonathan Viquerat in May 2026.
Hexagons in a pentagon	13	s = 5.10107+	5.149011514	−4.79e-02	-0.940	behind	Found by Bhavithran Ananthan in July 2026.
Hexagons in a pentagon	14	s = 5.29198+	5.325191471	−3.32e-02	-0.628	behind	Found by Jake Loyd in June 2026.
Hexagons in a pentagon	15	s = 5.41337+	5.597283830	−1.84e-01	-3.397	behind	Found by Jake Loyd in June 2026.
Hexagons in a pentagon	16	s = 5.61409+	5.619880187	−5.79e-03	-0.103	behind	Found by Jake Loyd in June 2026.
Hexagons in a pentagon	17	s = 5.82103+	5.826465576	−5.44e-03	-0.093	behind	Found by Jake Loyd in June 2026.
Hexagons in a pentagon	18	s = 5.94471+	6.027336799	−8.26e-02	-1.390	behind	Found by Jonathan Viquerat in May 2026.
Hexagons in a pentagon	19	s = 6.10977+	6.130026376	−2.03e-02	-0.332	behind	Found by Jonathan Viquerat in May 2026.
Hexagons in a pentagon	20	s = 6.24667+	6.255128713	−8.46e-03	-0.135	behind	Found by Jake Loyd in June 2026.
Hexagons in a pentagon	21	s = 6.39216+	6.603284138	−2.11e-01	-3.303	behind	Found by Jonathan Viquerat in August 2026.
Hexagons in a pentagon	22	s = 6.53472+	6.616762015	−8.20e-02	-1.255	behind	Found by Bhavithran Ananthan in July 2026.
Hexagons in a pentagon	23	s = 6.66271+	6.727108139	−6.44e-02	-0.967	behind	Found by Jake Loyd in June 2026.
Hexagons in a pentagon	24	s = 6.77466+	6.894234244	−1.20e-01	-1.765	behind	Found by Jake Loyd in June 2026.
Hexagons in a pentagon	25	s = 6.89098+	6.894112888	−3.13e-03	-0.045	behind	Found by Bhavithran Ananthan in July 2026.
Hexagons in a pentagon	26	s = 7.04734+	7.097949920	−5.06e-02	-0.718	behind	Found by Aristotle Papowitz in July 2026.
Hexagons in a pentagon	27	s = 7.15307+	7.243836160	−9.08e-02	-1.269	behind	Found by Aristotle Papowitz in July 2026.
Hexagons in a pentagon	28	s = 7.24805+	7.463399196	−2.15e-01	-2.971	behind	Found by Jonathan Viquerat in August 2026.
Hexagons in a pentagon	29	s = 7.37833+	7.406337512	−2.80e-02	-0.380	behind	Found by Jonathan Viquerat in August 2026.
Hexagons in a pentagon	30	s = 7.45985+	7.462430944	−2.58e-03	-0.035	behind	Found by Aristotle Papowitz in July 2026.
Hexagons in a pentagon	31	s = 7.63254+	7.821505910	−1.89e-01	-2.476	behind	Found by Jonathan Viquerat in August 2026.
Hexagons in a pentagon	32	s = 7.76619+	7.988944739	−2.23e-01	-2.868	behind	Found by Bhavithran Ananthan in July 2026.
Hexagons in a square	2	s = (1+2√3)/√2 = 3.156+	3.156596572	−4.79e-08	-0.000	reproduced
Hexagons in a square	3	s = 9(6–√3)/11 = 3.491+	3.491958452	−2.20e-08	-0.000	reproduced	Found by Maurizio Morandi in March 2026.
Hexagons in a square	4	s = (7–√3)/√2 = 3.725+	3.725002621	−2.43e-08	-0.000	reproduced	Found by Maurizio Morandi in March 2026.
Hexagons in a square	5	s = 7(3–√3)/2 = 4.437+	4.437822251	−7.79e-08	-0.000	reproduced	Found by Maurizio Morandi in March 2026.
Hexagons in a square	6	s = 20(9–2√3)/23 = 4.813+	4.814309278	−4.85e-04	-0.010	reproduced	Found by Maurizio Morandi in March 2026.
Hexagons in a square	7	s = 3√3 = 5.196+	5.196152441	−1.85e-08	-0.000	reproduced
Hexagons in a square	8	s = 3√3 = 5.196+	5.196169448	−1.70e-05	-0.000	reproduced
Hexagons in a square	9	s = (13–3√3)/√2 = 5.518+	5.586322326	−6.82e-02	-1.235	behind	Found by Maurizio Morandi in March 2026.
Hexagons in a square	10	s = 6.10469+	6.139442824	−3.48e-02	-0.569	behind	Found by Jonathan Viquerat in April 2026.
Hexagons in a square	11	s = 6.33218+	6.342786233	−1.06e-02	-0.167	behind	Found by Maksymilian Jankowski in April 2026.
Hexagons in a square	12	s = 43(5–√3)/22 = 6.387+	6.463461328	−7.61e-02	-1.192	behind	Found by Maurizio Morandi in March 2026.
Hexagons in a square	13	s = 6.75549+	6.880645246	−1.25e-01	-1.853	behind	Found by Timo Berthold et al in May 2026.
Hexagons in a square	14	s = 4√3 = 6.928+	6.928735303	−5.32e-04	-0.008	reproduced
Hexagons in a square	15	s = 6.96367+	7.471144542	−5.07e-01	-7.287	behind	Found by Maksymilian Jankowski in April 2026.
Hexagons in a square	16	s = (19–5√3)/√2 = 7.311+	7.312060087	−7.56e-04	-0.010	reproduced	Found by Maurizio Morandi in April 2026.
Hexagons in a square	17	s = 7.60383+	7.613511307	−9.68e-03	-0.127	behind	Found by Maksymilian Jankowski in April 2026.
Hexagons in a square	18	s = 32(9–2√3)/23 = 7.702+	8.020652511	−3.19e-01	-4.136	behind	Found by Maurizio Morandi in April 2026.
Hexagons in a square	19	s = 25(3–√3)/4 = 7.924+	7.935427436	−1.07e-02	-0.136	behind	Found by Maurizio Morandi in April 2026.
Hexagons in a square	20	s = 74(21–4√3)/131 = 7.948+	8.023019262	−7.41e-02	-0.932	behind	Found by Maurizio Morandi in April 2026.
Hexagons in a square	21	s = 8.381+	8.454500609	−7.35e-02	-0.877	behind	Found by Jonathan Viquerat in April 2026.
Hexagons in a square	22	s = 8.568+	8.661774136	−9.38e-02	-1.094	behind	Found by Jonathan Viquerat in April 2026.
Hexagons in a square	23	s = 5√3 = 8.660+	8.773274457	−1.13e-01	-1.305	behind	Found by Jonathan Viquerat in April 2026.
Hexagons in a square	24	s = 8.795+	8.976423306	−1.81e-01	-2.063	behind	Found by Jonathan Viquerat in April 2026.
Hexagons in a square	25	s = 30(4√3–3)/13 = 9.065+	9.073135561	−8.05e-03	-0.089	behind	Found by Jonathan Viquerat in April 2026.
Hexagons in a square	26	s = 9.22083+	9.283343907	−6.25e-02	-0.678	behind	Found by Bhavithran Ananthan in July 2026.
Hexagons in a square	27	s = 9.27733+	9.514754089	−2.37e-01	-2.559	behind	Found by Bhavithran Ananthan in July 2026.
Hexagons in a tan	2	s = 4.46410+	4.464101617	−1.62e-06	-0.000	reproduced
Hexagons in a tan	3	s = 4.94974+	4.949747470	−7.47e-06	-0.000	reproduced
Hexagons in a tan	4	s = 5.75097+	5.750978159	−8.16e-06	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Hexagons in a tan	5	s = 6.50265+	6.502661852	−1.19e-05	-0.000	behind	Found by Jonathan Viquerat in May 2026.
Hexagons in a tan	6	s = 6.74289+	6.742898534	−8.53e-06	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Hexagons in a tan	7	s = 7.39923+	7.451570119	−5.23e-02	-0.707	behind	Found by Jonathan Viquerat in May 2026.
Hexagons in a tan	8	s = 7.83340+	7.844935132	−1.15e-02	-0.147	behind	Found by Jonathan Viquerat in May 2026.
Hexagons in a tan	9	s = 8.28267+	8.283291528	−6.22e-04	-0.008	behind	Found by Jonathan Viquerat in May 2026.
Hexagons in a tan	10	s = 8.53604+	8.956949395	−4.21e-01	-4.931	behind	Found by Jonathan Viquerat in May 2026.
Hexagons in a tan	11	s = 9.06093+	9.071395972	−1.05e-02	-0.116	behind	Found by Jonathan Viquerat in May 2026.
Hexagons in a tan	12	s = 9.41319+	9.808078313	−3.95e-01	-4.195	behind	Found by Jonathan Viquerat in May 2026.
Hexagons in a tan	13	s = 9.70087+	9.709132820	−8.26e-03	-0.085	behind	Found by Bhavithran Ananthan in July 2026.
Hexagons in a tan	14	s = 10.03836+	10.443615740	−4.05e-01	-4.037	behind	Found by Jonathan Viquerat in May 2026.
Hexagons in a tan	15	s = 10.32919+	10.505659878	−1.76e-01	-1.708	behind	Found by Jonathan Viquerat in May 2026.
Hexagons in a tan	16	s = 10.71312+	11.345667211	−6.33e-01	-5.904	behind	Found by Bhavithran Ananthan in July 2026.
Hexagons in a tan	17	s = 10.97884+	11.002867955	−2.40e-02	-0.219	behind	Found by Jonathan Viquerat in May 2026.
Hexagons in a tan	18	s = 11.27299+	11.722584467	−4.50e-01	-3.988	behind	Found by Jonathan Viqueratl in May 2026.
Hexagons in a tan	19	s = 11.49013+	11.899952185	−4.10e-01	-3.567	behind	Found by Jonathan Viquerat in May 2026.
Hexagons in a tan	20	s = 11.77041+	12.204805030	−4.34e-01	-3.691	behind	Found by Jonathan Viquerat in May 2026.
Hexagons in a triangle	2	s = 5	5.000000002	−2.00e-09	-0.000	reproduced
Hexagons in a triangle	3	s = 5	5.000000002	−2.00e-09	-0.000	reproduced
Hexagons in a triangle	4	s = 6	6.000000005	−4.96e-09	-0.000	reproduced
Hexagons in a triangle	5	s = 5(1+√3)/2 = 6.8301+	6.830127141	−1.22e-07	-0.000	reproduced	Found by Maurizio Morandi in April 2015.
Hexagons in a triangle	6	s = 2(1+√6) = 6.89897+	6.898982802	−3.32e-06	-0.000	reproduced	Found by Jonathan Viquerat in April 2026.
Hexagons in a triangle	7	s = 8	8.000000137	−1.37e-07	-0.000	reproduced
Hexagons in a triangle	8	s = 25/3 = 8.3333+	8.571330343	−2.38e-01	-2.856	behind	Found by Erich Friedman in April 2015.
Hexagons in a triangle	9	s = 8.64494+	8.660436142	−1.55e-02	-0.179	behind	Found by Bhavithran Ananthan in July 2026.
Hexagons in a triangle	10	s = 5√3 = 8.6602+	8.724733385	−6.45e-02	-0.745	behind
Hexagons in a triangle	11	s = 9.54823+	9.732051441	−1.84e-01	-1.925	behind	Found by Jonathan Viquerat in April 2026.
Hexagons in a triangle	12	s = 9.96429+	10.137567175	−1.73e-01	-1.739	behind	Found by Bhavithran Ananthan in July 2026.
Hexagons in a triangle	13	s = 10.28857+	10.392305037	−1.04e-01	-1.008	behind	Found by Bhavithran Ananthan in July 2026.
Hexagons in a triangle	14	s = 6√3 = 10.3923+	10.486857122	−9.46e-02	-0.910	behind
Hexagons in a triangle	15	s = 6√3 = 10.3923+	10.464654420	−7.23e-02	-0.696	behind
Hexagons in a triangle	16	s = 11.36383+	11.667663088	−3.04e-01	-2.674	behind	Found by Timo Berthold et al in May 2026.
Hexagons in a triangle	17	s = 11.63454+	12.099534132	−4.65e-01	-3.997	behind	Found by Jonathan Viquerat in August 2026.
Hexagons in a triangle	18	s = 11.91421+	12.219619049	−3.05e-01	-2.563	behind	Found by Jake Loyd in May 2026.
Hexagons in a triangle	19	s = 12	12.256864849	−2.57e-01	-2.141	behind
Hexagons in a triangle	20	s = 7√3 = 12.1243+	12.192384391	−6.80e-02	-0.561	behind
Hexagons in a triangle	21	s = 7√3 = 12.1243+	12.125851770	−1.50e-03	-0.012	behind
Hexagons in a triangle	22	s = 12.99518+	13.007086163	−1.19e-02	-0.092	behind	Found by Jonathan Viquerat in May 2026.
Hexagons in a triangle	23	s = 13.39989+	13.442473671	−4.26e-02	-0.318	behind	Found by Jake Loyd in June 2026.
Hexagons in a triangle	24	s = 13.61925+	13.966720728	−3.47e-01	-2.551	behind	Found by Thomas Greenleaf in June 2026.
Hexagons in a triangle	25	s = 13.77683+	13.979257917	−2.02e-01	-1.469	behind	Found by Jake Loyd in June 2026.
Hexagons in a triangle	26	s = 7√3 = 13.85677+	14.023877881	−1.67e-01	-1.206	behind
Hexagons in a triangle	27	s = 7√3 = 13.85677+	13.968289991	−1.12e-01	-0.805	behind
Hexagons in a triangle	28	s = 7√3 = 13.85677+	13.962619333	−1.06e-01	-0.764	behind
Hexagons in a triangle	29	s = 14.78557+	15.158510811	−3.73e-01	-2.522	behind	Found by Haowei Lin in July 2026.
Hexagons in a triangle	30	s = 15	15.145681760	−1.46e-01	-0.971	behind
Hexagons in a triangle	31	s = 15	15.013522906	−1.35e-02	-0.090	behind
Hexagons in a triangle	32	s = 15.47573+	15.593129679	−1.17e-01	-0.759	behind	Found by Haowei Lin in July 2026.
Hexagons in an L	2	s = √3 = 1.73205+	1.732050808	−6.93e-10	-0.000	reproduced
Hexagons in an L	3	s = 1.88648+	1.886483830	−3.83e-06	-0.000	reproduced	Found by Jonathan Viquerat in June 2026.
Hexagons in an L	4	s = 2.41072+	2.418007196	−7.29e-03	-0.302	behind	Found by Jonathan Viquerat in June 2026.
Hexagons in an L	5	s = 2.59807+	2.598076245	−6.25e-06	-0.000	reproduced	Found by Jonathan Viquerat in June 2026.
Hexagons in an L	6	s = 2.90072+	2.900723594	−3.59e-06	-0.000	reproduced	Found by Jonathan Viquerat in June 2026.
Hexagons in an L	7	s = 3.08493+	3.152617949	−6.77e-02	-2.194	behind	Found by Jonathan Viquerat in June 2026.
Hexagons in an L	8	s = 3.26559+	3.285549951	−2.00e-02	-0.611	behind	Found by Jonathan Viquerat in June 2026.
Hexagons in an L	9	s = 3.39536+	3.397223501	−1.86e-03	-0.055	behind	Found by Jonathan Viquerat in June 2026.
Hexagons in an L	10	s = 2√3 = 3.46410+	3.464104855	−3.24e-06	-0.000	reproduced
Hexagons in an L	11	s = 3.48851+	3.609361556	−1.21e-01	-3.464	behind	Found by Jonathan Viquerat in June 2026.
Hexagons in an L	12	s = 3.68106+	3.684491867	−3.43e-03	-0.093	behind	Found by Jonathan Viquerat in June 2026.
Hexagons in an L	13	s = 3.94486+	3.953640396	−8.78e-03	-0.223	behind	Found by Jonathan Viquerat in June 2026.
Hexagons in an L	14	s = 4.09579+	4.121299441	−2.55e-02	-0.623	behind	Found by Jonathan Viquerat in June 2026.
Hexagons in an L	15	s = 4.2134+	4.226635280	−1.32e-02	-0.314	behind	Found by Jonathan Viquerat in June 2026.
Hexagons in an L	16	s = 4.27526+	4.393725093	−1.18e-01	-2.771	behind	Found by Jonathan Viquerat in June 2026.
Hexagons in an L	17	s = 4.51508+	4.559402470	−4.43e-02	-0.982	behind	Found by Jonathan Viquerat in June 2026.
Hexagons in an L	18	s = 4.59397+	4.772506921	−1.79e-01	-3.886	behind	Found by Jonathan Viquerat in June 2026.
Hexagons in an L	19	s = 4.70835+	4.786427500	−7.81e-02	-1.658	behind	Found by Jonathan Viquerat in June 2026.
Hexagons in an L	20	s = 4.75480+	4.755577704	−7.78e-04	-0.016	behind	Found by Jonathan Viquerat in June 2026.
Hexagons in an L	21	s = 4.90214+	4.962190930	−6.01e-02	-1.225	behind	Found by Jonathan Viquerat in September 2026.
Hexagons in an L	22	s = 4.93211+	5.203163551	−2.71e-01	-5.496	behind	Found by Jonathan Viquerat in September 2026.
Hexagons in an octagon	2	s = 2√3/(1+√2) = 1.43487+	1.434877871	−5.74e-10	-0.000	reproduced
Hexagons in an octagon	3	s = 3+2√6–2√2–2√3 = 1.60645+	1.606450746	−6.43e-10	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Hexagons in an octagon	4	s = 1.75630+	1.756300707	−7.07e-07	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Hexagons in an octagon	5	s = 1.98707+	1.987076725	−6.72e-06	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Hexagons in an octagon	6	s = 2.16435+	2.166020224	−1.67e-03	-0.077	behind	Found by Nicolas Campailla in May 2026.
Hexagons in an octagon	7	s = 2.18284+	2.185668273	−2.83e-03	-0.130	behind	Found by Jonathan Viquerat in May 2026.
Hexagons in an octagon	8	s = 2.40792+	2.407922002	−2.00e-06	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Hexagons in an octagon	9	s = 2.62665+	2.635542528	−8.89e-03	-0.339	behind	Found by Jonathan Viquerat in May 2026.
Hexagons in an octagon	10	s = 2.74238+	2.742383805	−3.81e-06	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Hexagons in an octagon	11	s = 4√3/(1+√2) = 2.86975+	2.885213255	−1.55e-02	-0.539	behind	Found by Jonathan Viquerat in May 2026.
Hexagons in an octagon	12	s = 2.92139+	2.975953865	−5.46e-02	-1.868	behind	Found by Timo Berthold et al in May 2026.
Hexagons in an octagon	13	s = 3.07201+	3.143116289	−7.11e-02	-2.315	behind	Found by Jonathan Viquerat in May 2026.
Hexagons in an octagon	14	s = 3.13475+	3.157819688	−2.31e-02	-0.736	behind	Found by Jonathan Viquerat in May 2026.
Hexagons in an octagon	15	s = 3.28379+	3.362235689	−7.84e-02	-2.389	behind	Found by Timo Berthold et al in May 2026.
Hexagons in an octagon	16	s = 3.37007+	3.373940328	−3.87e-03	-0.115	behind	Found by Timo Berthold et al in May 2026.
Hexagons in an octagon	17	s = 3.47655+	3.510232976	−3.37e-02	-0.969	behind	Found by Jake Loyd in June 2026.
Hexagons in an octagon	18	s = 3.56008+	3.602195001	−4.21e-02	-1.183	behind	Found by Timo Berthold et al in May 2026.
Hexagons in an octagon	19	s = 5√3/(1+√2) = 3.58719+	3.605927450	−1.87e-02	-0.522	behind	Found by Jonathan Viquerat in May 2026.
Hexagons in an octagon	20	s = 3.72605+	3.733249358	−7.20e-03	-0.193	behind	Found by Bhavithran Ananthan in July 2026.
Hexagons in an octagon	21	s = 3.81006+	3.947977892	−1.38e-01	-3.620	behind	Found by Bhavithran Ananthan in July 2026.
Hexagons in an octagon	22	s = 3.91915+	3.972401580	−5.33e-02	-1.359	behind	Found by Thomas Greenleaf in June 2026.
L's in a circle	2	r = √13/2 = 1.802+	1.838477657	−3.57e-02	-1.981	behind	Found by David W. Cantrell in June 2005.
L's in a circle	3	r = √305/8 = 2.183+	2.183031178	−2.88e-08	-0.000	reproduced	Found by Maurizio Morandi in August 2007.
L's in a circle	4	r = √5 = 2.236+	2.467669237	−2.32e-01	-10.358	behind	Found by Erich Friedman in June 2005.
L's in a circle	5	r = 2.56858+	2.701273547	−1.33e-01	-5.166	behind	Found by Jake Loyd in June 2026.
L's in a circle	6	r = √8249/32 = 2.838+	2.917124492	−7.89e-02	-2.779	behind	Found by Erich Friedman in June 2005.
L's in a circle	7	r = √34/2 = 2.915+	3.208641115	−2.93e-01	-10.057	behind	Found by Erich Friedman in June 2005.
L's in a circle	8	r = √10 = 3.162+	3.288323765	−1.26e-01	-3.986	behind	Found by Erich Friedman in June 2005.
L's in a circle	9	r = 3.36482+	3.494502283	−1.30e-01	-3.854	behind	Found by Jake Loyd in June 2026.
L's in a circle	10	r = 3.490+	3.704363824	−2.14e-01	-6.142	behind	Found by Maurizio Morandi in June 2026.
L's in a circle	11	r = 3.68165+	3.919051561	−2.37e-01	-6.448	behind	Found by Jake Loyd in June 2026.
L's in a circle	12	r = 3.80266+	4.107243066	−3.05e-01	-8.010	behind	Found by Jake Loyd in June 2026.
L's in a circle	13	r = 3.94961+	4.318398990	−3.69e-01	-9.337	behind	Found by Jake Loyd in June 2026.
L's in a circle	14	r = √17 = 4.123+	4.476409698	−3.53e-01	-8.569	behind	Found by David W. Cantrell in August 2007.
L's in a circle	15	r = 4.214+	4.389230133	−1.75e-01	-4.158	behind	Found by Maurizio Morandi in August 2007.
L's in a circle	16	r = √74/2 = 4.301+	4.753476159	−4.52e-01	-10.516	behind	Found by Maurizio Morandi in September 2008.
L's in a circle	17	r = 2√5 = 4.472+	4.650548801	−1.78e-01	-3.990	behind	Found by Maurizio Morandi in September 2008.
L's in a circle	18	r = √86609/64 = 4.598+	5.006390519	−4.08e-01	-8.874	behind	Found by Maurizio Morandi in September 2008.
L's in a circle	19	r = 4.70546+	5.137988770	−4.33e-01	-9.192	behind	Found by Jake Loyd in June 2026.
L's in a circle	20	r = 4.77260+	5.006958019	−2.34e-01	-4.910	behind	Found by Jake Loyd in June 2026.
L's in a circle	21	r = 5.09246+	5.617523088	−5.25e-01	-10.311	behind	Found by Jonathan Viquerat in August 2026.
L's in a circle	22	r = 5.21859+	5.449743897	−2.31e-01	-4.429	behind	Found by Jonathan Viquerat in August 2026.
L's in a circle	23	r = 5.30468+	5.932184358	−6.28e-01	-11.829	behind	Found by Jonathan Viquerat in August 2026.
L's in a domino	2	s = 2	2.000000001	−8.00e-10	-0.000	reproduced
L's in a domino	3	s = 5/2 = 2.5	2.500000001	−1.00e-09	-0.000	reproduced
L's in a domino	4	s = 6(1+√2)/5 = 2.897+	3.000000013	−1.03e-01	-3.553	behind	Found by Erich Friedman in April 2026.
L's in a domino	5	s = 3	3.000000001	−1.20e-09	-0.000	reproduced
L's in a domino	6	s = 3	3.000000001	−1.20e-09	-0.000	reproduced
L's in a domino	7	s = 7/3+√2 = 3.747+	4.000000002	−2.52e-01	-6.737	behind	Found by Erich Friedman in April 2026.
L's in a domino	8	s = 4	4.000374442	−3.74e-04	-0.009	behind
L's in a domino	9	s = 4	4.059665940	−5.97e-02	-1.492	behind
L's in a domino	10	s = 4	4.098558160	−9.86e-02	-2.464	behind
L's in a domino	11	s = 3(6+√2)/5 = 4.448+	4.514999983	−6.65e-02	-1.494	behind	Found by Maurizio Morandi in April 2026.
L's in a domino	12	s = 9/2 = 4.5	4.519711236	−1.97e-02	-0.438	reproduced
L's in a domino	13	s = (14+11√2)/6 = 4.926+	5.514782547	−5.89e-01	-11.951	behind	Found by Maurizio Morandi in April 2026.
L's in a domino	14	s = 5	5.520838956	−5.21e-01	-10.417	behind
L's in a domino	15	s = 5	5.213747181	−2.14e-01	-4.275	behind
L's in a domino	16	s = 5	6.007645836	−1.0076	-20.153	behind
L's in a domino	17	s = 3+7√2/4 = 5.474+	5.879531928	−4.05e-01	-7.392	behind	Found by Maurizio Morandi in April 2026.
L's in a domino	18	s = 11/2 = 5.5	6.777301300	−1.2773	-23.224	behind
L's in a domino	19	s = 3+2√2 = 5.828+	6.000163758	−1.72e-01	-2.947	behind	Found by Maurizio Morandi in April 2026.
L's in a domino	20	s = 6	6.737304419	−7.37e-01	-12.288	behind
L's in a domino	21	s = 6	6.002026411	−2.03e-03	-0.034	behind
L's in a domino	22	s = 6	6.125135880	−1.25e-01	-2.086	behind
L's in a domino	23	s = 6	6.158544202	−1.59e-01	-2.642	behind
L's in a domino	24	s = 6	7.335283642	−1.3353	-22.255	behind
L's in a hexagon	2	s = 12^(1/4) = 1.861+	1.861209719	−7.45e-10	-0.000	reproduced	Found by Maurizio Morandi in May 2026.
L's in a hexagon	3	s = 1/2 + √3 = 2.232+	2.345396256	−1.13e-01	-5.078	behind	Found by Maurizio Morandi in May 2026.
L's in a hexagon	4	s = 2.50337+	2.597045137	−9.37e-02	-3.742	behind	Found by Jake Loyd in June 2026.
L's in a hexagon	5	s = 2.85988+	3.016462853	−1.57e-01	-5.475	behind	Found by Jake Loyd in May 2026
L's in a hexagon	6	s = 3.04254+	3.296724953	−2.54e-01	-8.354	behind	Found by Jake Loyd in June 2026.
L's in a hexagon	7	s = 3.25359+	3.481010864	−2.27e-01	-6.990	behind	Found by Jake Loyd in June 2026.
L's in a hexagon	8	s = 2√3 = 3.464+	3.660155527	−1.96e-01	-5.660	behind
L's in a hexagon	9	s = 3.65374+	3.730611769	−7.69e-02	-2.104	behind	Found by Jake Loyd in June 2026.
L's in a hexagon	10	s = 3.80531+	4.143900398	−3.39e-01	-8.898	behind	Found by Jake Loyd in June 2026.
L's in a hexagon	11	s = 7/√3 = 4.041+	4.170520155	−1.29e-01	-3.194	behind
L's in a hexagon	12	s = 4.15868+	4.618802156	−4.60e-01	-11.064	behind	Found by Jake Loyd in June 2026.
L's in a hexagon	13	s = 4.33273+	4.796461635	−4.64e-01	-10.703	behind	Found by Jake Loyd in June 2026.
L's in a hexagon	14	s = 4.46716+	4.812697970	−3.46e-01	-7.735	behind	Found by Jake Loyd in June 2026.
L's in a hexagon	15	s = 8/√3 = 4.61880+	5.004881514	−3.86e-01	-8.359	behind
L's in a hexagon	16	s = 4.72806+	5.209188115	−4.81e-01	-10.176	behind	Found by Aapo Lipponen in July 2026.
L's in a hexagon	17	s = 4.93064+	5.826276567	−8.96e-01	-18.165	behind	Found by Aaden Abraham in July 2026.
L's in a hexagon	18	s = 5.09795+	5.196301569	−9.84e-02	-1.929	behind	Found by Aapo Lipponen in July 2026.
L's in a hexagon	19	s = 3√3 = 5.19615+	5.316509961	−1.20e-01	-2.316	behind	Found by Maurizio Morandi in July 2026.
L's in a hexagon	20	s = 2+17√3/9 = 5.27165+	5.653607000	−3.82e-01	-7.245	behind	Found by Maurizio Morandi in August 2026.
L's in a hexagon	21	s = (13+5√3)/4 = 5.41506+	5.607170102	−1.92e-01	-3.548	behind	Found by Maurizio Morandi in July 2026.
L's in a hexagon	22	s = 7(1+1/√3)/2 = 5.52072+	5.759468273	−2.39e-01	-4.324	behind	Found by Maurizio Morandi in August 2026.
L's in a hexagon	23	s = 7√6/3 = 5.71547+	5.842662889	−1.27e-01	-2.225	behind	Found by Aaden Abraham in July 2026.
L's in a hexagon	24	s = 10/√3 = 5.77350+	6.852530162	−1.0790	-18.689	behind	Found by Aaden Abraham in July 2026.
L's in a hexagon	25	s = 7/3+2√3 = 5.79743+	6.670881300	−8.73e-01	-15.066	behind	Found by Maurizio Morandi in August 2026.
L's in a hexagon	26	s = 9/2+5√3/6 = 5.94337+	6.497263970	−5.54e-01	-9.319	behind	Found by Maurizio Morandi in August 2026.
L's in a hexagon	27	s = 9/2+11√3/12 = 6.08771+	6.690304008	−6.03e-01	-9.898	behind	Found by Maurizio Morandi in July 2026.
L's in a hexagon	28	s = 7/2+19√/12 = 6.24241+	6.755081205	−5.13e-01	-8.213	behind	Found by Maurizio Morandi in July 2026.
L's in a hexagon	29	s = 11/√3 = 6.35085+	6.979601795	−6.29e-01	-9.900	behind	Found by Aaden Abraham in July 2026.
L's in a hexagon	30	s = (11+√3)/2 = 6.36602+	6.999862792	−6.34e-01	-9.957	behind	Found by Maurizio Morandi in July 2026.
L's in a pentagon	2	s = 2.33322+	2.333225280	−5.28e-06	-0.000	reproduced
L's in a pentagon	3	s = 2.79081+	2.835425599	−4.46e-02	-1.599	behind	Found by Jonathan Viquerat in May 2026.
L's in a pentagon	4	s = 3.07149+	3.071493579	−3.58e-06	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
L's in a pentagon	5	s = 3.41569+	3.534744261	−1.19e-01	-3.486	behind	Found by Jake Loyd in June 2026.
L's in a pentagon	6	s = 3.74743+	3.866262935	−1.19e-01	-3.171	behind	Found by Jake Loyd in June 2026.
L's in a pentagon	7	s = 3.96756+	4.230121800	−2.63e-01	-6.618	behind	Found by Jake Loyd in June 2026.
L's in a pentagon	8	s = 4.25642+	4.348816400	−9.24e-02	-2.171	behind	Found by Jake Loyd in June 2026.
L's in a pentagon	9	s = 4.50713+	4.786312823	−2.79e-01	-6.194	behind	Found by Jake Loyd in June 2026.
L's in a pentagon	10	s = 3√5–3+3√(1–2/√5) = 4.65767+	4.896305721	−2.13e-01	-4.580	behind	Found by Jake Loyd in June 2026.
L's in a pentagon	11	s = 4.86103+	5.499103726	−6.38e-01	-13.126	behind	Found by Jake Loyd in June 2026.
L's in a pentagon	12	s = 5.07519+	5.589446321	−5.14e-01	-10.133	behind	Found by Jake Loyd in June 2026.
L's in a pentagon	13	s = 5.29475+	5.447805637	−1.53e-01	-2.891	behind	Found by Jake Loyd in June 2026.
L's in a pentagon	14	s = 5.49989+	5.641632514	−1.42e-01	-2.577	behind	Found by Jake Loyd in June 2026.
L's in a pentagon	15	s = 5.63035+	5.866756194	−2.36e-01	-4.199	behind	Found by Jake Loyd in June 2026.
L's in a pentagon	16	s = 5.77738+	6.333255302	−5.56e-01	-9.622	behind	Found by Jake Loyd in June 2026.
L's in a pentagon	17	s = 5.92697+	6.149545169	−2.23e-01	-3.755	behind	Found by Jake Loyd in June 2026.
L's in a pentagon	18	s = 6.16318+	6.882869254	−7.20e-01	-11.677	behind	Found by Jake Loyd in June 2026.
L's in a pentagon	19	s = 6.33939+	6.588545708	−2.49e-01	-3.930	behind	Found by Jake Loyd in June 2026.
L's in a pentagon	20	s = 6.45886+	7.059241382	−6.00e-01	-9.295	behind	Found by Jake Loyd in June 2026.
L's in a pentagon	21	s = 4√5–7/2+√(25–10√5) = 7.06887+	7.301104174	−2.32e-01	-3.285	behind	Found by Maurizio Morandi in August 2026.
L's in a pentagon	22	s = 4√5–7/2+√(25–10√5) = 7.06887+	7.433872086	−3.65e-01	-5.164	behind	Found by Maurizio Morandi in August 2026.
L's in a pentagon	23	s = 4√5–7/2+√(25–10√5) = 7.06887+	8.213220212	−1.1443	-16.189	behind	Found by Maurizio Morandi in August 2026.
L's in a pentagon	24	s = 4√5–7/2+√(25–10√5) = 7.06887+	7.560596580	−4.92e-01	-6.956	behind	Found by Maurizio Morandi in August 2026.
L's in a pentagon	25	s = 7√5–14+18√(1–2/√5) = 7.50103+	9.152320621	−1.6513	-22.014	behind	Found by Maurizio Morandi in August 2026.
L's in a pentagon	26	s = 7√5–14+18√(1–2/√5) = 7.50103+	9.256622641	−1.7556	-23.405	behind	Found by Maurizio Morandi in August 2026.
L's in a pentagon	27	s = 7√5–14+18√(1–2/√5) = 7.50103+	9.495205364	−1.9942	-26.585	behind	Found by Maurizio Morandi in August 2026.
L's in a pentagon	28	s = 4√5–3+6√(1–2/√5) = 7.89379+	10.273501020	−2.3797	-30.147	behind	Found by Maurizio Morandi in August 2026.
L's in a pentagon	29	s = 4√5–3+6√(1–2/√5) = 7.89379+	7.919210282	−2.54e-02	-0.322	behind	Found by Maurizio Morandi in August 2026.
L's in a pentagon	30	s = 4√5–3+6√(1–2/√5) = 7.89379+	11.164303847	−3.2705	-41.431	behind	Found by Maurizio Morandi in August 2026.
L's in a square	2	s = 3	3.000000001	−1.20e-09	-0.000	reproduced
L's in a square	3	s = (3 + 3√2) / 2 = 3.621+	3.621320345	−1.45e-09	-0.000	reproduced	Found by Serhiy Grabarchuk in July 2005.
L's in a square	4	s = 4	4.000000002	−1.60e-09	-0.000	reproduced
L's in a square	5	s = 4	4.687741121	−6.88e-01	-17.194	behind
L's in a square	6	s = 7 / √2 = 4.949+	5.000000002	−5.03e-02	-1.015	behind	Found by Erich Friedman in June 2005.
L's in a square	7	s = 5	5.559648748	−5.60e-01	-11.193	behind
L's in a square	8	s = 5	6.000000105	−1.0000	-20.000	behind
L's in a square	9	s = 5.81902+	6.001666798	−1.83e-01	-3.139	behind	Found by Aapo Lipponen in July 2026.
L's in a square	10	s = 6	6.000003240	−3.24e-06	-0.000	reproduced
L's in a square	11	s = 6	6.190161464	−1.90e-01	-3.169	behind
L's in a square	12	s = 6	6.000084194	−8.42e-05	-0.001	behind
L's in a square	13	s = 4 + 2√2 = 6.828+	7.240894024	−4.12e-01	-6.041	behind	Found by Maurizio Morandi in June 2012.
L's in a square	14	s = 7	7.951601482	−9.52e-01	-13.594	behind
L's in a square	15	s = 7	8.416133301	−1.4161	-20.230	behind
L's in a square	16	s = 7	8.014047892	−1.0140	-14.486	behind
L's in a square	17	s = 19/3 + √2 = 7.747+	9.705806161	−1.9583	-25.278	behind	Found by Maurizio Morandi in June 2012.
L's in a square	18	s = 13/2 + √2 = 7.914+	9.869962235	−1.9557	-24.713	behind	Found by Maurizio Morandi in June 2012.
L's in a square	19	s = 8	8.004256597	−4.26e-03	-0.053	behind
L's in a square	20	s = 8	8.004886225	−4.89e-03	-0.061	behind
L's in a square	21	s = 8	9.007947202	−1.0079	-12.599	behind
L's in a square	22	s = 3 + 4√2 = 8.656+	9.979855242	−1.3230	-15.284	behind	Found by Maurizio Morandi in June 2012.
L's in a square	23	s = 15/2 + √2 = 8.914+	9.001503714	−8.73e-02	-0.979	behind	Found by Maurizio Morandi in June 2012.
L's in a square	24	s = 9	11.074372884	−2.0744	-23.049	behind
L's in a square	25	s = 9	12.298400800	−3.2984	-36.649	behind
L's in a square	26	s = 9	12.166465678	−3.1665	-35.183	behind
L's in a square	27	s = 9	10.009685870	−1.0097	-11.219	behind
L's in a square	28	s = 7 + 2√2 = 9.828+	11.238526973	−1.4101	-14.348	behind	Found by Maurizio Morandi in May 2026.
L's in a tan	2	s = 3√2 = 4.242+	4.242640689	−1.70e-09	-0.000	reproduced
L's in a tan	3	s = 5	5.000000002	−2.00e-09	-0.000	reproduced
L's in a tan	4	s = 4√2 = 5.656+	5.828427144	−1.72e-01	-3.033	behind	Found by Maurizio Morandi in July 2012
L's in a tan	5	s = 2 + 3√2 = 6.242+	6.949771383	−7.07e-01	-11.329	behind	Found by Maurizio Morandi in July 2012.
L's in a tan	6	s = 7	7.000185567	−1.86e-04	-0.003	behind
L's in a tan	7	s = 7	7.778174656	−7.78e-01	-11.117	behind
L's in a tan	8	s = 11/√2 = 7.778+	8.242640845	−4.64e-01	-5.972	behind
L's in a tan	9	s = 8	9.192388567	−1.1924	-14.905	behind
L's in a tan	10	s = 6√2 = 8.485+	8.868376058	−3.83e-01	-4.515	behind
L's in a tan	11	s = 9	9.003645016	−3.65e-03	-0.041	behind
L's in a tan	12	s = 9	9.903497756	−9.03e-01	-10.039	behind
L's in a tan	13	s = 2 + 11/√2 = 9.778+	10.801757451	−1.0236	-10.468	behind	Found by Maurizio Morandi in July 2012.
L's in a tan	14	s = 7√2 = 9.899+	11.242640885	−1.3431	-13.569	behind
L's in a tan	15	s = 10	11.137117314	−1.1371	-11.371	behind
L's in a tan	16	s = 15/√2 = 10.606+	11.008200014	−4.02e-01	-3.787	behind
L's in a tan	17	s = 8 + 2√2 = 10.828+	11.007000945	−1.79e-01	-1.649	behind	Found by Maurizio Morandi in January 2025.
L's in a tan	18	s = 11	12.353970185	−1.3540	-12.309	behind
L's in a tan	19	s = 8√2 = 11.313+	12.005596071	−6.92e-01	-6.116	behind	Found by Maurizio Morandi in January 2025.
L's in a tan	20	s = 4 + 11/√2 = 11.778+	15.788035212	−4.0099	-34.045	behind	Found by Maurizio Morandi in January 2025.
L's in a tan	21	s = 12	12.828699113	−8.29e-01	-6.906	behind
L's in a tan	22	s = 12	14.471002634	−2.4710	-20.592	behind
L's in a triangle	2	s = 4 + 2/√3 = 5.15470+	5.154700540	−2.06e-09	-0.000	reproduced
L's in a triangle	3	s = 3 + 3√3/2 = 5.59807+	5.598076214	−2.24e-09	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
L's in a triangle	4	s = 6.58646+	6.618802177	−3.23e-02	-0.491	behind	Found by Jonathan Viquerat in May 2026.
L's in a triangle	5	s = 6 + 2/√3 = 7.15470+	7.386751549	−2.32e-01	-3.243	behind	Found by Jonathan Viquerat in May 2026.
L's in a triangle	6	s = 4 + 2√3 = 7.46410+	7.732050956	−2.68e-01	-3.590	behind	Found by Maurizio Morandi in May 2026.
L's in a triangle	7	s = 7 + 2/√3 = 8.15470+	8.309401124	−1.55e-01	-1.897	behind	Found by Jonathan Viquerat in May 2026.
L's in a triangle	8	s = 7 + √3 = 8.73205+	9.308578082	−5.77e-01	-6.602	behind	Found by Jonathan Viquerat in May 2026.
L's in a triangle	9	s = 5 + 7/√3 = 9.04145+	9.389690663	−3.48e-01	-3.852	behind	Found by Maurizio Morandi in May 2026.
L's in a triangle	10	s = 6 + 2√3 = 9.46410+	10.158671484	−6.95e-01	-7.339	behind	Found by Maurizio Morandi in May 2026.
L's in a triangle	11	s = 4 + 10/√3 = 9.77350+	10.543669557	−7.70e-01	-7.880	behind	Found by Maurizio Morandi in May 2026.
L's in a triangle	12	s = 10.30175+	11.104703966	−8.03e-01	-7.794	behind	Found by Aapo Lipponen in July 2026.
L's in a triangle	13	s = 9 + √3 = 10.73205+	11.598910760	−8.67e-01	-8.077	behind	Found by Maurizio Morandi in May 2026.
L's in a triangle	14	s = 7 + 7/√3 = 11.04145+	12.033956750	−9.93e-01	-8.989	behind	Found by Maurizio Morandi in May 2026.
L's in a triangle	15	s = 5 + 11/√3 = 11.35085+	12.044698914	−6.94e-01	-6.113	behind	Found by Maurizio Morandi in May 2026.
L's in a triangle	16	s = 10 + √3 = 11.73205+	12.183715088	−4.52e-01	-3.850	behind	Found by Maurizio Morandi in May 2026.
L's in a triangle	17	s = 4 + 14/√3 = 12.08290+	12.733696635	−6.51e-01	-5.386	behind	Found by Maurizio Morandi in May 2026.
L's in a triangle	18	s = 9 + 2√3 = 12.46410+	13.701406967	−1.2373	-9.927	behind	Found by Maurizio Morandi in May 2026.
L's in a triangle	19	s = 11 + √3 = 12.73205+	13.313289332	−5.81e-01	-4.565	behind	Found by Maurizio Morandi in May 2026.
L's in a triangle	20	s = 13.00966+	13.624588726	−6.15e-01	-4.727	behind	Found by Aapo Lipponen in July 2026.
L's in a triangle	21	s = 13.30935+	13.806774338	−4.97e-01	-3.737	behind	Found by Aapo Lipponen in July 2026.
L's in a triangle	22	s = 2 + 20/√3 = 13.54700+	14.279556029	−7.33e-01	-5.407	behind	Found by Maurizio Morandi in June 2026.
L's in a triangle	23	s = 14.19776+	15.888888496	−1.6911	-11.911	behind	Found by Aapo Lipponen in July 2026.
L's in a triangle	24	s = 15.00964+	15.507431689	−4.98e-01	-3.316	behind	Found by Aapo Lipponen in July 2026.
L's in a triangle	25	s = 15.20151+	16.338080284	−1.1366	-7.477	behind	Found by Aapo Lipponen in July 2026.
L's in a triangle	26	s = 15.22482+	15.285748525	−6.09e-02	-0.400	behind	Found by Aapo Lipponen in July 2026.
L's in a triangle	27	s = 15.65894+	18.004449727	−2.3455	-14.979	behind	Found by Aapo Lipponen in July 2026.
L's in a triangle	28	s = 16.14341+	17.751403312	−1.6080	-9.961	behind	Found by Aapo Lipponen in July 2026.
L's in a triangle	29	s = 16.39862+	16.248807784	+1.50e-01	0.914	beaten	Found by Aapo Lipponen in July 2026.
L's in a triangle	30	s = 16.46648+	16.387913898	+7.86e-02	0.477	beaten	Found by Aapo Lipponen in July 2026.
L's in an L	2	s = 2	2.000000001	−8.00e-10	-0.000	reproduced
L's in an L	3	s = 2	2.000000001	−8.00e-10	-0.000	reproduced
L's in an L	4	s = 2	2.500000035	−5.00e-01	-25.000	behind
L's in an L	5	s = 5/2 = 2.5	2.766058055	−2.66e-01	-10.642	behind
L's in an L	6	s = 1 + 4√2/3 = 2.885+	3.000000001	−1.14e-01	-3.965	behind	Found by Maurizio Morandi in July 2012.
L's in an L	7	s = 3	3.000000008	−7.80e-09	-0.000	reproduced
L's in an L	8	s = 3	3.024069525	−2.41e-02	-0.802	behind
L's in an L	9	s = 3	3.616929642	−6.17e-01	-20.564	behind
L's in an L	10	s = 7/2 = 3.5	3.988150976	−4.88e-01	-13.947	behind
L's in an L	11	s = 7/3 + √2 = 3.747+	4.009766409	−2.62e-01	-6.998	behind	Found by Maurizio Morandi in July 2012.
L's in an L	12	s = (19 + 9√2) / 8 = 3.965+	4.014630916	−4.86e-02	-1.227	behind	Found by Maurizio Morandi in July 2012.
L's in an L	13	s = 4	4.119791710	−1.20e-01	-2.995	behind
L's in an L	14	s = 4	4.001371943	−1.37e-03	-0.034	behind
L's in an L	15	s = 4	4.463028414	−4.63e-01	-11.576	behind
L's in an L	16	s = 4	4.531039045	−5.31e-01	-13.276	behind
L's in an L	17	s = 9/2 = 4.5	5.009163648	−5.09e-01	-11.315	behind
L's in an L	18	s = 9/2 = 4.5	5.000241007	−5.00e-01	-11.116	behind
L's in an L	19	s = 3 + 5√2/4 = 4.767+	5.069744837	−3.02e-01	-6.335	behind	Found by Maurizio Morandi in June 2026.
L's in an L	20	s = 3(6 + 5√2)/8 = 4.901+	5.003695349	−1.02e-01	-2.082	behind	Found by Maurizio Morandi in June 2026.
L's in an L	21	s = 5	5.179017747	−1.79e-01	-3.580	behind
L's in an L	22	s = 5	5.539286028	−5.39e-01	-10.786	behind
L's in an L	23	s = 5	5.524807816	−5.25e-01	-10.496	behind
L's in an L	24	s = 5	6.007678155	−1.0077	-20.154	behind
L's in an L	25	s = 5	6.037571023	−1.0376	-20.751	behind
L's in an octagon	2	s = √(5–√2–√(8√2–9)) = 1.43690+	1.436905880	−5.75e-10	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
L's in an octagon	3	s = 10(3–2√2) = 1.71572+	1.734478077	−1.87e-02	-1.093	behind	Found by Aapo Lipponen in July 2026.
L's in an octagon	4	s = 3(2–√2) = 1.75735+	1.984773653	−2.27e-01	-12.941	behind	Found by Aapo Lipponen in July 2026
L's in an octagon	5	s = 5/(1+√2) = 2.07106+	2.071067850	−3.82e-08	-0.000	reproduced	Found by Jonathan Viquerat in May 2026
L's in an octagon	6	s = 13(3–2√2) = 2.23044+	2.414213600	−1.84e-01	-8.239	behind	Found by Jonathan Viquerat in May 2026.
L's in an octagon	7	s = 4(2–√2) = 2.34314+	2.574118585	−2.31e-01	-9.857	behind	Found by Maurizio Morandi in May 2026.
L's in an octagon	8	s = 6(√2–1) = 2.48528+	2.536326847	−5.10e-02	-2.054	behind	Found by Maurizio Morandi in May 2026.
L's in an octagon	9	s = 11(3√2–4) = 2.66904+	2.861793004	−1.93e-01	-7.222	behind	Found by Maurizio Morandi in May 2026.
L's in an octagon	10	s = 2(11–√2)/7 = 2.73879+	3.111391110	−3.73e-01	-13.604	behind	Found by Maurizio Morandi in May 2026.
L's in an octagon	11	s = 7(√2–1) = 2.89949+	3.139674404	−2.40e-01	-8.284	behind	Found by Maurizio Morandi in May 2026.
L's in an octagon	12	s = 5(2–√2) = 2.92893+	3.299621604	−3.71e-01	-12.656	behind	Found by Maurizio Morandi in May 2026.
L's in an octagon	13	s = 13(3√2–4) = 3.15432+	3.314640731	−1.60e-01	-5.082	behind	Found by Maurizio Morandi in May 2026.
L's in an octagon	14	s = 5(4√2–5) = 3.28427+	3.541263623	−2.57e-01	-7.825	behind	Found by Maurizio Morandi in August 2026.
L's in an octagon	15	s = 25(8–5√2)/7 = 3.31761+	3.454278732	−1.37e-01	-4.119	behind	Found by Maurizio Morandi in May 2026.
L's in an octagon	16	s = 20(3–2√2) = 3.43145+	3.813869370	−3.82e-01	-11.144	behind	Found by Maurizio Morandi in May 2026.
L's in an octagon	17	s = 6(2–√2) = 3.51471+	4.187220735	−6.73e-01	-19.134	behind	Found by Maurizio Morandi in May 2026.
L's in an octagon	18	s = 25(2–√2)/4 = 3.66116+	3.811264717	−1.50e-01	-4.100	behind	Found by Maurizio Morandi in May 2026.
L's in an octagon	19	s = 9(√2–1) = 3.72792+	4.048003676	−3.20e-01	-8.586	behind	Found by Maurizio Morandi in May 2026.
L's in an octagon	20	s = 22(3–2√2) = 3.77460+	4.047569142	−2.73e-01	-7.232	behind	Found by Maurizio Morandi in May 2026.
L's in an octagon	21	s = 16(3√2–4) = 3.88225+	4.268214483	−3.86e-01	-9.942	behind	Found by Maurizio Morandi in August 2026.
L's in an octagon	22	s = 27(2–√2)/4 = 3.95405+	4.409123544	−4.55e-01	-11.509	behind	Found by Maurizio Morandi in July 2026.
L's in an octagon	23	s = 7(2–√2) = 4.10050+	4.255395259	−1.55e-01	-3.777	behind	Found by Maurizio Morandi in July 2026.
L's in an octagon	24	s = 10(√2–1) = 4.14213+	5.062687516	−9.21e-01	-22.224	behind	Found by Maurizio Morandi in July 2026.
L's in an octagon	25	s = 10(√2–1) = 4.14213+	4.743914781	−6.02e-01	-14.528	behind	Found by Maurizio Morandi in July 2026.
L's in an octagon	26	s = 25(3–2√2) = 4.28932+	4.828461170	−5.39e-01	-12.569	behind	Found by Maurizio Morandi in July 2026.
L's in an octagon	27	s = 15(1–1/√2) = 4.39339+	4.611055926	−2.18e-01	-4.954	behind	Found by Maurizio Morandi in July 2026.
L's in an octagon	28	s = 31(2–√2)/4 = 4.53984+	4.694260845	−1.54e-01	-3.401	behind	Found by Maurizio Morandi in July 2026.
L's in an octagon	29	s = 11(√2–1) = 4.55634+	5.178420005	−6.22e-01	-13.653	behind	Found by Maurizio Morandi in July 2026.
L's in an octagon	30	s = 11(√2–1) = 4.55634+	5.649494197	−1.0931	-23.992	behind	Found by Maurizio Morandi in July 2026.
Octagons in a circle	2	r = √(13/4+2√2) = 2.46544+	2.465446649	−1.14e-08	-0.000	reproduced
Octagons in a circle	3	r = 2.71611+	2.716111075	−1.07e-06	-0.000	reproduced	Found by Jonathan Viquerat in June 2026.
Octagons in a circle	4	r = √(9/2+3√2) = 2.95679+	2.956795711	−3.19e-08	-0.000	reproduced
Octagons in a circle	5	r = 3.37974+	3.379820258	−8.03e-05	-0.002	behind	Found by Jonathan Viquerat in June 2026.
Octagons in a circle	6	r = 3.69797+	3.697970689	−6.89e-07	-0.000	reproduced	Found by Jonathan Viquerat in June 2026.
Octagons in a circle	7	r = 3.77329+	3.773295999	−6.00e-06	-0.000	reproduced	Found by Jonathan Viquerat in June 2026.
Octagons in a circle	8	r = 4.12460+	4.124607953	−7.95e-06	-0.000	reproduced	Found by Jonathan Viquerat in June 2026.
Octagons in a circle	9	r = 4.46088+	4.460885628	−5.63e-06	-0.000	reproduced	Found by Jonathan Viquerat in June 2026.
Octagons in a circle	10	r = 4.72215+	4.734565567	−1.24e-02	-0.263	behind	Found by Jonathan Viquerat in June 2026.
Octagons in a circle	11	r = 4.88201+	4.928760828	−4.68e-02	-0.958	behind	Found by Jonathan Viquerat in June 2026.
Octagons in a circle	12	r = 5.00001+	5.012459081	−1.24e-02	-0.249	behind	Found by Jonathan Viquerat in June 2026.
Octagons in a circle	13	r = 5.23457+	5.236575556	−2.01e-03	-0.038	behind	Found by Jonathan Viquerat in June 2026.
Octagons in a circle	14	r = 5.34130+	5.342875543	−1.58e-03	-0.029	behind	Found by Haowei Lin in July 2026.
Octagons in a circle	15	r = 5.60687+	5.667142634	−6.03e-02	-1.075	behind	Found by Jonathan Viquerat in June 2026.
Octagons in a circle	16	r = 5.73295+	5.737432741	−4.48e-03	-0.078	behind	Found by Haowei Lin in July 2026.
Octagons in a circle	17	r = 5.94448+	5.997766318	−5.33e-02	-0.896	behind	Found by Jonathan Viquerat in June 2026.
Octagons in a circle	18	r = 6.05966+	6.061644054	−1.98e-03	-0.033	behind	Found by Haowei Lin in July 2026.
Octagons in a circle	19	r = 6.07328+	6.113552674	−4.03e-02	-0.663	behind	Found by Jonathan Viquerat in June 2026.
Octagons in a circle	20	r = 6.36724+	6.371636086	−4.40e-03	-0.069	behind	Found by Haowei Lin in July 2026.
Octagons in a circle	21	r = 6.48101+	6.611823149	−1.31e-01	-2.018	behind	Found by Jonathan Viquerat in August 2026.
Octagons in a circle	22	r = 6.70466+	6.728243837	−2.36e-02	-0.352	behind	Found by Jonathan Viquerat in August 2026.
Octagons in a circle	23	r = 6.85820+	7.042142331	−1.84e-01	-2.682	behind	Found by Jonathan Viquerat in August 2026.
Octagons in a circle	24	r = 6.96998+	7.246050265	−2.76e-01	-3.961	behind	Found by Jonathan Viquerat in August 2026.
Octagons in a circle	25	r = 7.12165+	7.149872981	−2.82e-02	-0.396	behind	Found by Jonathan Viquerat in August 2026.
Octagons in a domino	2	s = 1 + √2 = 2.41421+	2.414213563	−9.66e-10	-0.000	reproduced
Octagons in a domino	3	s = 3.51366+	3.513669803	−9.80e-06	-0.000	reproduced	Found by Aapo Lipponen in July 2026.
Octagons in a domino	4	s = 2 + 7√2/5 = 3.97989+	3.979898989	−1.59e-09	-0.000	reproduced	Found by Aapo Lipponen in July 2026.
Octagons in a domino	5	s = 13/6 + 3/√2 = 4.28798+	4.287987012	−1.72e-09	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Octagons in a domino	6	s = (16 + 11√2)/7 = 4.50804+	4.508049886	−1.80e-09	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Octagons in a domino	7	s = 2 + 2√2 = 4.82842+	4.828427207	−8.20e-08	-0.000	reproduced
Octagons in a domino	8	s = 2 + 2√2 = 4.82842+	4.828427127	−2.05e-09	-0.000	reproduced
Octagons in a domino	9	s = 8/3 + 2√2 = 5.49509+	5.498073907	−2.98e-03	-0.054	behind	Found by Jonathan Viquerat in May 2026.
Octagons in a domino	10	s = 3 + 2√2 = 5.82842+	5.887046420	−5.86e-02	-1.006	behind	Found by Jonathan Viquerat in May 2026.
Octagons in a domino	11	s = 16/5 + 2√2 = 6.02842+	6.028486462	−5.93e-05	-0.001	behind	Found by Jonathan Viquerat in May 2026.
Octagons in a domino	12	s = 6.31126+	6.311649619	−3.90e-04	-0.006	behind	Found by Jonathan Viquerat in May 2026.
Octagons in a domino	13	s = 6.51128+	6.564719387	−5.34e-02	-0.821	behind	Found by Aapo Lipponen in July 2026.
Octagons in a domino	14	s = (21 + 13√2)/6 = 6.56412+	6.565255911	−1.13e-03	-0.017	behind	Found by Jonathan Viquerat in May 2026.
Octagons in a domino	15	s = (47 + 29√2)/13 = 6.77016+	6.773696874	−3.53e-03	-0.052	behind	Found by Jonathan Viquerat in May 2026.
Octagons in a domino	16	s = 7.10456+	7.203698308	−9.91e-02	-1.395	behind	Found by Jonathan Viquerat in May 2026.
Octagons in a domino	17	s = 3 + 3√2 = 7.24264+	7.247614754	−4.97e-03	-0.069	behind
Octagons in a domino	18	s = 3 + 3√2 = 7.24264+	7.244382766	−1.74e-03	-0.024	behind
Octagons in a domino	19	s = 7.77123+	8.093879707	−3.23e-01	-4.152	behind	Found by Jonathan Viquerat in May 2026.
Octagons in a domino	20	s = 8.03947+	8.163785164	−1.24e-01	-1.546	behind	Found by Jonathan Viquerat in May 2026.
Octagons in a domino	21	s = 8.21837+	8.244426701	−2.61e-02	-0.317	behind	Found by Bhavithran Ananthan in July 2026.
Octagons in a domino	22	s = 8.34004+	8.396834751	−5.68e-02	-0.681	behind	Found by Thomas Greenleaf in June 2026.
Octagons in a hexagon	2	s = 2.70289+	2.702888728	+1.27e-06	0.000	reproduced
Octagons in a hexagon	3	s = 2.88958+	2.889628768	−4.88e-05	-0.002	behind	Found by Mohamed Metwalli in June 2026.
Octagons in a hexagon	4	s = 11+8√2–16/√3–4√6 = 3.27814+	3.278145237	−1.64e-08	-0.000	reproduced	Found by Mohamed Metwalli in June 2026.
Octagons in a hexagon	5	s = 3.71848+	3.718485425	−5.42e-06	-0.000	reproduced	Found by Jonathan Viquerat in June 2026.
Octagons in a hexagon	6	s = 3.94730+	3.947306375	−6.38e-06	-0.000	reproduced	Found by Aristotle Papowitz in July 2026.
Octagons in a hexagon	7	s = 3.97716+	3.977162459	−2.46e-06	-0.000	reproduced	Found by Jonathan Viquerat in June 2026.
Octagons in a hexagon	8	s = 4.56653+	4.566540151	−1.02e-05	-0.000	behind	Found by Jonathan Viquerat in June 2026.
Octagons in a hexagon	9	s = 4.93304+	4.933045515	−5.51e-06	-0.000	reproduced	Found by Jonathan Viquerat in June 2026.
Octagons in a hexagon	10	s = 5.06929+	5.096117760	−2.68e-02	-0.529	behind	Found by Jonathan Viquerat in June 2026.
Octagons in a hexagon	11	s = 5.34796+	5.377736880	−2.98e-02	-0.557	behind	Found by Bhavithran Ananthan in July 2026.
Octagons in a hexagon	12	s = 5.38669+	5.404365212	−1.77e-02	-0.328	behind	Found by Jonathan Viquerat in June 2026.
Octagons in a hexagon	13	s = 5.75470+	5.769627955	−1.49e-02	-0.259	behind	Found by Jonathan Viquerat in June 2026.
Octagons in a hexagon	14	s = 5.77752+	5.789778162	−1.23e-02	-0.212	behind	Found by Jonathan Viquerat in June 2026.
Octagons in a hexagon	15	s = 6.13744+	6.167523051	−3.01e-02	-0.490	behind	Found by Bhavithran Ananthan in June 2026.
Octagons in a hexagon	16	s = 6.21438+	6.216000707	−1.62e-03	-0.026	behind	Found by Jonathan Viquerat in June 2026.
Octagons in a hexagon	17	s = 6.35725+	6.435913850	−7.87e-02	-1.237	behind	Found by Jonathan Viquerat in June 2026.
Octagons in a hexagon	18	s = 6.42774+	6.467107797	−3.94e-02	-0.612	behind	Found by Bhavithran Ananthan in July 2026.
Octagons in a hexagon	19	s = 6.44696+	6.453901322	−6.94e-03	-0.108	behind	Found by Bhavithran Ananthan in July 2026.
Octagons in a hexagon	20	s = 6.99419+	7.105167231	−1.11e-01	-1.587	behind	Found by Leo Strijbos in August 2026.
Octagons in a pentagon	2	s = 3.35605+	3.356053089	−3.09e-06	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Octagons in a pentagon	3	s = 3.74411+	3.744125629	−1.56e-05	-0.000	behind	Found by Bhavithran Ananthan in May 2026.
Octagons in a pentagon	4	s = 4.10125+	4.101259755	−9.76e-06	-0.000	reproduced	Found by Bhavithran Ananthan in July 2026.
Octagons in a pentagon	5	s = 4.33300+	4.338166880	−5.17e-03	-0.119	behind	Found by Jonathan Viquerat in May 2026.
Octagons in a pentagon	6	s = 4.77007+	4.770075637	−5.64e-06	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Octagons in a pentagon	7	s = = 5.25544+	5.255443053	−3.05e-06	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Octagons in a pentagon	8	s = 5.61662+	5.616625037	−5.04e-06	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Octagons in a pentagon	9	s = 5.96580+	5.966496329	−6.96e-04	-0.012	behind	Found by Jonathan Viquerat in May 2026.
Octagons in a pentagon	10	s = 6.28146+	6.281467372	−7.37e-06	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Octagons in a pentagon	11	s = 6.46576+	6.477600748	−1.18e-02	-0.183	behind	Found by Jonathan Viquerat in May 2026.
Octagons in a pentagon	12	s = 6.71763+	6.765336264	−4.77e-02	-0.710	behind	Found by Jonathan Viquerat in May 2026.
Octagons in a pentagon	13	s = 6.97061+	7.006375605	−3.58e-02	-0.513	behind	Found by Aapo Lipponen in July 2026.
Octagons in a pentagon	14	s = 7.16083+	7.164110941	−3.28e-03	-0.046	behind	Found by Jonathan Viquerat in May 2026.
Octagons in a pentagon	16	s = 7.61505+	7.676917130	−6.19e-02	-0.812	behind	Found by Bhavithran Ananthan in June 2026.
Octagons in a pentagon	17	s = 7.91419+	8.052589169	−1.38e-01	-1.749	behind	Found by Bhavithran Ananthan in July 2026.
Octagons in a pentagon	18	s = 8.12567+	8.178768942	−5.31e-02	-0.653	behind	Found by Bhavithran Ananthan in June 2026.
Octagons in a pentagon	19	s = 8.34354+	8.510419321	−1.67e-01	-2.000	behind	Found by Bhavithran Ananthan in July 2026.
Octagons in a pentagon	20	s = 8.54202+	8.553474367	−1.15e-02	-0.134	behind	Found by Bhavithran Ananthan in July 2026.
Octagons in a pentagon	21	s = 8.74315+	8.824920693	−8.18e-02	-0.935	behind	Found by Jonathan Viquerat in August 2026.
Octagons in a pentagon	22	s = 8.96230+	9.041282801	−7.90e-02	-0.881	behind	Found by Jonathan Viquerat in August 2026.
Octagons in a pentagon	23	s = 9.11759+	9.232124794	−1.15e-01	-1.256	behind	Found by Jonathan Viquerat in August 2026.
Octagons in a pentagon	24	s = 9.27761+	9.635884297	−3.58e-01	-3.862	behind	Found by Jonathan Viquerat in August 2026.
Octagons in a pentagon	25	s = 9.45135+	10.018740785	−5.67e-01	-6.003	behind	Found by Jonathan Viquerat in August 2026.
Octagons in a square	2	s = 2 + 3√2/2 = 4.12132+	4.121320345	−1.65e-09	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Octagons in a square	3	s = 2 + 2√2 = 4.82842+	4.828427127	−1.93e-09	-0.000	reproduced
Octagons in a square	4	s = 2 + 2√2 = 4.82842+	4.828427127	−1.93e-09	-0.000	reproduced
Octagons in a square	5	s = 3 + 2√2 = 5.82842+	5.828427127	−2.33e-09	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Octagons in a square	6	s = (11√2+17)/5 = 6.51126+	6.511269959	−1.22e-07	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Octagons in a square	7	s = (5√2+7)/2 = 7.03553+	7.035534036	−1.30e-07	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Octagons in a square	8	s = 3 + 3√2 = 7.24264+	7.242640824	−1.37e-07	-0.000	reproduced
Octagons in a square	9	s = 3 + 3√2 = 7.24264+	7.242640744	−5.67e-08	-0.000	reproduced
Octagons in a square	10	s = 4+3√2 = 8.24264+	8.242665853	−2.52e-05	-0.000	behind	Found by Jonathan Viquerat in May 2026.
Octagons in a square	11	s = 8.57596+	8.577141984	−1.18e-03	-0.014	behind	Found by Jonathan Viquerat in May 2026.
Octagons in a square	12	s = (23√2+38)/8 = 8.81586+	8.815977529	−1.14e-04	-0.001	behind	Found by Jonathan Viquerat in May 2026.
Octagons in a square	13	s = 9.19909+	9.224428004	−2.53e-02	-0.275	behind	Found by Jonathan Viquerat in May 2026.
Octagons in a square	14	s = (7√2+9)/2 = 9.44974+	9.657003865	−2.07e-01	-2.193	behind	Found by Jonathan Viquerat in May 2026.
Octagons in a square	15	s = 4 + 4√2 = 9.65685+	9.656968627	−1.14e-04	-0.001	behind	Found by Jonathan Viquerat in May 2026.
Octagons in a square	16	s = 4 + 4√2 = 9.65685+	9.656883440	−2.92e-05	-0.000	behind	Found by Jonathan Viquerat in May 2026.
Octagons in a square	17	s = 10.44973+	10.610969576	−1.61e-01	-1.543	behind	Found by Jonathan Viquerat in May 2026.
Octagons in a square	18	s = (17√2+29)/5 = 10.60832+	10.610292298	−1.97e-03	-0.019	behind	Found by Jonathan Viquerat in May 2026.
Octagons in a square	19	s = 10.96620+	11.138816867	−1.73e-01	-1.574	behind	Found by Haowei Lin in July 2026.
Octagons in a square	20	s = (39√2+67)/11 = 11.10493+	11.476972302	−3.72e-01	-3.350	behind	Found by Jonathan Viquerat in May 2026.
Octagons in a square	21	s = 11.47891+	11.500108152	−2.12e-02	-0.185	behind	Found by Grigory Merzon in August 2026.
Octagons in a square	22	s = 11.63403+	12.409669645	−7.76e-01	-6.667	behind	Found by Grigory Merzon in August 2026.
Octagons in a tan	2	s = 3+2√2 = 5.82842+	5.828427127	−2.33e-09	-0.000	reproduced
Octagons in a tan	3	s = 3+5/√2 = 6.53553+	6.535533909	−2.61e-09	-0.000	reproduced
Octagons in a tan	4	s = 4+5/√2 = 7.53553+	7.535533909	−3.01e-09	-0.000	reproduced
Octagons in a tan	5	s = 9/2+3√2 = 8.74264+	8.742640691	−3.50e-09	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Octagons in a tan	6	s = 4+7/√2 = 8.94974+	8.949747472	−3.58e-09	-0.000	reproduced
Octagons in a tan	7	s = 5+7/√2 = 9.94974+	9.949747562	−9.34e-08	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Octagons in a tan	8	s = 10.65684+	10.656854447	−1.44e-05	-0.000	behind	Found by Jonathan Viquerat in May 2026.
Octagons in a tan	9	s = 6+7/√2 = 10.94974+	10.949748652	−1.18e-06	-0.000	reproduced
Octagons in a tan	10	s = 5+9/√2 = 11.36396+	11.363967850	−6.82e-06	-0.000	reproduced
Octagons in a tan	11	s = 12.33328+	12.363961265	−3.07e-02	-0.249	behind	Found by Jonathan Viquerat in May 2026.
Octagons in a tan	12	s = 12.65684+	12.656858576	−1.86e-05	-0.000	behind	Found by Jonathan Viquerat in May 2026.
Octagons in a tan	13	s = 13.21750+	13.294957513	−7.75e-02	-0.586	behind	Found by Jonathan Viquerat in May 2026.
Octagons in a tan	14	s = 13/2+5√2 = 13.57106+	13.780657911	−2.10e-01	-1.544	behind	Found by Jonathan Viquerat in May 2026.
Octagons in a tan	15	s = 6+11/√2 = 13.77817+	13.787705633	−9.53e-03	-0.069	behind
Octagons in a tan	16	s = 8+9/√2 = 14.36396+	14.615184590	−2.51e-01	-1.749	behind
Octagons in a tan	17	s = 14.77816+	14.781904433	−3.74e-03	-0.025	behind	Found by Jonathan Viquerat in May 2026.
Octagons in a tan	18	s = 15.34720+	15.778446018	−4.31e-01	-2.810	behind	Found by Jonathan Viqueratl in May 2026.
Octagons in a tan	19	s = 15.68053+	15.795375241	−1.15e-01	-0.732	behind	Found by Jonathan Viquerat in May 2026.
Octagons in a tan	20	s = 15/2+6√2 = 15.98528+	16.781791848	−7.97e-01	-4.983	behind	Found by Jonathan Viquerat in May 2026.
Octagons in a tan	21	s = 7+13/√2 = 16.19238+	16.951389811	−7.59e-01	-4.687	behind
Octagons in a tan	22	s = 16.77817+	17.002903802	−2.25e-01	-1.339	behind	Found by Thomas Greenleaf in June 2026.
Octagons in a triangle	2	s = 6.79962+	6.799624261	−4.26e-06	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Octagons in a triangle	3	s = (6+5√2+4√3+3√6)/4 = 6.83693+	6.836935073	−5.27e-09	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Octagons in a triangle	4	s = 8.65211+	8.652115620	−5.62e-06	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Octagons in a triangle	5	s = 9.28498+	9.284990338	−1.03e-05	-0.000	behind	Found by Jonathan Viquerat in May 2026.
Octagons in a triangle	6	s = 9.31576+	9.315773043	−1.30e-05	-0.000	behind	Found by Jonathan Viquerat in May 2026.
Octagons in a triangle	7	s = 11.06632+	11.066335198	−1.52e-05	-0.000	behind	Found by Jonathan Viquerat in May 2026.
Octagons in a triangle	8	s = 11.51025+	11.512147192	−1.90e-03	-0.016	behind	Found by Jonathan Viquerat in May 2026.
Octagons in a triangle	9	s = 11.72998+	11.770509257	−4.05e-02	-0.346	behind
Octagons in a triangle	10	s = 11.80642+	11.807352390	−9.32e-04	-0.008	behind	Found by Jonathan Viquerat in May 2026.
Octagons in a triangle	11	s = 13.24689+	13.247442287	−5.52e-04	-0.004	behind	Found by Jonathan Viquerat in May 2026.
Octagons in a triangle	12	s = 13.62032+	13.621711162	−1.39e-03	-0.010	behind	Found by Bhavithran Ananthan in July 2026.
Octagons in a triangle	13	s = 14.04225+	14.182097385	−1.40e-01	-0.996	behind	Found by Jonathan Viquerat in May 2026.
Octagons in a triangle	14	s = 14.23921+	14.289454832	−5.02e-02	-0.353	behind	Found by Aristotle Papowitz in July 2026.
Octagons in a triangle	15	s = 14.28169+	14.309446328	−2.78e-02	-0.194	behind	Found by Jonathan Viquerat in May 2026.
Octagons in a triangle	16	s = 15.66136+	15.738897074	−7.75e-02	-0.495	behind	Found by Jonathan Viquerat in May 2026.
Octagons in a triangle	17	s = 16.06191+	16.140799233	−7.89e-02	-0.491	behind	Found by Bhavithran Ananthan in July 2026.
Octagons in a triangle	18	s = 16.40979+	16.603439127	−1.94e-01	-1.180	behind	Found by Aristotle Papowitz in July 2026.
Octagons in a triangle	19	s = 16.54447+	16.732511980	−1.88e-01	-1.137	behind	Found by Timo Berthold et al in May 2026.
Octagons in a triangle	20	s = 16.74196+	16.930929038	−1.89e-01	-1.129	behind	Found by Jonathan Viquerat in August 2026.
Octagons in a triangle	21	s = 16.78582+	16.896627913	−1.11e-01	-0.660	behind	Found by Bhavithran Ananthan in July 2026.
Octagons in a triangle	22	s = 17.96238+	18.443664205	−4.81e-01	-2.679	behind	Found by Bhavithran Ananthan in July 2026.
Octagons in a triangle	23	s = 18.39413+	19.697624202	−1.3035	-7.086	behind	Found by Jonathan Viquerat in August 2026.
Octagons in a triangle	24	s = 18.55975+	19.019579055	−4.60e-01	-2.478	behind	Found by Jonathan Viquerat in August 2026.
Octagons in a triangle	25	s = 18.94531+	19.007902903	−6.26e-02	-0.330	behind	Found by Jonathan Viquerat in August 2026.
Octagons in an L	2	s = 1+√2 = 2.41421+	2.414213563	−9.66e-10	-0.000	reproduced
Octagons in an L	3	s = 1+√2 = 2.41421+	2.414213563	−9.66e-10	-0.000	reproduced
Octagons in an L	4	s = 3/2+5√2/4 = 3.26776+	3.503437867	−2.36e-01	-7.212	behind	Found by Jonathan Viquerat in June 2026.
Octagons in an L	7	s = 2+3/√2 = 4.12132+	4.154183088	−3.29e-02	-0.797	behind	Found by Jonathan Viquerat in June 2026.
Octagons in an L	8	s = 4.36459+	4.364707537	−1.18e-04	-0.003	behind	Found by Jonathan Viquerat in June 2026.
Octagons in an L	9	s = 4.46274+	4.648394064	−1.86e-01	-4.160	behind	Found by Jonathan Viquerat in June 2026.
Octagons in an L	10	s = 4.69035+	4.690588521	−2.39e-04	-0.005	behind	Found by Jonathan Viquerat in June 2026.
Octagons in an L	11	s = 2+2√2 = 4.82842+	4.828427929	−8.04e-07	-0.000	reproduced
Octagons in an L	12	s = 2+2√2 = 4.82842+	4.828427221	−9.60e-08	-0.000	reproduced
Octagons in an L	13	s = 5.41620+	5.416596716	−3.97e-04	-0.007	behind	Found by Jonathan Viquerat in June 2026.
Octagons in an L	14	s = 8/3+2√2 = 5.49509+	5.834638278	−3.40e-01	-6.179	behind	Found by Jonathan Viquerat in June 2026.
Octagons in an L	15	s = 5.82002+	5.906163545	−8.61e-02	-1.480	behind	Found by Haowei Lin in June 2026.
Octagons in an L	16	s = 5.93197+	6.215628674	−2.84e-01	-4.782	behind	Found by Jonathan Viquerat in June 2026.
Octagons in an L	17	s = 6.10747+	6.263507543	−1.56e-01	-2.555	behind	Found by Jonathan Viquerat in June 2026.
Octagons in an L	18	s = 6.25520+	6.449509815	−1.94e-01	-3.106	behind	Found by Vasily (Kotomord) Stolbov in September 2026.
Octagons in an L	19	s = 6.39782+	6.650854074	−2.53e-01	-3.955	behind	Found by Vasily (Kotomord) Stolbov in September 2026.
Octagons in an L	20	s = 6.51126+	6.755644991	−2.44e-01	-3.753	behind	Found by Vasily (Kotomord) Stolbov in September 2026.
Octagons in an octagon	2	s = 2	2.000000001	−8.00e-10	-0.000	reproduced
Octagons in an octagon	3	s = 5–2√2 = 2.17157+	2.171572876	−8.69e-10	-0.000	reproduced	Found by Ignacio Vallejo in March 2026.
Octagons in an octagon	4	s = √(5+1/√2) = 2.38895+	2.388955202	−3.72e-08	-0.000	reproduced	Found by Ignacio Vallejo in March 2026.
Octagons in an octagon	5	s = 2+1/√2 = 2.70710+	2.707106825	−4.40e-08	-0.000	reproduced	Found by Ignacio Vallejo in March 2026.
Octagons in an octagon	6	s = 2.98894+	2.994721402	−5.78e-03	-0.193	behind	Found by Nicolas Campailla in May 2026.
Octagons in an octagon	7	s = 3	3.000000001	−1.44e-09	-0.000	reproduced
Octagons in an octagon	8	s = 3.27524+	3.275244129	−4.13e-06	-0.000	reproduced	Found by Grant Mowry in May 2026.
Octagons in an octagon	9	s = 2+√2 = 3.41421+	3.414213622	−5.96e-08	-0.000	reproduced	Found by Ignacio Vallejo in March 2026.
Octagons in an octagon	10	s = 3+1/√2 = 3.70710+	3.707106847	−6.59e-08	-0.000	reproduced	Found by Ignacio Vallejo in March 2026.
Octagons in an octagon	11	s = 3.93256+	3.976950185	−4.44e-02	-1.129	behind	Found by Timo Berthold et al in May 2026.
Octagons in an octagon	12	s = 4	4.000065406	−6.54e-05	-0.002	behind
Octagons in an octagon	13	s = 7–2√2 = 4.17157+	4.271396945	−9.98e-02	-2.393	behind	Found by Ignacio Vallejo in March 2026.
Octagons in an octagon	14	s = 4.28135+	4.344300409	−6.30e-02	-1.470	behind	Found by Timo Berthold et al in May 2026.
Octagons in an octagon	15	s = 4.45584+	4.535533999	−7.97e-02	-1.789	behind	Found by Timo Berthold et al in May 2026.
Octagons in an octagon	16	s = 4.59803+	4.598845179	−8.15e-04	-0.018	behind	Found by Timo Berthold et al in May 2026.
Octagons in an octagon	17	s = 4.75690+	4.760369313	−3.47e-03	-0.073	behind	Found by Timo Berthold et al in May 2026.
Octagons in an octagon	18	s = 4.85681+	4.909739266	−5.29e-02	-1.090	behind	Found by Timo Berthold et al in May 2026.
Octagons in an octagon	19	s = 4.93550+	4.940323666	−4.82e-03	-0.098	behind	Found by Timo Berthold et al in May 2026.
Octagons in an octagon	20	s = 5.06727+	5.129586557	−6.23e-02	-1.230	behind	Found by Timo Berthold et al in May 2026.
Octagons in an octagon	21	s = 5.19695+	5.263451608	−6.65e-02	-1.280	behind	Found by Timo Berthold et al in May 2026.
Octagons in an octagon	22	s = 5.35686+	5.661324379	−3.04e-01	-5.684	behind	Found by Bhavithran Ananthan in July 2026.
Octagons in an octagon	23	s = 4+√2 = 5.41421+	5.528321548	−1.14e-01	-2.108	behind	Found by Bhavithran Ananthan in July 2026.
Octagons in an octagon	24	s = 5.55414+	5.745304526	−1.91e-01	-3.442	behind	Found by Bhavithran Ananthan in July 2026.
Octagons in an octagon	25	s = 5.65411+	5.849996309	−1.96e-01	-3.464	behind	Found by Bhavithran Ananthan in July 2026.
Octagons in an octagon	26	s = 5.73828+	5.761017158	−2.27e-02	-0.396	behind	Found by Bhavithran Ananthan in July 2026.
Octagons in an octagon	27	s = 5.81167+	5.978187859	−1.67e-01	-2.865	behind	Found by Bhavithran Ananthan in July 2026.
Octagons in an octagon	28	s = 3+2√2 = 5.82842+	5.911489381	−8.31e-02	-1.425	behind	Found by Ignacio Vallejo in March 2026.
Octagons in an octagon	29	s = 6.05649+	6.396532603	−3.40e-01	-5.615	behind	Found by Bhavithran Ananthan in July 2026.
Octagons in an octagon	30	s = 6.15306+	6.256289405	−1.03e-01	-1.678	behind	Found by Timo Berthold et al in May 2026.
Pentagons in a circle	2	r = √(5+2√5)/2 = 1.53884+	1.538841777	−8.58e-09	-0.000	reproduced
Pentagons in a circle	3	r = (1+√5)/2 = 1.61803+	1.618033989	−6.48e-10	-0.000	reproduced
Pentagons in a circle	4	r = 1.82971+	1.829715501	−5.50e-06	-0.000	reproduced	Found by Jonathan Viquerat in April 2026.
Pentagons in a circle	5	r = 2.03271+	2.032742950	−3.29e-05	-0.002	behind	Found by Jonathan Viquerat in April 2026.
Pentagons in a circle	6	r = √((25+11√5)/10) = 2.22703+	2.227032761	−3.20e-08	-0.000	reproduced	Found by Jonathan Viquerat in April 2026.
Pentagons in a circle	7	r = 2.29470+	2.294709904	−9.90e-06	-0.000	reproduced	Found by Jake Loyd in June 2026.
Pentagons in a circle	8	r = 2.48128+	2.481280615	−6.15e-07	-0.000	reproduced	Found by Jonathan Viquerat in April 2026.
Pentagons in a circle	9	r = 2.70169+	2.702506269	−8.16e-04	-0.030	behind	Found by Jake Loyd in June 2026.
Pentagons in a circle	10	r = 2.79768+	2.817419929	−1.97e-02	-0.706	behind	Found by Jonathan Viquerat in April 2026.
Pentagons in a circle	11	r = 2.90171+	2.923890003	−2.22e-02	-0.764	behind	Found by Jake Loyd in June 2026.
Pentagons in a circle	12	r = 3.01808+	3.021129165	−3.05e-03	-0.101	behind	Found by Jake Loyd in June 2026.
Pentagons in a circle	13	r = 3.07768+	3.095583921	−1.79e-02	-0.582	behind	Found by Jake Loyd in June 2026.
Pentagons in a circle	14	r = 3.23377+	3.235792618	−2.02e-03	-0.063	behind	Found by Jonathan Viquerat in June 2026.
Pentagons in a circle	15	r = 3.33877+	3.338774038	−4.04e-06	-0.000	reproduced	Found by Jake Loyd in June 2026.
Pentagons in a circle	16	r = 3.43657+	3.554747630	−1.18e-01	-3.439	behind	Found by Jonathan Viquerat in April 2026.
Pentagons in a circle	17	r = 3.50888+	3.512319087	−3.44e-03	-0.098	behind	Found by Jake Loyd in June 2026.
Pentagons in a circle	18	r = 3.61619+	3.671250900	−5.51e-02	-1.523	behind	Found by Jake Loyd in June 2026.
Pentagons in a circle	19	r = 3.67189+	3.828163953	−1.56e-01	-4.256	behind	Found by Jake Loyd in June 2026.
Pentagons in a circle	20	r = 3.80052+	3.803935853	−3.42e-03	-0.090	behind	Found by Jake Loyd in June 2026.
Pentagons in a circle	21	r = 3.90693+	4.077701577	−1.71e-01	-4.371	behind	Found by Haowei Lin in July 2026.
Pentagons in a circle	22	r = 3.99781+	4.164726374	−1.67e-01	-4.175	behind	Found by Haowei Lin in July 2026.
Pentagons in a circle	23	r = 4.07193+	4.232458169	−1.61e-01	-3.942	behind	Found by Haowei Lin in July 2026.
Pentagons in a circle	24	r = 4.12402+	4.126817735	−2.80e-03	-0.068	behind	Found by Haowei Lin in July 2026.
Pentagons in a circle	25	r = 4.23945+	4.248276858	−8.83e-03	-0.208	behind	Found by Jonathan Viquerat in August 2026.
Pentagons in a domino	2	s = 1.55460+	1.554603919	−3.92e-06	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Pentagons in a domino	3	s = 2.10051+	2.100514157	−4.16e-06	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Pentagons in a domino	4	s = 2.33739+	2.337395572	−5.57e-06	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Pentagons in a domino	5	s = 2.47315+	2.473151364	−1.36e-06	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Pentagons in a domino	6	s = 2.69228+	2.692281362	−1.36e-06	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Pentagons in a domino	7	s = 2.91977+	2.919770575	−5.75e-07	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Pentagons in a domino	8	s = 3.07696+	3.077676643	−7.17e-04	-0.023	behind	Found by Jonathan Viquerat in May 2026.
Pentagons in a domino	9	s = 3.33456+	3.337244404	−2.68e-03	-0.081	behind	Found by Jonathan Viquerat in May 2026.
Pentagons in a domino	10	s = 3.51930+	3.521467760	−2.17e-03	-0.062	behind	Found by Bhavithran Ananthan in July 2026.
Pentagons in a domino	11	s = 3.61313+	3.813880962	−2.01e-01	-5.556	behind	Found by Jonathan Viquerat in May 2026.
Pentagons in a domino	12	s = 3.74837+	3.801336396	−5.30e-02	-1.413	behind	Found by Jonathan Viquerat in May 2026.
Pentagons in a domino	13	s = 3.88151+	3.915549064	−3.40e-02	-0.877	behind	Found by Bhavithran Ananthan in July 2026.
Pentagons in a domino	14	s = 3.92746+	3.928896236	−1.44e-03	-0.037	behind	Found by Jonathan Viquerat in May 2026.
Pentagons in a domino	15	s = 4.11731+	4.274427732	−1.57e-01	-3.816	behind	Found by Bhavithran Ananthan in July 2026.
Pentagons in a domino	16	s = 4.27934+	4.388397442	−1.09e-01	-2.548	behind	Found by Jonathan Viquerat in May 2026.
Pentagons in a domino	17	s = 4.38233+	4.485243949	−1.03e-01	-2.348	behind	Found by Jonathan Viquerat in September 2026.
Pentagons in a domino	18	s = 4.54032+	4.651376094	−1.11e-01	-2.446	behind	Found by Thomas Greenleaf in June 2026.
Pentagons in a domino	19	s = 4.67483+	4.792826193	−1.18e-01	-2.524	behind	Found by Bhavithran Ananthan in July 2026.
Pentagons in a domino	20	s = 4.79125+	4.920634445	−1.29e-01	-2.700	behind	Found by Thomas Greenleaf in June 2026.
Pentagons in a domino	21	s = 4.87601+	5.118345238	−2.42e-01	-4.970	behind	Found by Jonathan Viquerat in September 2026.
Pentagons in a domino	22	s = 4.93220+	5.166009565	−2.34e-01	-4.740	behind	Found by Thomas Greenleaf in June 2026.
Pentagons in a domino	23	s = 5.01785+	5.024373569	−6.52e-03	-0.130	behind	Found by Jonathan Viquerat in September 2026.
Pentagons in a domino	24	s = 5.07794+	5.440361129	−3.62e-01	-7.137	behind	Found by Jonathan Viquerat in September 2026.
Pentagons in a domino	25	s = 5.22623+	5.232913383	−6.68e-03	-0.128	behind	Found by Jonathan Viquerat in September 2026.
Pentagons in a hexagon	2	s = 1.53879+	1.538841787	−5.18e-05	-0.003	behind
Pentagons in a hexagon	3	s = 1.73240+	1.732454637	−5.46e-05	-0.003	behind
Pentagons in a hexagon	4	s = 1.97666+	1.976689306	−2.93e-05	-0.001	behind	Found by Ethan Riddle in May 2026.
Pentagons in a hexagon	5	s = 2.21822+	2.218267573	−4.76e-05	-0.002	behind	Found by Nicolas Campailla in May 2026.
Pentagons in a hexagon	6	s = 2.32293+	2.322939333	−9.33e-06	-0.000	reproduced	Found by Bhavithran Ananthan in July 2026.
Pentagons in a hexagon	7	s = (2√5–1+√(15–6√5))/2 s = 2.36527+	2.365272305	−4.18e-08	-0.000	reproduced	Found by Nicolas Campailla in May 2026.
Pentagons in a hexagon	8	s = 2.71922+	2.719228626	−8.63e-06	-0.000	reproduced	Found by Bhavithran Ananthan in July 2026.
Pentagons in a hexagon	9	s = 2.86967+	2.921189914	−5.15e-02	-1.795	behind	Found by Nicolas Campailla in May 2026.
Pentagons in a hexagon	10	s = 2.93664+	2.938528126	−1.89e-03	-0.064	behind	Found by Bhavithran Ananthan in July 2026.
Pentagons in a hexagon	11	s = 3.16125+	3.176383439	−1.51e-02	-0.479	behind	Found by Jonathan Viquerat in May 2026.
Pentagons in a hexagon	12	s = 3.21458+	3.220488333	−5.91e-03	-0.184	behind	Found by Jake Loyd in June 2026.
Pentagons in a hexagon	13	s = 3.40902+	3.455629674	−4.66e-02	-1.367	behind	Found by Nicolas Campailla in August 2026.
Pentagons in a hexagon	14	s = 3.46643+	3.469838856	−3.41e-03	-0.098	behind	Found by Jonathan Viquerat in May 2026.
Pentagons in a hexagon	15	s = 3.63499+	3.666247359	−3.13e-02	-0.860	behind	Found by Jake Loyd in June 2026.
Pentagons in a hexagon	16	s = 3.69895+	3.802266412	−1.03e-01	-2.793	behind	Found by Nicolas Campailla in August 2026.
Pentagons in a hexagon	17	s = 3.75774+	3.845510368	−8.78e-02	-2.336	behind	Found by Jonathan Viquerat in May 2026.
Pentagons in a hexagon	18	s = 3.84479+	3.872668630	−2.79e-02	-0.725	behind	Found by Jake Loyd in June 2026.
Pentagons in a hexagon	19	s = 3.88271+	3.971076273	−8.84e-02	-2.276	behind	Found by Jonathan Viquerat in August 2026.
Pentagons in a hexagon	20	s = 4.14048+	4.170694700	−3.02e-02	-0.730	behind	Found by Jake Loyd in June 2026.
Pentagons in a hexagon	21	s = 4.24003+	4.394155309	−1.54e-01	-3.635	behind	Found by Jake Loyd in June 2026.
Pentagons in a hexagon	22	s = 4.32443+	4.329422721	−4.99e-03	-0.115	behind	Found by Jake Loyd in June 2026.
Pentagons in a hexagon	23	s = 4.39703+	4.564554224	−1.68e-01	-3.810	behind	Found by Jake Loyd in June 2026.
Pentagons in a hexagon	24	s = 4.46360+	4.468493804	−4.89e-03	-0.110	behind	Found by Jake Loyd in June 2026.
Pentagons in a hexagon	25	s = 4.57861+	4.590374896	−1.18e-02	-0.257	behind	Found by Jake Loyd in June 2026.
Pentagons in a hexagon	26	s = 4.66031+	4.831126159	−1.71e-01	-3.665	behind	Found by Aristotle Papowitz in July 2026.
Pentagons in a hexagon	27	s = 4.71710+	4.928822799	−2.12e-01	-4.488	behind	Found by Jonathan Viquerat in August 2026.
Pentagons in a hexagon	28	s = 4.84364+	4.851745050	−8.11e-03	-0.167	behind	Found by Jonathan Viquerat in September 2026.
Pentagons in a hexagon	29	s = 4.91003+	5.142652078	−2.33e-01	-4.738	behind	Found by Aristotle Papowitz in July 2026.
Pentagons in a hexagon	30	s = 4.96406+	4.979695985	−1.56e-02	-0.315	behind	Found by Aristotle Papowitz in July 2026.
Pentagons in a hexagon	31	s = 5.09223+	5.353584588	−2.61e-01	-5.132	behind	Found by Jonathan Viquerat in September 2026.
Pentagons in a pentagon	2	s = 2	2.000000001	−8.00e-10	-0.000	reproduced
Pentagons in a pentagon	3	s = √5 = 2.23606+	2.236067978	−8.94e-10	-0.000	reproduced	Found by Jonathan Viquerat in April 2026.
Pentagons in a pentagon	4	s = 2.44719+	2.447213637	−2.36e-05	-0.001	behind	Found by Jonathan Viquerat in April 2026.
Pentagons in a pentagon	5	s = (3+√5)/2 = 2.61803+	2.618034034	−4.49e-08	-0.000	reproduced
Pentagons in a pentagon	6	s = (3+√5)/2 = 2.61803+	2.618033997	−7.92e-09	-0.000	reproduced
Pentagons in a pentagon	7	s = 3.07866+	3.078689381	−2.94e-05	-0.001	behind	Found by Jonathan Viquerat in April 2026.
Pentagons in a pentagon	8	s = 3.33514+	3.335174397	−3.44e-05	-0.001	behind	Found by Jonathan Viquerat in April 2026.
Pentagons in a pentagon	9	s = 3.44956+	3.591143681	−1.42e-01	-4.104	behind	Found by Jonathan Viquerat in April 2026.
Pentagons in a pentagon	10	s = 3.68324+	3.782754750	−9.95e-02	-2.702	behind	Found by Jonathan Viquerat in April 2026.
Pentagons in a pentagon	11	s = 3.79704+	3.949599238	−1.53e-01	-4.018	behind	Found by Jonathan Viquerat in April 2026.
Pentagons in a pentagon	12	s = 3.96926+	4.018778648	−4.95e-02	-1.248	behind	Found by Jonathan Viquerat in April 2026.
Pentagons in a pentagon	13	s = 4.06523+	4.083045409	−1.78e-02	-0.438	behind	Found by Jonathan Viquerat in April 2026.
Pentagons in a pentagon	14	s = 4.21111+	4.413638461	−2.03e-01	-4.809	behind	Found by Grant Mowry in May 2026.
Pentagons in a pentagon	15	s = 2+√5 = 4.23606+	4.535311297	−2.99e-01	-7.064	behind
Pentagons in a pentagon	16	s = 4.41636+	4.794346619	−3.78e-01	-8.559	behind	Found by Jonathan Viquerat in April 2026.
Pentagons in a pentagon	17	s = 4.65536+	4.764750648	−1.09e-01	-2.350	behind	Found by Jonathan Viquerat in August 2026.
Pentagons in a pentagon	18	s = 4.77541+	4.978152073	−2.03e-01	-4.246	behind	Found by Jonathan Viquerat in April 2026.
Pentagons in a pentagon	19	s = 4.95267+	4.956898662	−4.23e-03	-0.085	behind	Found by Bhavithran Ananthan in July 2026.
Pentagons in a pentagon	20	s = 5.03404+	5.369119309	−3.35e-01	-6.656	behind	Found by Jake Loyd in June 2026.
Pentagons in a pentagon	21	s = 5.15638+	5.204611317	−4.82e-02	-0.935	behind	Found by Jake Loyd in June 2026.
Pentagons in a pentagon	22	s = 5.26645+	5.589358256	−3.23e-01	-6.131	behind	Found by Grant Mowry in May 2026.
Pentagons in a pentagon	23	s = 5.34696+	5.730275656	−3.83e-01	-7.169	behind	Found by Jake Loyd in June 2026.
Pentagons in a pentagon	24	s = 5.49109+	5.842309001	−3.51e-01	-6.396	behind	Found by Jake Loyd in June 2026.
Pentagons in a pentagon	25	s = 5.58099+	5.593813556	−1.28e-02	-0.230	behind	Found by Jake Loyd in June 2026.
Pentagons in a pentagon	26	s = 5.67207+	5.922670948	−2.51e-01	-4.418	behind	Found by Jonathan Viquerat in August 2026.
Pentagons in a pentagon	27	s = 5.75528+	6.061087462	−3.06e-01	-5.314	behind	Found by Jonathan Viquerat in August 2026.
Pentagons in a pentagon	28	s = 5.84493+	5.979889677	−1.35e-01	-2.309	behind	Found by Jonathan Viquerat in August 2026.
Pentagons in a pentagon	29	s = 5.91835+	6.341279340	−4.23e-01	-7.146	behind	Found by Jonathan Viquerat in August 2026.
Pentagons in a square	2	s = (1+√5)[√(250+110√5) – 5(1+√5)]/8 s = 2.46345+	2.463451666	−1.45e-08	-0.000	reproduced
Pentagons in a square	3	s = (4+5√5/2)√(5+2√5)–55/4–23√5/4 s = 2.90811+	2.908117286	−1.73e-09	-0.000	reproduced	Found by Jonathan Viquerat in April 2026.
Pentagons in a square	4	s = ((3–√5)√(5–√5)+7√10+√2)/8 s = 3.10252+	3.102525061	−4.94e-08	-0.000	reproduced	Found by Jonathan Viquerat in April 2026.
Pentagons in a square	5	s = 3.54903+	3.549034820	−4.82e-06	-0.000	reproduced	Found by Jonathan Viquerat in April 2026.
Pentagons in a square	6	s = 3.88299+	3.882991496	−1.50e-06	-0.000	reproduced	Found by Haowei Lin in July 2026.
Pentagons in a square	7	s = 4.18037+	4.180370664	−6.64e-07	-0.000	reproduced	Found by Nicolas Campailla in May 2026.
Pentagons in a square	8	s = 4.38190+	4.382209203	−3.09e-04	-0.007	behind	Found by Aristotle Papowitz in July 2026.
Pentagons in a square	9	s = 4.60033+	4.600329612	+3.88e-07	0.000	reproduced	Found by Jonathan Viquerat in April 2026.
Pentagons in a square	10	s = 4.90581+	4.977249750	−7.14e-02	-1.456	behind	Found by Jonathan Viquerat in June 2026.
Pentagons in a square	11	s = 5.11555+	5.170365461	−5.48e-02	-1.072	behind	Found by Jonathan Viquerat in August 2026.
Pentagons in a square	12	s = 5.23221+	5.232214467	−4.47e-06	-0.000	reproduced	Found by Timo Berthold et al in May 2026.
Pentagons in a square	13	s = 5.52102+	5.525524355	−4.50e-03	-0.082	behind	Found by Jake Loyd in June 2026.
Pentagons in a square	14	s = 5.69659+	5.799064180	−1.02e-01	-1.799	behind	Found by Jake Loyd in June 2026.
Pentagons in a square	15	s = 5.90118+	5.979706156	−7.85e-02	-1.331	behind	Found by Jonathan Viquerat in August 2026.
Pentagons in a square	16	s = 6.06452+	6.179132659	−1.15e-01	-1.890	behind	Found by Timo Berthold et al in April 2026.
Pentagons in a square	17	s = 6.23761+	6.302798703	−6.52e-02	-1.045	behind	Found by Jonathan Viquerat in June 2026.
Pentagons in a square	18	s = 6.32565+	6.508455254	−1.83e-01	-2.890	behind	Found by Bhavithran Ananthan in July 2026.
Pentagons in a square	19	s = 6.55781+	6.572081506	−1.43e-02	-0.218	behind	Found by Jake Loyd in June 2026.
Pentagons in a square	20	s = 6.66135+	6.976451811	−3.15e-01	-4.730	behind	Found by Haowei Lin in July 2026.
Pentagons in a square	21	s = 6.85368+	7.064813207	−2.11e-01	-3.081	behind	Found by Jake Loyd in June 2026.
Pentagons in a square	22	s = 7.04445+	7.465578915	−4.21e-01	-5.978	behind	Found by Haowei Lin in July 2026.
Pentagons in a square	23	s = 7.20624+	7.234675610	−2.84e-02	-0.395	behind	Found by Jake Loyd in June 2026.
Pentagons in a square	24	s = 7.33690+	7.624266977	−2.87e-01	-3.917	behind	Found by Jake Loyd in June 2026.
Pentagons in a square	25	s = 7.45360+	7.482682945	−2.91e-02	-0.390	behind	Found by Jake Loyd in June 2026.
Pentagons in a square	26	s = 7.58176+	8.115832817	−5.34e-01	-7.044	behind	Found by Jonathan Viquerat in August 2026.
Pentagons in a square	27	s = 7.67948+	8.181873124	−5.02e-01	-6.542	behind	Found by Jonathan Viquerat in August 2026.
Pentagons in a square	28	s = 7.82010+	8.371779231	−5.52e-01	-7.055	behind	Found by Jonathan Viquerat in August 2026.
Pentagons in a square	29	s = 7.98512+	8.382051971	−3.97e-01	-4.971	behind	Found by Jonathan Viquerat in August 2026.
Pentagons in a square	30	s = 8.10222+	8.712424872	−6.10e-01	-7.531	behind	Found by Jonathan Viquerat in August 2026.
Pentagons in a tan	2	s = 3.52014+	3.520147023	−7.02e-06	-0.000	reproduced
Pentagons in a tan	3	s = 3.97792+	3.977926918	−6.92e-06	-0.000	reproduced
Pentagons in a tan	4	s = 4.63338+	4.633390129	−1.01e-05	-0.000	behind	Found by Jonathan Viquerat in May 2026.
Pentagons in a tan	5	s = 5.16518+	5.165184087	−4.09e-06	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Pentagons in a tan	6	s = 5.48233+	5.482338720	−8.72e-06	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Pentagons in a tan	7	s = 6.03679+	6.072389297	−3.56e-02	-0.590	behind	Found by Jonathan Viquerat in May 2026.
Pentagons in a tan	8	s = 6.30671+	6.342233331	−3.55e-02	-0.563	behind	Found by Jonathan Viquerat in May 2026.
Pentagons in a tan	9	s = 6.69536+	6.730541813	−3.52e-02	-0.525	behind	Found by Jonathan Viquerat in May 2026.
Pentagons in a tan	10	s = 6.98078+	6.986535249	−5.76e-03	-0.082	behind	Found by Jonathan Viquerat in May 2026.
Pentagons in a tan	11	s = 7.34729+	7.356668434	−9.38e-03	-0.128	behind	Found by Jonathan Viquerat in May 2026.
Pentagons in a tan	12	s = 7.54006+	7.730059944	−1.90e-01	-2.520	behind	Found by Jonathan Viquerat in May 2026.
Pentagons in a tan	13	s = 7.82906+	7.952175499	−1.23e-01	-1.573	behind	Found by Jonathan Viquerat in May 2026.
Pentagons in a tan	14	s = 8.16828+	8.177480758	−9.20e-03	-0.113	behind	Found by Bhavithran Ananthan in July 2026.
Pentagons in a tan	15	s = 8.45706+	8.529294504	−7.22e-02	-0.854	behind	Found by Bhavithran Ananthan in July 2026.
Pentagons in a tan	16	s = 8.66023+	8.805006366	−1.45e-01	-1.672	behind	Found by Jonathan Viquerat in May 2026.
Pentagons in a tan	17	s = 8.89679+	8.910664637	−1.39e-02	-0.156	behind	Found by Jonathan Viquerat in September 2026.
Pentagons in a tan	18	s = 9.08713+	9.402519728	−3.15e-01	-3.471	behind	Found by Jonathan Viqueratl in May 2026.
Pentagons in a tan	19	s = 9.38489+	9.959806374	−5.75e-01	-6.126	behind	Found by Thomas Greenleaf in June 2026.
Pentagons in a tan	20	s = 9.61296+	9.660614931	−4.77e-02	-0.496	behind	Found by Bhavithran Ananthan in July 2026.
Pentagons in a tan	21	s = 9.79121+	10.557804803	−7.67e-01	-7.829	behind	Found by Jonathan Viquerat in September 2026.
Pentagons in a tan	22	s = 10.01063+	10.558520468	−5.48e-01	-5.473	behind	Found by Jonathan Viquerat in September 2026.
Pentagons in a tan	23	s = 10.24859+	10.868894011	−6.20e-01	-6.053	behind	Found by Jonathan Viquerat in September 2026.
Pentagons in a tan	24	s = 10.45171+	11.218786936	−7.67e-01	-7.339	behind	Found by Jonathan Viquerat in September 2026.
Pentagons in a tan	25	s = 10.63197+	11.422741332	−7.91e-01	-7.438	behind	Found by Jonathan Viquerat in September 2026.
Pentagons in a triangle	3	s = √((75+33√5)/8) – (3–√5)/4 = 4.12164+	4.121647331	−1.75e-09	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Pentagons in a triangle	4	s = 5.21983+	5.219832877	−2.88e-06	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Pentagons in a triangle	5	s = 5.55809+	5.558094107	−4.11e-06	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Pentagons in a triangle	6	s = 5.63540+	5.635408351	−8.35e-06	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Pentagons in a triangle	7	s = 6.50034+	6.500348494	−8.49e-06	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Pentagons in a triangle	8	s = 6.81133+	6.811339286	−9.29e-06	-0.000	reproduced	Found by Bhavithran Ananthan in July 2026.
Pentagons in a triangle	9	s = 7.08969+	7.133094454	−4.34e-02	-0.612	behind	Found by Bhavithran Ananthan in July 2026.
Pentagons in a triangle	10	s = 7.17235+	7.172357541	−7.54e-06	-0.000	reproduced	Found by Bhavithran Ananthan in July 2026.
Pentagons in a triangle	11	s = 7.93748+	7.959054849	−2.16e-02	-0.272	behind	Found by Jonathan Viquerat in May 2026.
Pentagons in a triangle	12	s = 8.19117+	8.474290825	−2.83e-01	-3.456	behind	Found by Jonathan Viquerat in May 2026.
Pentagons in a triangle	13	s = 8.37807+	8.380000536	−1.93e-03	-0.023	behind	Found by Jonathan Viquerat in May 2026.
Pentagons in a triangle	14	s = 8.58917+	8.642812245	−5.36e-02	-0.625	behind	Found by Haowei Lin in July 2026.
Pentagons in a triangle	15	s = 8.69161+	8.712795504	−2.12e-02	-0.244	behind	Found by Jake Loyd in June 2026.
Pentagons in a triangle	16	s = 9.29700+	9.438377123	−1.41e-01	-1.521	behind	Found by Haowei Lin in July 2026.
Pentagons in a triangle	17	s = 9.57797+	9.848759925	−2.71e-01	-2.827	behind	Found by Jake Loyd in June 2026.
Pentagons in a triangle	18	s = 9.78077+	9.798076145	−1.73e-02	-0.177	behind	Found by Jake Loyd in June 2026.
Pentagons in a triangle	19	s = 9.92567+	10.272642989	−3.47e-01	-3.496	behind	Found by Haowei Lin in July 2026.
Pentagons in a triangle	20	s = 10.09879+	10.131722981	−3.29e-02	-0.326	behind	Found by Jake Loyd in June 2026.
Pentagons in a triangle	21	s = 10.17148+	10.421273096	−2.50e-01	-2.456	behind	Found by Bhavithran Ananthan in July 2026.
Pentagons in a triangle	22	s = 10.75818+	10.802112923	−4.39e-02	-0.408	behind	Found by Jake Loyd in June 2026.
Pentagons in a triangle	23	s = 10.99100+	11.079288515	−8.83e-02	-0.803	behind	Found by Jake Loyd in June 2026.
Pentagons in a triangle	24	s = 11.17511+	11.538972758	−3.64e-01	-3.256	behind	Found by Jake Loyd in June 2026.
Pentagons in a triangle	25	s = 11.32392+	11.868875419	−5.45e-01	-4.812	behind	Found by Jake Loyd in June 2026.
Pentagons in a triangle	26	s = 11.45549+	11.833966172	−3.78e-01	-3.304	behind	Found by Aristotle Papowitz in July 2026.
Pentagons in a triangle	27	s = 11.59873+	11.944451168	−3.46e-01	-2.981	behind	Found by Jonathan Viquerat in August 2026.
Pentagons in a triangle	28	s = 11.69225+	11.738971435	−4.67e-02	-0.400	behind	Found by Jonathan Viquerat in August 2026.
Pentagons in a triangle	29	s = 12.18197+	12.796734826	−6.15e-01	-5.047	behind	Found by Bhavithran Ananthan in July 2026.
Pentagons in a triangle	30	s = 12.38240+	12.942428416	−5.60e-01	-4.523	behind	Found by Yue Huang in August 2026.
Pentagons in a triangle	31	s = 12.58207+	12.654142762	−7.21e-02	-0.573	behind	Found by Jonathan Viquerat in August 2026.
Pentagons in a triangle	32	s = 12.70492+	13.130599833	−4.26e-01	-3.351	behind	Found by Yue Huang in August 2026.
Pentagons in a triangle	33	s = 12.85985+	12.963576055	−1.04e-01	-0.807	behind	Found by Yue Huang in August 2026.
Pentagons in a triangle	34	s = 12.97563+	13.064453441	−8.88e-02	-0.685	behind	Found by Yue Huang in August 2026.
Pentagons in a triangle	35	s = 13.10941+	13.170252389	−6.08e-02	-0.464	behind	Found by Bhavithran Ananthan in July 2026.
Pentagons in a triangle	36	s = 13.17841++	13.230130086	−5.17e-02	-0.392	behind	Found by Yue Huang in August 2026.
Pentagons in a triangle	37	s = 13.63430+	13.741194009	−1.07e-01	-0.784	behind	Found by Yue Huang in August 2026.
Pentagons in a triangle	38	s = 13.82313+	13.929125129	−1.06e-01	-0.767	behind	Found by Yue Huang in August 2026.
Pentagons in a triangle	39	s = 13.97521+	14.116620361	−1.41e-01	-1.012	behind	Found by Yue Huang in August 2026.
Pentagons in a triangle	40	s = 14.13674+	14.246617265	−1.10e-01	-0.777	behind	Found by Yue Huang in August 2026.
Pentagons in an L	2	s = √(5+2√5)/2 = 1.53884+	1.538841769	−6.16e-10	-0.000	reproduced
Pentagons in an L	3	s = 1.55425+	1.554247558	+2.44e-06	0.000	reproduced	Found by Jonathan Viquerat in June 2026.
Pentagons in an L	4	s = 1.96918+	1.969181031	−1.03e-06	-0.000	reproduced	Found by Jonathan Viquerat in June 2026.
Pentagons in an L	5	s = 2.12433+	2.124337268	−7.27e-06	-0.000	reproduced	Found by Jonathan Viquerat in June 2026.
Pentagons in an L	6	s = 2.30512+	2.305121415	−1.42e-06	-0.000	reproduced	Found by Jonathan Viquerat in June 2026.
Pentagons in an L	7	s = 2.41732+	2.512760188	−9.54e-02	-3.948	behind	Found by Jonathan Viquerat in June 2026.
Pentagons in an L	8	s = 2.54164+	2.579041095	−3.74e-02	-1.472	behind	Found by Jonathan Viquerat in June 2026.
Pentagons in an L	9	s = 2.67860+	2.681223410	−2.62e-03	-0.098	behind	Found by Jonathan Viquerat in June 2026.
Pentagons in an L	10	s = 2.80245+	2.869649395	−6.72e-02	-2.398	behind
Pentagons in an L	11	s = 2.94662+	2.949422497	−2.80e-03	-0.095	behind	Found by Jonathan Viquerat in June 2026.
Pentagons in an L	12	s = 3.07460+	3.089182762	−1.46e-02	-0.474	behind	Found by Jonathan Viquerat in June 2026.
Pentagons in an L	13	s = 3.22359+	3.255494293	−3.19e-02	-0.990	behind	Found by Jonathan Viquerat in September 2026.
Pentagons in an L	14	s = 3.35014+	3.385781451	−3.56e-02	-1.064	behind	Found by Jonathan Viquerat in June 2026.
Pentagons in an L	15	s = 3.46668+	3.619897935	−1.53e-01	-4.420	behind	Found by Jonathan Viquerat in September 2026.
Pentagons in an L	16	s = 3.55643+	3.614731007	−5.83e-02	-1.639	behind	Found by Jonathan Viquerat in September 2026.
Pentagons in an L	17	s = 3.61458+	3.713293496	−9.87e-02	-2.731	behind	Found by Jonathan Viquerat in September 2026.
Pentagons in an L	18	s = 3.73452+	3.878828293	−1.44e-01	-3.864	behind	Found by Jonathan Viquerat in September 2026.
Pentagons in an L	19	s = 3.81113+	3.898183102	−8.71e-02	-2.284	behind	Found by Jonathan Viquerat in June 2026.
Pentagons in an L	20	s = 3.86901+	4.064649032	−1.96e-01	-5.057	behind	Found by Jonathan Viquerat in June 2026.
Pentagons in an L	21	s = 3.95816+	4.274526969	−3.16e-01	-7.993	behind	Found by Jonathan Viquerat in September 2026.
Pentagons in an L	22	s = 4.02153+	4.366930635	−3.45e-01	-8.589	behind	Found by Jonathan Viquerat in September 2026.
Pentagons in an L	23	s = 4.13155+	4.437208953	−3.06e-01	-7.398	behind	Found by Jonathan Viquerat in September 2026.
Pentagons in an L	24	s = 4.22847+	4.505371177	−2.77e-01	-6.548	behind	Found by Jonathan Viquerat in September 2026.
Pentagons in an octagon	2	s = 1.17774+	1.177778520	−3.85e-05	-0.003	behind
Pentagons in an octagon	3	s = 1.28954+	1.289544405	−4.40e-06	-0.000	reproduced	Found by Nicolas Campailla in May 2026.
Pentagons in an octagon	4	s = 1.42986+	1.429889753	−2.98e-05	-0.002	behind
Pentagons in an octagon	5	s = 1.61756+	1.617560353	−3.53e-07	-0.000	reproduced	Found by Nicolas Campailla in May 2026.
Pentagons in an octagon	6	s = 1.78003+	1.788113221	−8.08e-03	-0.454	behind	Found by Nicolas Campailla in May 2026.
Pentagons in an octagon	7	s = 1.82343+	1.823439320	−9.32e-06	-0.001	reproduced	Found by Timo Berthold et al in May 2026.
Pentagons in an octagon	8	s = 1.95989+	1.959891558	−1.56e-06	-0.000	reproduced	Found by Nicolas Campailla in May 2026.
Pentagons in an octagon	9	s = (√5+√(5+√5))/√(10–2√5) s = 2.09517+	2.095179356	−3.44e-08	-0.000	reproduced	Found by Nicolas Campailla in May 2026.
Pentagons in an octagon	10	s = 2.21135+	2.235582981	−2.42e-02	-1.096	behind	Found by Timo Berthold et al in May 2026.
Pentagons in an octagon	11	s = 2.33111+	2.335338641	−4.23e-03	-0.181	behind	Found by Timo Berthold et al in May 2026.
Pentagons in an octagon	12	s = 2.39327+	2.395332140	−2.06e-03	-0.086	behind	Found by Timo Berthold et al in May 2026.
Pentagons in an octagon	13	s = 2.49776+	2.538265310	−4.05e-02	-1.622	behind	Found by Jake Loyd in June 2026.
Pentagons in an octagon	14	s = 2.56564+	2.612459706	−4.68e-02	-1.825	behind	Found by Jake Loyd in June 2026.
Pentagons in an octagon	15	s = 2.68123+	2.689060999	−7.83e-03	-0.292	behind	Found by Timo Berthold et al in May 2026.
Pentagons in an octagon	16	s = 2.75249+	2.757023771	−4.53e-03	-0.165	behind	Found by Jake Loyd in June 2026.
Pentagons in an octagon	17	s = 2.81043+	2.836431575	−2.60e-02	-0.925	behind	Found by Jake Loyd in June 2026.
Pentagons in an octagon	18	s = 2.89321+	2.940975509	−4.78e-02	-1.651	behind	Found by Jake Loyd in June 2026.
Pentagons in an octagon	19	s = 2.95527+	3.064955961	−1.10e-01	-3.712	behind	Found by Jake Loyd in June 2026.
Pentagons in an octagon	20	s = 3.04679+	3.233707767	−1.87e-01	-6.135	behind	Found by Jake Loyd in June 2026.
Pentagons in an octagon	21	s = 3.11874+	3.131416581	−1.27e-02	-0.406	behind	Found by Jake Loyd in June 2026.
Pentagons in an octagon	22	s = 3.19144+	3.298788548	−1.07e-01	-3.364	behind	Found by Jake Loyd in June 2026.
Pentagons in an octagon	23	s = 3.25129+	3.261623304	−1.03e-02	-0.318	behind	Found by Jake Loyd in June 2026.
Pentagons in an octagon	24	s = 3.28718+	3.414822051	−1.28e-01	-3.883	behind	Found by Jake Loyd in June 2026.
Pentagons in an octagon	25	s = 3.36617+	3.561583244	−1.95e-01	-5.805	behind	Found by Jake Loyd in June 2026.
Pentagons in an octagon	26	s = 3.42775+	3.455472117	−2.77e-02	-0.809	behind	Found by Jake Loyd in June 2026.
Pentagons in an octagon	27	s = 3.49942+	3.679609860	−1.80e-01	-5.149	behind	Found by Bhavithran Ananthan in July 2026.
Pentagons in an octagon	28	s = 3.56402+	3.581872376	−1.79e-02	-0.501	behind	Found by Bhavithran Ananthan in July 2026.
Pentagons in an octagon	29	s = 3.61848+	3.830801164	−2.12e-01	-5.868	behind	Found by Bhavithran Ananthan in July 2026.
Pentagons in an octagon	30	s = 3.66678+	3.681375358	−1.46e-02	-0.398	behind	Found by Aristotle Papowitz in July 2026.
Pentagons in an octagon	31	s = 3.74379+	3.771373700	−2.76e-02	-0.737	behind	Found by Bhavithran Ananthan in July 2026.
Squares in a circle	3	r = 5 √17 / 16 = 1.288+	1.288470527	−1.89e-08	-0.000	reproduced	Found by Erich Friedman in 1997.
Squares in a circle	5	r = √10 / 2 = 1.581+	1.581138853	−2.24e-08	-0.000	reproduced	Found by Erich Friedman in 1997.
Squares in a circle	6	r = 1.688+*	1.688542998	−5.43e-04	-0.032	reproduced	Found by Erich Friedman in 1997.
Squares in a circle	7	r = √13 / 2 = 1.802+	1.802775669	−3.12e-08	-0.000	reproduced	Found by Erich Friedman in 1997.
Squares in a circle	8	r = 1.978+*	1.978770990	−7.71e-04	-0.039	reproduced	Found by David W. Cantrell in March 2002.
Squares in a circle	9	r = √1105 / 16 = 2.077+	2.079104956	−1.51e-03	-0.073	behind	Found by Erich Friedman in 1997.
Squares in a circle	10	r = 3 √2 / 2 = 2.121+	2.208294872	−8.70e-02	-4.101	behind	Found by Erich Friedman in 1997.
Squares in a circle	11	r = 2.21386+	2.243802098	−2.99e-02	-1.352	behind	Found by Milan Kovacic in May 2006.
Squares in a circle	12	r = √5 = 2.236+	2.236690869	−6.23e-04	-0.028	reproduced	Found by Erich Friedman in 1997.
Squares in a circle	13	r = 2.3607+	2.362340660	−1.64e-03	-0.069	behind	Found by David W. Cantrell in November 2010.
Squares in a circle	14	r = 2.5	2.508088662	−8.09e-03	-0.324	reproduced	Found by Erich Friedman in 1997.
Squares in a circle	15	r = 2.533+	2.674964623	−1.42e-01	-5.605	behind	Found by by David W. Cantrell in June 2002.
Squares in a circle	16	r = √11009 / 40 = 2.623+	2.698932546	−7.58e-02	-2.891	behind	Found by Erich Friedman in 1997.
Squares in a circle	17	r = 2.67687+	2.851896469	−1.75e-01	-6.538	behind	Found by Milan Kovacic in May 2026.
Squares in a circle	18	r = √481 / 8 = 2.741+	2.834176924	−9.27e-02	-3.382	behind	Found by David W. Cantrell in March 2002.
Squares in a circle	19	r = 2.80150+	2.921035406	−1.20e-01	-4.267	behind	Found by Milan Kovacic in May 2026.
Squares in a circle	20	r = 2.893+	2.937398150	−4.44e-02	-1.535	behind	Found by David W. Cantrell in June 2002.
Squares in a circle	21	r = √34 / 2 = 2.915+	2.933307701	−1.78e-02	-0.612	behind	Found by Erich Friedman in 1997.
Squares in a circle	22	r = 3.03239+	3.050244380	−1.79e-02	-0.589	behind	Found by Haowei Lin in July 2026.
Squares in a circle	23	r = 3.06738+	3.074670953	−7.29e-03	-0.238	behind	Found by Milan Kovacic in May 2026.
Squares in a circle	24	r = 3.10940+	3.164020371	−5.46e-02	-1.757	behind	Found by Milan Kovacic in May 2026.
Squares in a circle	25	r = 3.17450+	3.197204146	−2.27e-02	-0.715	behind	Found by Haowei Lin in July 2026.
Squares in a circle	26	r = √41 / 2 = 3.201+	3.361567769	−1.60e-01	-4.999	behind	Found by Erich Friedman in 1997.
Squares in a circle	27	r = 3.26050+	3.262403219	−1.90e-03	-0.058	behind	Found by Milan Kovacic in May 2026.
Squares in a circle	28	r = 3.33147+	3.349314484	−1.78e-02	-0.536	behind	Found by Milan Kovacic in May 2026.
Squares in a circle	29	r = 3.39309+	3.548800615	−1.56e-01	-4.589	behind	Found by Milan Kovacic in May 2026.
Squares in a circle	30	r = 3.45962+	3.552473988	−9.29e-02	-2.684	behind	Found by Milan Kovacic in May 2026.
Squares in a circle	31	r = 3.52771+	3.628973122	−1.01e-01	-2.871	behind	Found by Haowei Lin in July 2026.
Squares in a circle	32	r = 3.57340+	3.618317444	−4.49e-02	-1.257	behind	Found by Milan Kovacic in May 2026.
Squares in a circle	33	r = 3.60010+	3.622540437	−2.24e-02	-0.623	behind	Found by Haowei Lin in July 2026.
Squares in a circle	34	r = 3.62911+	3.775070338	−1.46e-01	-4.022	behind	Found by Jonathan Viquerat in August 2026.
Squares in a circle	35	r = √53 / 2 = 3.640+	3.730446391	−9.04e-02	-2.483	behind	Found by David Eppstein in March 2002.
Squares in a domino	2	s = 1	1.000000000	−4.00e-10	-0.000	reproduced
Squares in a domino	3	s = 3/2 = 1.5	1.500000017	−1.69e-08	-0.000	reproduced
Squares in a domino	4	s = 1.930+	1.930283341	−2.83e-04	-0.015	reproduced	Found by Evert Stenlund in June 2010.
Squares in a domino	5	s = 2	2.000000001	−8.00e-10	-0.000	reproduced
Squares in a domino	6	s = 2	2.000000001	−8.00e-10	-0.000	reproduced
Squares in a domino	7	s = 2	2.000000001	−8.00e-10	-0.000	reproduced
Squares in a domino	8	s = 2	2.000000001	−8.95e-10	-0.000	reproduced
Squares in a domino	9	s = 2 + √2/3 = 2.471+	2.471404565	−4.42e-08	-0.000	reproduced	Found by Evert Stenlund in June 2010.
Squares in a domino	10	s = 5/2 = 2.5	2.500000340	−3.40e-07	-0.000	reproduced
Squares in a domino	11	s = 2.779+	2.845948096	−6.69e-02	-2.409	behind	Found by Evert Stenlund in June 2010.
Squares in a domino	12	s = 6 (1 + √2) / 5 = 2.897+	2.943862560	−4.68e-02	-1.616	behind	Found by Maurizio Morandi in June 2010.
Squares in a domino	13	s = 2.976+	3.000012683	−2.40e-02	-0.807	behind	Found by David W. Cantrell in July 2012.
Squares in a domino	14	s = 3	3.000004058	−4.06e-06	-0.000	behind
Squares in a domino	15	s = 3	3.000000055	−5.46e-08	-0.000	reproduced
Squares in a domino	16	s = 3	3.007466940	−7.47e-03	-0.249	behind
Squares in a domino	17	s = 3	3.000021618	−2.16e-05	-0.001	behind
Squares in a domino	18	s = 3	3.053333806	−5.33e-02	-1.778	behind
Squares in a domino	19	s = 3 + 1/√5 = 3.447+	3.504699774	−5.75e-02	-1.668	behind	Found by Maurizio Morandi in June 2010.
Squares in a domino	20	s = 7/2 = 3.5	3.506880725	−6.88e-03	-0.197	reproduced
Squares in a domino	21	s = 7/2 = 3.5	3.506959679	−6.96e-03	-0.199	reproduced
Squares in a domino	22	s = 3.745+	3.805191378	−6.02e-02	-1.607	behind	Found by David W. Cantrell in July 2012.
Squares in a domino	23	s = 3.83525+	3.910560051	−7.53e-02	-1.964	behind	Found by Thomas Greenleaf in June 2026.
Squares in a domino	24	s = 3.88184+	4.000578016	−1.19e-01	-3.059	behind	Found by Aapo Lipponen in July 2026.
Squares in a domino	25	s = 3.939+	4.002666377	−6.37e-02	-1.616	behind	Found by David W. Cantrell in August 2012.
Squares in a domino	26	s = 3.98019+	4.019494300	−3.93e-02	-0.987	behind	Found by Aapo Lipponen in July 2026.
Squares in a domino	27	s = 4	4.016261631	−1.63e-02	-0.407	behind
Squares in a domino	28	s = 4	4.004711863	−4.71e-03	-0.118	behind
Squares in a domino	29	s = 4	4.023727153	−2.37e-02	-0.593	behind
Squares in a domino	30	s = 4	4.048340589	−4.83e-02	-1.209	behind
Squares in a domino	31	s = 4	4.039337974	−3.93e-02	-0.983	behind
Squares in a domino	32	s = 4	4.041595169	−4.16e-02	-1.040	behind
Squares in a domino	33	s = 3 + √2 = 4.414+	4.506072614	−9.19e-02	-2.081	behind	Found by Maurizio Morandi in July 2012.
Squares in a domino	34	s = 4 + √2/3 = 4.471+	4.500855727	−2.95e-02	-0.659	behind	Found by David W. Cantrell in July 2012.
Squares in a domino	35	s = 9/2 = 4.5	4.501648003	−1.65e-03	-0.037	reproduced
Squares in a domino	36	s = 9/2 = 4.5	4.502418193	−2.42e-03	-0.054	reproduced
Squares in a domino	37	s = 4.71758+	4.816440323	−9.89e-02	-2.096	behind	Found by Aapo Lipponen in July 2026.
Squares in a domino	38	s = 4.79816+	4.952417596	−1.54e-01	-3.215	behind
Squares in a domino	39	s = 4.83693+	4.953563013	−1.17e-01	-2.411	behind	Found by Aapo Lipponen in July 2026.
Squares in a domino	40	s = 4.895+	4.987389614	−9.24e-02	-1.887	behind	Found by Sigvart Brendberg in June 2023.
Squares in a domino	41	s = 4.927+	5.001019688	−7.40e-02	-1.502	behind	Found by Sigvart Brendberg in June 2023.
Squares in a domino	42	s = 4.96862+	5.001211664	−3.26e-02	-0.656	behind	Found by Aapo Lipponen in July 2026.
Squares in a domino	43	s = 5	5.004886610	−4.89e-03	-0.098	behind
Squares in a domino	44	s = 5	5.006809839	−6.81e-03	-0.136	behind
Squares in a domino	45	s = 5	5.002525087	−2.53e-03	-0.051	behind
Squares in a domino	46	s = 5	5.037433540	−3.74e-02	-0.749	behind
Squares in a domino	47	s = 5	5.005194946	−5.19e-03	-0.104	behind
Squares in a domino	48	s = 5	5.052985839	−5.30e-02	-1.060	behind
Squares in a domino	49	s = 5	5.003600396	−3.60e-03	-0.072	behind
Squares in a domino	50	s = 5	5.004550937	−4.55e-03	-0.091	behind
Squares in a hexagon	2	s = 2/√3 = 1.15470+	1.154700539	−4.62e-10	-0.000	reproduced
Squares in a hexagon	3	s = (1+√3)/2 = 1.36602+	1.366025431	−2.72e-08	-0.000	reproduced	Found by Maurizio Morandi in March 2026.
Squares in a hexagon	4	s = 2/3^(1/4) = 1.51967+	1.519671396	−2.47e-08	-0.000	reproduced	Found by Maurizio Morandi in March 2026.
Squares in a hexagon	5	s = √3 = 1.73205+	1.732053054	−2.25e-06	-0.000	reproduced
Squares in a hexagon	6	s = 1.821+	1.839593818	−1.86e-02	-1.021	behind	Found by Maurizio Morandi in March 2026.
Squares in a hexagon	7	s = (√2)3^(1/4) = 1.86120+	1.863316067	−2.11e-03	-0.113	behind	Found by Maurizio Morandi in March 2026.
Squares in a hexagon	8	s = 2.15378+	2.154700883	−9.21e-04	-0.043	behind	Found by Ian Watson in April 2026.
Squares in a hexagon	9	s = 1/2+√3 = 2.23205+	2.273624338	−4.16e-02	-1.863	behind	Found by Jonathan Viquerat in April 2026.
Squares in a hexagon	10	s = 4/√3 = 2.30940+	2.341434785	−3.20e-02	-1.387	behind
Squares in a hexagon	11	s = 2.40944+	2.415429026	−5.99e-03	-0.249	behind	Found by Jonathan Viquerat in April 2026.
Squares in a hexagon	12	s = 1+5√3/6 = 2.44337+	2.491391926	−4.80e-02	-1.965	behind	Found by Maurizio Morandi in March 2026.
Squares in a hexagon	13	s = 2.572+	2.612174538	−4.02e-02	-1.562	behind	Found by Maurizio Morandi in April 2026.
Squares in a hexagon	14	s = 2.62126+	2.720280630	−9.90e-02	-3.778	behind	Found by Jonathan Viquerat in April 2026.
Squares in a hexagon	15	s = 2.75364+	2.798884748	−4.52e-02	-1.643	behind	Found by Grant Mowry in May 2026.
Squares in a hexagon	16	s = 2.82002+	2.822293530	−2.27e-03	-0.081	behind	Found by Spencer Leach in May 2026.
Squares in a hexagon	17	s = 2.87264+	2.945932570	−7.33e-02	-2.551	behind	Found by Jake Loyd in May 2026.
Squares in a hexagon	18	s = 2.92104+	2.926935777	−5.90e-03	-0.202	behind	Found by Haowei Lin in July 2026.
Squares in a hexagon	19	s = 2.93508+	3.105415123	−1.70e-01	-5.803	behind	Found by Haowei Lin in July 2026.
Squares in a hexagon	20	s = 3.16122+	3.185909144	−2.47e-02	-0.781	behind	Found by Leo Strijbos in August 2026.
Squares in a hexagon	21	s = (23+11√3)/13 = 3.23481+	3.272925862	−3.81e-02	-1.178	behind	Found by Spencer Leach in May 2026.
Squares in a hexagon	22	s = 3.31432+	3.332971092	−1.87e-02	-0.563	behind	Found by Jake Loyd in June 2026.
Squares in a hexagon	23	s = 3.36407+	3.468317961	−1.04e-01	-3.099	behind	Found by Jake Loyd in June 2026.
Squares in a hexagon	24	s = 3.40286+	3.434238926	−3.14e-02	-0.922	behind	Found by Thomas Greenleaf in June 2026.
Squares in a hexagon	25	s = 2√3 = 3.46410+	3.626214420	−1.62e-01	-4.680	behind
Squares in a hexagon	26	s = 3.49276+	3.546696498	−5.39e-02	-1.544	behind	Found by Jake Loyd in June 2026.
Squares in a hexagon	27	s = (9+7√3)/6 = 3.52072+	3.578408745	−5.77e-02	-1.638	behind	Found by Erich Friedman in April 2026.
Squares in a hexagon	28	s = 3.61976+	3.744904643	−1.25e-01	-3.457	behind	Found by Leo Strijbos in August 2026.
Squares in a hexagon	29	s = 3.66437+	3.833321505	−1.69e-01	-4.611	behind	Found by Ian Watson in April 2026.
Squares in a hexagon	30	s = 3.69552+	3.940992365	−2.45e-01	-6.642	behind	Found by Aristotle Papowitz in July 2026.
Squares in a hexagon	31	s = 3.78143+	3.808666109	−2.72e-02	-0.720	behind	Found by Jake Loyd in June 2026.
Squares in a hexagon	32	s = 3.84140+	4.051050663	−2.10e-01	-5.458	behind	Found by Jake Loyd in June 2026.
Squares in a hexagon	33	s = 3.86634+	3.966166152	−9.98e-02	-2.582	behind	Found by Jake Loyd in June 2026.
Squares in a hexagon	34	s = 3.91853+	4.043168726	−1.25e-01	-3.181	behind	Found by Jake Loyd in June 2026.
Squares in a hexagon	35	s = 3.98201+	4.048565765	−6.66e-02	-1.671	behind	Found by Jake Loyd in June 2026.
Squares in a hexagon	36	s = 4.02042+	4.042818709	−2.24e-02	-0.557	behind	Found by Jake Loyd in June 2026.
Squares in a hexagon	37	s = 7/√3 = 4.04145+	4.088343479	−4.69e-02	-1.160	behind
Squares in a hexagon	38	s = 4.18035+	4.209068140	−2.87e-02	-0.687	behind	Found by Leo Strijbos in August 2026.
Squares in a hexagon	39	s = 4.24512+	4.298510400	−5.34e-02	-1.258	behind	Found by Jake Loyd in June 2026.
Squares in a hexagon	40	s = 4.30171+	4.352847644	−5.11e-02	-1.189	behind	Found by Aristotle Papowitz in July 2026.
Squares in a pentagon	2	s = 4√(1–2/√5)+√5–2 s = 1.535+	1.535746779	−1.68e-08	-0.000	reproduced	Found by Erich Friedman in March 2012.
Squares in a pentagon	3	s = 1.695+	1.695619534	−6.20e-04	-0.037	reproduced	Found by David W. Cantrell in July 2012.
Squares in a pentagon	4	s = 1.861+	1.861668600	−6.69e-04	-0.036	reproduced	Found by Maurizio Morandi in July 2012.
Squares in a pentagon	5	s = 1 + cos(18°) s = 1.951+	1.961492731	−1.05e-02	-0.538	behind	Found by Erich Friedman in March 2012.
Squares in a pentagon	6	s = 6√(1–2/√5)+√5–2 s = 2.185+	2.185586185	−2.99e-08	-0.000	reproduced	Found by Erich Friedman in March 2012.
Squares in a pentagon	7	s = 6√(1–2/√5)+2√5–4 s = 2.421+	2.439120211	−1.75e-02	-0.721	behind	Found by Erich Friedman in July 2012.
Squares in a pentagon	8	s = 2.565+	2.575452180	−1.05e-02	-0.407	behind	Found by David W. Cantrell in July 2012.
Squares in a pentagon	9	s = 2.693+	2.705412398	−1.24e-02	-0.461	behind	Found by Timo Berthold et al in January 2026.
Squares in a pentagon	10	s = 2.793+	2.796366316	−3.37e-03	-0.121	behind	Found by Timo Berthold et al in January 2026.
Squares in a pentagon	11	s = 2.890+	2.894847645	−4.85e-03	-0.168	behind	Found by Timo Berthold et al in January 2026.
Squares in a pentagon	12	s = 2.969+	2.988831874	−1.98e-02	-0.668	behind	Found by Timo Berthold et al in January 2026.
Squares in a pentagon	13	s = 3.12074+	3.260925160	−1.40e-01	-4.492	behind	Found by Jake Loyd in June 2026.
Squares in a pentagon	14	s = 3.187+	3.238140851	−5.11e-02	-1.605	behind	Found by David W. Cantrell in July 2012.
Squares in a pentagon	15	s = (√(125–38√5)+8–2√5)/3 s = 3.284+	3.323328356	−3.84e-02	-1.170	behind	Found by David W. Cantrell in July 2012.
Squares in a pentagon	16	s = 3.47851+	3.487260725	−8.75e-03	-0.252	behind	Found by Jonathan Viquerat in May 2026.
Squares in a pentagon	17	s = 3.541+	3.551622973	−1.06e-02	-0.300	behind	Found by Ignacio Vallejo in March 2026.
Squares in a pentagon	18	s = 3.62598+	3.798832169	−1.73e-01	-4.767	behind	Found by Haowei Lin in July 2026.
Squares in a pentagon	19	s = 3.70918+	3.746958133	−3.78e-02	-1.019	behind	Found by Jake Loyd in June 2026.
Squares in a pentagon	20	s = 3.79775+	4.003692666	−2.06e-01	-5.423	behind	Found by Jake Loyd in June 2026.
Squares in a pentagon	21	s = 3.86365+	4.108757032	−2.45e-01	-6.344	behind	Found by Jake Loyd in June 2026.
Squares in a pentagon	22	s = 3.93347+	3.953242830	−1.98e-02	-0.503	behind	Found by Jake Loyd in June 2026.
Squares in a pentagon	23	s = 4.00109+	4.261907893	−2.61e-01	-6.519	behind	Found by Jake Loyd in June 2026.
Squares in a pentagon	24	s = 4.10103+	4.269012680	−1.68e-01	-4.096	behind	Found by Jake Loyd in June 2026.
Squares in a pentagon	25	s = 4.16727+	4.435230459	−2.68e-01	-6.430	behind	Found by Jake Loyd in June 2026.
Squares in a pentagon	26	s = 4.22150+	4.517877255	−2.96e-01	-7.021	behind	Found by Jake Loyd in June 2026.
Squares in a pentagon	27	s = 4.34851+	4.530329757	−1.82e-01	-4.181	behind	Found by Jake Loyd in June 2026.
Squares in a pentagon	28	s = 4.41576+	4.492800662	−7.70e-02	-1.745	behind	Found by Jake Loyd in June 2026.
Squares in a pentagon	29	s = 4.49879+	4.547264797	−4.85e-02	-1.078	behind	Found by Jake Loyd in June 2026.
Squares in a pentagon	30	s = 4.54753+	4.801140634	−2.54e-01	-5.577	behind	Found by Jake Loyd in June 2026.
Squares in a pentagon	31	s = 4.62404+	4.795992228	−1.72e-01	-3.719	behind	Found by Jake Loyd in June 2026.
Squares in a pentagon	32	s = 4.70000+	4.797175656	−9.72e-02	-2.068	behind	Found by Jake Loyd in June 2026.
Squares in a pentagon	33	s = 4.75331+	5.013852295	−2.61e-01	-5.481	behind	Found by Jake Loyd in June 2026.
Squares in a pentagon	34	s = 4.81345+	4.949130031	−1.36e-01	-2.819	behind	Found by Jake Loyd in June 2026.
Squares in a pentagon	35	s = 4.86283+	5.104013179	−2.41e-01	-4.960	behind	Found by Jake Loyd in June 2026.
Squares in a pentagon	36	s = 4.93131+	5.073658317	−1.42e-01	-2.887	behind	Found by Jake Loyd in June 2026.
Squares in a pentagon	37	s = 4.97801+	5.277323000	−2.99e-01	-6.013	behind	Found by Jake Loyd in June 2026.
Squares in a pentagon	38	s = 5.04838+	5.354653659	−3.06e-01	-6.067	behind	Found by Jake Loyd in June 2026.
Squares in a pentagon	39	s = 5.13653+	5.264976421	−1.28e-01	-2.501	behind	Found by Jake Loyd in June 2026.
Squares in a pentagon	40	s = 5.16849+	5.333307992	−1.65e-01	-3.189	behind	Found by Jake Loyd in June 2026.
Squares in a tan	2	s = 2√2 = 2.828+	2.828427126	−1.13e-09	-0.000	reproduced
Squares in a tan	3	s = 3	3.000000001	−1.20e-09	-0.000	reproduced
Squares in a tan	4	s = 5 / √2 = 3.535	3.535533907	−1.41e-09	-0.000	reproduced	Found by Erich Friedman in March 2005.
Squares in a tan	5	s = 4	4.000000038	−3.75e-08	-0.000	reproduced	Found by Erich Friedman in March 2005.
Squares in a tan	6	s = 4	4.000020476	−2.05e-05	-0.001	behind
Squares in a tan	7	s = 3 + √2 = 4.414+	4.414213564	−1.77e-09	-0.000	reproduced	Found by Erich Friedman in March 2005.
Squares in a tan	8	s = 2 + 2√2 = 4.828+	4.828427216	−9.12e-08	-0.000	reproduced	Found by Erich Friedman in March 2005.
Squares in a tan	9	s = 7 / √2 = 4.949+	4.950013603	−2.66e-04	-0.005	reproduced	Found by Erich Friedman in March 2005.
Squares in a tan	10	s = 5	5.002812540	−2.81e-03	-0.056	behind
Squares in a tan	11	s = 4 + √2 = 5.414+	5.656875253	−2.43e-01	-4.482	behind	Found by Erich Friedman in March 2005.
Squares in a tan	12	s = 4√2 = 5.656+	5.656855022	−7.72e-07	-0.000	reproduced	Found by Erich Friedman in March 2005.
Squares in a tan	13	s = 3 + 2√2 = 5.828+	6.067680002	−2.39e-01	-4.105	behind	Found by Erich Friedman in March 2005.
Squares in a tan	14	s = 6	6.004579332	−4.58e-03	-0.076	behind	Found by Erich Friedman in March 2005.
Squares in a tan	15	s = 6	6.003513107	−3.51e-03	-0.059	behind
Squares in a tan	16	s = 9 / √2 = 6.363+	6.366891734	−2.93e-03	-0.046	behind	Found by Erich Friedman in March 2005.
Squares in a tan	17	s = 5 + √2 = 6.414+	6.422776591	−8.56e-03	-0.134	behind	Found by Erich Friedman in March 2005.
Squares in a tan	18	s = 4 + 2√2 = 6.828+	7.004173014	−1.76e-01	-2.574	behind	Found by Erich Friedman in March 2005.
Squares in a tan	19	s = 2 + 7 / √2 = 6.949+	7.005592713	−5.58e-02	-0.804	behind	Found by David W. Cantrell in May 2005.
Squares in a tan	20	s = 7	7.050367250	−5.04e-02	-0.720	behind	Found by Erich Friedman in March 2005.
Squares in a tan	21	s = 7	7.075816964	−7.58e-02	-1.083	behind
Squares in a tan	22	s = 1 + 9 / √2 = 7.363+	7.778867109	−4.15e-01	-5.635	behind	Found by Erich Friedman in March 2005.
Squares in a tan	23	s = 6 + √2 = 7.414+	7.782491174	−3.68e-01	-4.967	behind	Found by Erich Friedman in March 2005.
Squares in a tan	24	s = 7 + 1 / √2 = 7.707+	7.782624959	−7.55e-02	-0.980	behind	Found by David W. Cantrell in May 2005.
Squares in a tan	25	s = 11 / √2 = 7.778+	7.803619398	−2.54e-02	-0.327	behind
Squares in a tan	26	s = 5 + 2√2 = 7.828+	8.055926950	−2.27e-01	-2.906	behind	Found by Erich Friedman in March 2026.
Squares in a tan	27	s = 8	8.078384883	−7.84e-02	-0.980	behind	Inherited published construction at n=28; not a newly discovered record
Squares in a tan	28	s = 8	8.179365403	−1.79e-01	-2.242	behind
Squares in a triangle	2	s = 2 + 2 / √3 = 3.154+	3.154700540	−1.27e-09	-0.000	reproduced
Squares in a triangle	3	s = 3 / 2 + √3 = 3.232+	3.232050809	−1.31e-09	-0.000	reproduced	Found by Erich Friedman in 1997.
Squares in a triangle	4	s = 3 + 2 / √3 = 4.154+	4.154700608	−6.95e-08	-0.000	reproduced	Found by Erich Friedman in 1997.
Squares in a triangle	5	s = 2 + 4 / √3 = 4.309+	4.309401143	−6.63e-08	-0.000	reproduced	Found by Erich Friedman in 1997.
Squares in a triangle	6	s = 2 + 4 / √3 = 4.309+	4.309401157	−8.00e-08	-0.000	reproduced	Found by Erich Friedman in 1997.
Squares in a triangle	7	s = 4 + 2 / √3 = 5.154+	5.154700631	−9.26e-08	-0.000	reproduced	Found by Erich Friedman in 1997.
Squares in a triangle	8	s = 5.301+	5.309401248	−8.40e-03	-0.158	behind	Found by David W. Cantrell in July 2002.
Squares in a triangle	9	s = 3 + 4 / √3 = 5.309+	5.313137041	−3.74e-03	-0.070	behind	Found by Erich Friedman in 1997.
Squares in a triangle	10	s = 2 + 2 √3 = 5.464+	5.651955688	−1.88e-01	-3.438	behind	Found by Erich Friedman in 1997.
Squares in a triangle	11	s = 5 + 2 / √3 = 6.154+	6.154973397	−2.73e-04	-0.004	reproduced	Found by Erich Friedman in 1997.
Squares in a triangle	12	s = 6.301+	6.464101811	−1.63e-01	-2.589	behind	Found by David W. Cantrell in July 2002.
Squares in a triangle	13	s = 4 + 4 / √3 = 6.309+	6.618803355	−3.09e-01	-4.904	behind	Found by Erich Friedman in 1997.
Squares in a triangle	14	s = 3 + 2 √3 = 6.464+	6.466274895	−2.17e-03	-0.034	behind	Found by Erich Friedman in 1997.
Squares in a triangle	15	s = 3 + 2 √3 = 6.464+	6.467309355	−3.21e-03	-0.050	behind	Found by Erich Friedman in 1997.
Squares in a triangle	16	s = 6 + 2 / √3 = 7.154+	7.272753177	−1.18e-01	-1.650	behind	Found by Erich Friedman in 1997.
Squares in a triangle	17	s = 7.301+	7.387467732	−8.65e-02	-1.184	behind	Found by David W. Cantrell in July 2002.
Squares in a triangle	18	s = 5 + 4 / √3 = 7.309+	7.619365660	−3.10e-01	-4.241	behind	Found by Erich Friedman in 1997.
Squares in a triangle	19	s = 4 + 2 √3 = 7.464+	7.474726208	−1.06e-02	-0.142	behind	Found by Erich Friedman in 1997.
Squares in a triangle	20	s = 7.61695+	7.911191754	−2.94e-01	-3.863	behind	Found by Haowei Lin in July 2026.
Squares in a triangle	21	s = 3 + 8 / √3 = 7.618+	7.636178468	−1.74e-02	-0.228	behind	Found by Erich Friedman in 1997.
Squares in a triangle	22	s = 7 + 2 / √3 = 8.15470+	8.345753629	−1.91e-01	-2.343	behind	Found by Erich Friedman in 1997.
Squares in a triangle	23	s = 8.301+	8.311768325	−1.08e-02	-0.130	behind	Found by David W. Cantrell in July 2002.
Squares in a triangle	24	s = 6 + 4 / √3 = 8.309+	8.734108340	−4.25e-01	-5.111	behind	Found by Erich Friedman in 1997.
Squares in a triangle	25	s = 5 + 2 √3 = 8.464+	8.886352658	−4.22e-01	-4.989	behind	Found by Erich Friedman in 1997.
Squares in a triangle	26	s = 4 + 8 / √3 = 8.618+	8.784183316	−1.65e-01	-1.919	behind	Found by Erich Friedman in 1997.
Squares in a triangle	27	s = 4 + 8 / √3 = 8.618+	9.317287836	−6.98e-01	-8.105	behind	Found by Erich Friedman in 1997.
Squares in a triangle	28	s = 3 + 10 / √3 = 8.773+	8.943754375	−1.70e-01	-1.941	behind	Found by Erich Friedman in 1997.
Squares in a triangle	29	s = 8 + 2 / √3 = 9.154+	9.421084421	−2.66e-01	-2.910	behind	Found by Erich Friedman in 1997.
Squares in a triangle	30	s = 9.301+	9.654371077	−3.53e-01	-3.799	behind	Found by David W. Cantrell in July 2002.
Squares in a triangle	31	s = 7 + 4 / √3 = 9.309+	9.480651961	−1.71e-01	-1.840	behind	Found by Erich Friedman in 1997.
Squares in a triangle	32	s = 6 + 2 √3 = 9.464+	10.024325937	−5.60e-01	-5.920	behind	Found by Erich Friedman in 1997.
Squares in a triangle	33	s = 5 + 8 / √3 = 9.618+	10.207228500	−5.88e-01	-6.118	behind	Found by Erich Friedman in 1997.
Squares in a triangle	34	s = 5 + 8 / √3 = 9.618+	10.329626708	−7.11e-01	-7.391	behind	Found by Erich Friedman in 1997.
Squares in a triangle	35	s = 4 + 10 / √3 = 9.773+	10.429995262	−6.56e-01	-6.717	behind	Found by Erich Friedman in 1997.
Squares in a triangle	36	s = 4 + 10 / √3 = 9.773+	9.981073334	−2.08e-01	-2.124	behind	Found by Erich Friedman in 1997.
Squares in a triangle	37	s = 10.15299+	10.255190295	−1.02e-01	-1.007	behind	Found by Gianluca Costantino in May 2026.
Squares in a triangle	38	s = 10.304+	10.323153254	−1.92e-02	-0.186	behind	Found by Gianluca Costantino in April 2026.
Squares in a triangle	39	s = 8 + 4 / √3 = 10.30940+	10.469492522	−1.60e-01	-1.553	behind	Found by Bhavithran Ananthan in July 2026.
Squares in a triangle	40	s = 7 + 2√3 = 10.46410+	10.627605650	−1.64e-01	-1.563	behind	Found by Bhavithran Ananthan in July 2026.
Squares in a triangle	41	s = 10.61880+	10.873318836	−2.55e-01	-2.397	behind	Found by Aristotle Papowitz in July 2026.
Squares in a triangle	42	s = 10.61880+	10.956624317	−3.38e-01	-3.181	behind	Found by Aristotle Papowitz in July 2026.
Squares in a triangle	43	s = 10.77350+	11.180800037	−4.07e-01	-3.781	behind	Found by Aristotle Papowitz in July 2026.
Squares in an L	2	s = 2	2.000000001	−8.00e-10	-0.000	reproduced
Squares in an L	3	s = 2	2.000000001	−8.00e-10	-0.000	reproduced
Squares in an L	4	s = 3	3.000000036	−3.65e-08	-0.000	reproduced
Squares in an L	5	s = 3	3.000000051	−5.10e-08	-0.000	reproduced
Squares in an L	6	s = (5√2 + 4) / 3 = 3.690+	3.691334552	−9.79e-04	-0.027	reproduced	Found by David W. Cantrell in June 2005.
Squares in an L	7	s = √2 + 5/2 = 3.914+	3.915343702	−1.13e-03	-0.029	behind	Found by Erich Friedman in June 2005.
Squares in an L	8	s = 4	4.000000061	−6.08e-08	-0.000	reproduced
Squares in an L	9	s = 4	4.000000073	−7.34e-08	-0.000	reproduced
Squares in an L	10	s = 4	4.000000070	−7.04e-08	-0.000	reproduced
Squares in an L	11	s = 4	4.000000070	−7.03e-08	-0.000	reproduced
Squares in an L	12	s = 4	4.000000701	−7.01e-07	-0.000	reproduced
Squares in an L	13	s = 2 + 2√2 = 4.828+	4.895813581	−6.74e-02	-1.396	behind	Found by Maurizio Morandi in October 2008.
Squares in an L	14	s = 4.98674+	5.002000611	−1.53e-02	-0.306	behind	Found by Jonathan Viquerat in June 2026.
Squares in an L	15	s = 5	5.003011320	−3.01e-03	-0.060	behind
Squares in an L	16	s = 5	5.015997543	−1.60e-02	-0.320	behind
Squares in an L	17	s = 4/3 + 3√2 = 5.575+	5.605236667	−2.93e-02	-0.525	behind	Found by Maurizio Morandi in October 2008.
Squares in an L	18	s = (2√2 + 14) / 3 = 5.609+	5.856553319	−2.47e-01	-4.405	behind	Found by Erich Friedman in June 2005.
Squares in an L	19	s = 5.792+	6.002631432	−2.11e-01	-3.637	behind	Found by David W. Cantrell in July 2012.
Squares in an L	20	s = 5.937+	6.002105950	−6.51e-02	-1.097	behind	Found by David W. Cantrell in July 2012.
Squares in an L	21	s = 6	6.023955403	−2.40e-02	-0.399	behind
Squares in an L	22	s = 6	6.062729102	−6.27e-02	-1.045	behind
Squares in an L	23	s = 6	6.044976525	−4.50e-02	-0.750	behind
Squares in an L	24	s = 6	6.004111686	−4.11e-03	-0.069	behind
Squares in an L	25	s = 6	6.074412912	−7.44e-02	-1.240	behind
Squares in an L	26	s = 6	6.002733569	−2.73e-03	-0.046	behind
Squares in an L	27	s = 6	6.001992905	−1.99e-03	-0.033	behind
Squares in an L	28	s = 6 + √2/2 = 6.707+	6.985747884	−2.79e-01	-4.154	behind	Found by Maurizio Morandi in September 2015.
Squares in an L	29	s = 6.840+	7.459934584	−6.20e-01	-9.063	behind	Found by Maurizio Morandi in September 2015.
Squares in an L	30	s = 7	7.010822287	−1.08e-02	-0.155	behind
Squares in an L	31	s = 7	7.002962693	−2.96e-03	-0.042	behind
Squares in an L	32	s = 7	7.005621988	−5.62e-03	-0.080	behind
Squares in an L	33	s = 7	7.004567238	−4.57e-03	-0.065	behind
Squares in an L	34	s = 7.513+	8.002545447	−4.90e-01	-6.516	behind	Found by Joe DeVincentis in September 2015.
Squares in an L	35	s = 7.55991+	8.004606407	−4.45e-01	-5.882	behind	Found by Aapo Lipponen in July 2026.
Squares in an L	36	s = 7.730+	8.001601164	−2.72e-01	-3.514	behind	Found by Joe DeVincentis in September 2015.
Squares in an octagon	2	s = √(6–√2–√(20√2–26))/2 = 0.87669+	0.876699201	−1.34e-08	-0.000	reproduced	Found by Maurizio Morandi in December 2013.
Squares in an octagon	3	s = 18 – 12√2 = 1.02943+	1.029437267	−1.59e-08	-0.000	reproduced	Found by Erich Friedman in December 2013.
Squares in an octagon	4	s = √(4–2√2) = 1.08239+	1.082392211	−1.02e-08	-0.000	reproduced
Squares in an octagon	5	s = 3√2 – 3 = 1.24264+	1.242640688	−1.35e-09	-0.000	reproduced
Squares in an octagon	6	s = 7 – 4√2 = 1.34314+	1.343145772	−2.10e-08	-0.000	reproduced	Found by Maurizio Morandi in December 2013.
Squares in an octagon	7	s = √(5–√2–√(8√2–9)) = 1.43690+	1.436905902	−2.33e-08	-0.000	reproduced	Found by Maurizio Morandi in December 2013.
Squares in an octagon	8	s = 1.56962+	1.573237994	−3.62e-03	-0.231	behind	Found by Grant Mowry in May 2026.
Squares in an octagon	9	s = 3/√(2+√2) = 1.62358+	1.623588361	−6.05e-08	-0.000	reproduced
Squares in an octagon	10	s = 1.68171+	1.684765369	−3.06e-03	-0.182	behind	Found by Timo Berthold et al in May 2026.
Squares in an octagon	11	s = 1.73152+	1.731585028	−6.50e-05	-0.004	behind	Found by Jonathan Viquerat in May 2026.
Squares in an octagon	12	s = √(6–√2–√(20√2–26)) = 1.75339+	1.756171028	−2.77e-03	-0.158	behind	Found by Maurizio Morandi in December 2013.
Squares in an octagon	13	s = 1.89674+	1.973204278	−7.65e-02	-4.031	behind	Found by Grant Mowry in May 2026.
Squares in an octagon	14	s = 1.98302+	2.024750310	−4.17e-02	-2.104	behind	Found by Timo Berthold et al in May 2026.
Squares in an octagon	15	s = 2.03168+	2.076313287	−4.46e-02	-2.197	behind	Found by Jonathan Viquerat in May 2026.
Squares in an octagon	16	s = 5√2 – 5 = 2.07106+	2.071280707	−2.13e-04	-0.010	behind
Squares in an octagon	17	s = 5√2 – 5 = 2.07106+	2.215373368	−1.44e-01	-6.968	behind
Squares in an octagon	18	s = 2.16732+	2.197488029	−3.02e-02	-1.392	behind	Found by Timo Berthold et al in May 2026.
Squares in an octagon	19	s = 2.22435+	2.231756100	−7.41e-03	-0.333	behind	Found by Jake Loyd in May 2026.
Squares in an octagon	20	s = 2.28598+	2.380215831	−9.42e-02	-4.122	behind	Found by Jake Loyd in May 2026.
Squares in an octagon	21	s = sqrt(48–9√2–3√(104√2–126))/2 = 2.31833+	2.320377494	−2.04e-03	-0.088	behind	Found by Jake Loyd in May 2026.
Squares in an octagon	22	s = 2.41575+	2.489033373	−7.33e-02	-3.034	behind	Found by Jake Loyd in May 2026.
Squares in an octagon	23	s = 2.46879+	2.500336230	−3.15e-02	-1.278	behind	Found by Jake Loyd in May 2026.
Squares in an octagon	24	s = 6√2–6 = 2.48528+	2.486267418	−9.86e-04	-0.040	behind
Squares in an octagon	25	s = 17(2–√2)/4 = 2.48959+	2.645349445	−1.56e-01	-6.256	behind	Found by Jake Loyd in May 2026.
Squares in an octagon	26	s = 2.52709+	2.660164352	−1.33e-01	-5.266	behind	Found by Aristotle Papowitz in July 2026.
Squares in an octagon	27	s = 2.58584+	2.621139161	−3.53e-02	-1.365	behind	Found by Jake Loyd in May 2026.
Squares in an octagon	28	s = 2.62788+	2.634420489	−6.54e-03	-0.249	behind	Found by Jake Loyd in May 2026.
Squares in an octagon	29	s = 2.70553+	2.834751438	−1.29e-01	-4.776	behind	Found by Jake Loyd in May 2026.
Squares in an octagon	30	s = 2(11–√2)/7 = 2.73879+	2.902115756	−1.63e-01	-5.963	behind	Found by Maurizio Morandi in May 2026.
Squares in an octagon	31	s = 2.78401+	2.935265299	−1.51e-01	-5.433	behind	Found by Aapo Lipponen in July 2026.
Squares in an octagon	32	s = 2.83980+	2.943329060	−1.04e-01	-3.646	behind	Found by Aristotle Papowitz in July 2026.
Squares in an octagon	33	s = 2.85903+	2.901658423	−4.26e-02	-1.491	behind	Found by Aristotle Papowitz in July 2026.
Squares in an octagon	34	s = 7√2–7 = 2.89949+	2.929037239	−2.95e-02	-1.019	behind	Found by Mohamed Metwalli in June 2026.
Squares in an octagon	35	s = 2.90678+	2.921012364	−1.42e-02	-0.490	behind	Found by Aapo Lipponen in July 2026.
Squares in an octagon	36	s = 2.92870+	2.930048542	−1.35e-03	-0.046	behind	Found by Aristotle Papowitz in July 2026.
Squares in an octagon	37	s = 10–5√2 = 2.92893+	2.952199194	−2.33e-02	-0.794	behind
Squares in an octagon	38	s = 3.02060+	3.055268763	−3.47e-02	-1.148	behind	Found by Luke Kaiser in August 2026.
Squares in an octagon	39	s = 3.08204+	3.090412030	−8.37e-03	-0.272	behind	Found by Aapo Lipponen in July 2026.
Squares in an octagon	40	s = 3.14120+	3.161066489	−1.99e-02	-0.632	behind	Found by Aapo Lipponen in July 2026.
Tans in a circle	2	r = 1/√2 = .707+	0.707106781	−2.83e-10	-0.000	reproduced
Tans in a circle	3	r = (6 + √2)/8 = .926+	0.926776710	−1.51e-08	-0.000	reproduced	Found by Serhiy Grabarchuk in April 2005.
Tans in a circle	4	r = 1	1.033857506	−3.39e-02	-3.386	behind
Tans in a circle	5	r = 1.125+	1.127965887	−2.97e-03	-0.264	behind	Found by Maurizio Morandi in July 2007.
Tans in a circle	6	r = 1.198+	1.230269755	−3.23e-02	-2.694	behind	Found by Maurizio Morandi in July 2007.
Tans in a circle	7	r = 1.26287+	1.298359204	−3.55e-02	-2.810	behind	Found by Jake Loyd in June 2026.
Tans in a circle	8	r = √(1+1/√2) = 1.306+	1.332062978	−2.55e-02	-1.953	behind	Found by Serhiy Grabarchuk in April 2005.
Tans in a circle	9	r = 1.37381+	1.455392414	−8.16e-02	-5.938	behind	Found by Thomas Greenleaf in June 2026.
Tans in a circle	10	r = 1.42230+	1.459002929	−3.67e-02	-2.581	behind	Found by Thomas Greenleaf in June 2026.
Tans in a circle	11	r = 1.480+	1.592426035	−1.12e-01	-7.596	behind	Found by David W. Cantrell in August 2007.
Tans in a circle	12	r = 1.50878+	1.583266102	−7.45e-02	-4.937	behind	Found by Jake Loyd in June 2026.
Tans in a circle	13	r = 1.55348+	1.768541339	−2.15e-01	-13.844	behind	Found by Jake Loyd in June 2026.
Tans in a circle	14	r = √10/2 = 1.581+	1.801117015	−2.20e-01	-13.914	behind	Found by Serhiy Grabarchuk in April 2005.
Tans in a circle	15	r = 1.66443+	1.755911431	−9.15e-02	-5.496	behind	Found by Jake Loyd in June 2026.
Tans in a circle	16	r = 1.73588+	1.917203259	−1.81e-01	-10.446	behind	Found by Haowei Lin in July 2026.
Tans in a circle	17	r = 1.79723+	1.872598362	−7.54e-02	-4.194	behind	Found by Haowei Lin in July 2026.
Tans in a circle	18	r = 1.83366+	2.036503034	−2.03e-01	-11.062	behind	Found by Jake Loyd in June 2026.
Tans in a circle	19	r = 1.88814+	1.973825791	−8.57e-02	-4.538	behind	Found by Jake Loyd in June 2026.
Tans in a circle	20	r = 1.93661+	2.016251658	−7.96e-02	-4.112	behind	Found by Haowei Lin in July 2026.
Tans in a domino	2	s = 2√2/3 = .94280+	0.942809042	−3.77e-10	-0.000	reproduced	Found by Maurizio Morandi in June 2026.
Tans in a domino	3	s = .99900+	0.999003003	−3.00e-06	-0.000	reproduced	Found by Maurizio Morandi in June 2026.
Tans in a domino	4	s = 1	1.000000000	−4.00e-10	-0.000	reproduced
Tans in a domino	5	s = 1.30157+	1.303244691	−1.67e-03	-0.129	behind	Found by Jonathan Viquerat in June 2026.
Tans in a domino	6	s = 4/3 = 1.33333+	1.355000204	−2.17e-02	-1.625	behind	Found by Maurizio Morandi in June 2026.
Tans in a domino	7	s = √2 = 1.41421+	1.419367086	−5.15e-03	-0.364	behind
Tans in a domino	8	s = √2 = 1.41421+	1.513782719	−9.96e-02	-7.041	behind
Tans in a domino	9	s = 1.60710+	1.754613054	−1.48e-01	-9.179	behind	Found by Maurizio Morandi in June 2026.
Tans in a domino	10	s = 1 + 1/√2 = 1.70710+	1.771713934	−6.46e-02	-3.785	behind	Found by Maurizio Morandi in June 2026.
Tans in a domino	11	s = 1.74954+	1.916394459	−1.67e-01	-9.537	behind	Found by Aapo Lipponen in July 2026.
Tans in a domino	12	s = 3(1+√2)/4 = 1.81066+	1.998048024	−1.87e-01	-10.349	behind	Found by Maurizio Morandi in June 2026.
Tans in a domino	13	s = 1/2+√2 = 1.91421+	1.944687338	−3.05e-02	-1.592	behind	Found by Maurizio Morandi in June 2026.
Tans in a domino	14	s = (7+2√2)/5 = 1.96568+	2.015263222	−4.96e-02	-2.522	behind	Found by Maurizio Morandi in June 2026.
Tans in a domino	15	s = 2	2.039651770	−3.97e-02	-1.983	behind
Tans in a domino	16	s = 2	2.012810801	−1.28e-02	-0.641	behind
Tans in a domino	17	s = (7+4√2)/6 = 2.10947+	2.590358051	−4.81e-01	-22.796	behind	Found by Maurizio Morandi in June 2026.
Tans in a domino	18	s = 2.17527+	2.257584016	−8.23e-02	-3.784	behind	Found by Maurizio Morandi in June 2026.
Tans in a hexagon	2	s = (3+√3)/6 = .78867+	0.788675138	−3.09e-09	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Tans in a hexagon	3	s = .98882+	0.988828393	−8.39e-06	-0.001	reproduced	Found by Aapo Lippoen in July 2026.
Tans in a hexagon	4	s = 1.05845+	1.060623023	−2.17e-03	-0.205	behind	Found by Jonathan Viquerat in May 2026.
Tans in a hexagon	5	s = 1.13976+	1.206521484	−6.68e-02	-5.858	behind	Found by Jonathan Viquerat in May 2026.
Tans in a hexagon	6	s = 1.20610+	1.241260192	−3.52e-02	-2.915	behind	Found by Jonathan Viquerat in May 2026.
Tans in a hexagon	7	s = 1.30322+	1.323277920	−2.01e-02	-1.539	behind	Found by Thomas Greenleaf in June 2026.
Tans in a hexagon	8	s = 1.37728+	1.513097590	−1.36e-01	-9.861	behind	Found by Thomas Greenleaf in June 2026.
Tans in a hexagon	9	s = 1.44631+	1.610422909	−1.64e-01	-11.347	behind	Found by Thomas Greenleaf in June 2026.
Tans in a hexagon	10	s = 1.51366+	1.624540842	−1.11e-01	-7.325	behind	Found by Thomas Greenleaf in June 2026.
Tans in a hexagon	11	s = 1.59198+	1.632152964	−4.02e-02	-2.523	behind	Found by Jake Loyd in June 2026.
Tans in a hexagon	12	s = 1.65076+	1.714942884	−6.42e-02	-3.888	behind	Found by Jake Loyd in June 2026.
Tans in a hexagon	13	s = 1.70429+	1.788144572	−8.39e-02	-4.920	behind	Found by Jake Loyd in June 2026.
Tans in a hexagon	14	s = 1.76680+	1.984370339	−2.18e-01	-12.314	behind	Found by Jake Loyd in June 2026.
Tans in a hexagon	15	s = 1.82658+	2.037201548	−2.11e-01	-11.531	behind	Found by Jake Loyd in June 2026.
Tans in a hexagon	16	s = 1.88728+	1.901404475	−1.41e-02	-0.748	behind	Found by Jake Loyd in June 2026.
Tans in a hexagon	17	s = 1.93877+	1.981827839	−4.31e-02	-2.221	behind	Found by Jake Loyd in June 2026.
Tans in a hexagon	18	s = 1.99031+	2.038562224	−4.83e-02	-2.424	behind	Found by Jake Loyd in June 2026.
Tans in a hexagon	19	s = 2.03182+	2.314967080	−2.83e-01	-13.936	behind	Found by Jake Loyd in June 2026.
Tans in a hexagon	20	s = 2.1029+	2.161143424	−5.82e-02	-2.770	behind	Found by Jake Loyd in June 2026.
Tans in a hexagon	21	s = 2.14048+	2.366806296	−2.26e-01	-10.574	behind	Found by Jake Loyd in June 2026.
Tans in a hexagon	22	s = 2.19278+	2.383146217	−1.90e-01	-8.682	behind	Found by Jake Loyd in June 2026.
Tans in a pentagon	2	s = .93685+	0.936859710	−9.71e-06	-0.001	reproduced	Found by Jonathan Viquerat in May 2026.
Tans in a pentagon	3	s = 1.10580+	1.105796242	+3.76e-06	0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Tans in a pentagon	4	s = 1.28055+	1.280785801	−2.36e-04	-0.018	behind	Found by Aapo Lipponen in July 2026.
Tans in a pentagon	5	s = 1.38606+	1.386065049	−5.05e-06	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Tans in a pentagon	6	s = 1.50657+	1.551761291	−4.52e-02	-3.000	behind	Found by Jonathan Viquerat in May 2026.
Tans in a pentagon	7	s = 1.62694+	1.643618902	−1.67e-02	-1.025	behind	Found by Jonathan Viquerat in May 2026.
Tans in a pentagon	8	s = 1.71964+	1.807821457	−8.82e-02	-5.128	behind	Found by Jonathan Viquerat in May 2026.
Tans in a pentagon	9	s = 1.79909+	1.932526604	−1.33e-01	-7.417	behind	Found by Thomas Greenleaf in June 2026.
Tans in a pentagon	10	s = 1.87393+	1.988353470	−1.14e-01	-6.106	behind	Found by Thomas Greenleaf in June 2026.
Tans in a pentagon	11	s = 1.95640+	2.040666832	−8.43e-02	-4.307	behind	Found by Jake Loyd in June 2026.
Tans in a pentagon	12	s = 2.02754+	2.094219372	−6.67e-02	-3.289	behind	Found by Jake Loyd in June 2026.
Tans in a pentagon	13	s = 2.10941+	2.176649839	−6.72e-02	-3.188	behind	Found by Jake Loyd in June 2026.
Tans in a pentagon	14	s = 2.16639+	2.402834722	−2.36e-01	-10.914	behind	Found by Jake Loyd in June 2026.
Tans in a pentagon	15	s = 2.25710+	2.393924009	−1.37e-01	-6.062	behind	Found by Jake Loyd in June 2026.
Tans in a pentagon	16	s = 2.32695+	2.531867924	−2.05e-01	-8.806	behind	Found by Jake Loyd in June 2026.
Tans in a pentagon	17	s = 2.38607+	2.469756926	−8.37e-02	-3.507	behind	Found by Jake Loyd in June 2026.
Tans in a pentagon	18	s = 2.44578+	2.711505436	−2.66e-01	-10.865	behind	Found by Jake Loyd in June 2026.
Tans in a pentagon	19	s = 2.53585+	2.777210790	−2.41e-01	-9.518	behind	Found by Jake Loyd in June 2026.
Tans in a pentagon	20	s = 2.59169+	2.867840457	−2.76e-01	-10.655	behind	Found by Jake Loyd in June 2026.
Tans in a pentagon	21	s = 2.65501+	2.742475222	−8.75e-02	-3.294	behind	Found by Jake Loyd in June 2026.
Tans in a pentagon	22	s = 2.71124+	3.019915317	−3.09e-01	-11.385	behind	Found by Jake Loyd in June 2026.
Tans in a square	2	s = 1	1.000000000	−4.00e-10	-0.000	reproduced
Tans in a square	3	s = √2 = 1.414+	1.414213563	−5.66e-10	-0.000	reproduced
Tans in a square	4	s = √2 = 1.414+	1.414213563	−5.66e-10	-0.000	reproduced
Tans in a square	5	s = 1.788+	1.788569804	−5.70e-04	-0.032	reproduced	Found by Maurizio Morandi in August 2007.
Tans in a square	6	s = 1.937+	1.998974240	−6.20e-02	-3.199	behind	Found by Maurizio Morandi in February 2008.
Tans in a square	7	s = 1.999+	2.000000001	−1.00e-03	-0.050	reproduced	Found by Maurizio Morandi in August 2007.
Tans in a square	8	s = 2	2.000018476	−1.85e-05	-0.001	behind
Tans in a square	9	s = 3/2 + 1/√2 = 2.207+	2.356949615	−1.50e-01	-6.789	behind	Found by Erich Friedman in March 2005.
Tans in a square	10	s = 2.393+	2.601727233	−2.09e-01	-8.722	behind	Found by Maurizio Morandi in January 2008.
Tans in a square	11	s = 1 + √2 = 2.414+	2.624836148	−2.11e-01	-8.725	behind	Found by Maurizio Morandi in August 2007.
Tans in a square	12	s = 2.61115+	2.630802721	−1.97e-02	-0.753	behind	Found by Haowei Lin in July 2026.
Tans in a square	13	s = 2.688+	3.008628311	−3.21e-01	-11.928	behind	Found by Maurizio Morandi in March 2008.
Tans in a square	14	s = 2.76345+	2.854047963	−9.06e-02	-3.278	behind	Found by Haowei Lin in July 2026.
Tans in a square	15	s = 2.82735+	3.060035152	−2.33e-01	-8.230	behind	Found by Aapo Lipponen in July 2026.
Tans in a square	16	s = 2√2 = 2.828+	3.043632017	−2.15e-01	-7.610	behind
Tans in a square	17	s = 2.970+	3.446091479	−4.76e-01	-16.030	behind	Found by David W. Cantrell in August 2007.
Tans in a square	18	s = 3	3.064198962	−6.42e-02	-2.140	behind
Tans in a square	19	s = 3.201+	3.508781859	−3.08e-01	-9.615	behind	Found by Maurizio Morandi in February 2008.
Tans in a square	20	s = 3.26857+	3.556819788	−2.88e-01	-8.819	behind	Found by Aapo Lippoen in July 2026.
Tans in a square	21	s = 3.340+	3.959542464	−6.20e-01	-18.549	behind	Found by Maurizio Morandi in March 2008.
Tans in a square	22	s = 3.392+	3.514392618	−1.22e-01	-3.608	behind	Found by Maurizio Morandi in December 2007.
Tans in a square	23	s = 3.464+	3.609775406	−1.46e-01	-4.208	behind	Found by Maurizio Morandi in December 2007.
Tans in a square	24	s = 3.517+	3.959767771	−4.43e-01	-12.589	behind	Found by David W. Cantrell in August 2007.
Tans in a tan	2	s = √2 = 1.414+	1.414213563	−5.66e-10	-0.000	reproduced
Tans in a tan	3	s = (4+√2+2√(2+2√2))/5 = 1.96179+	1.961790004	−7.85e-10	-0.000	reproduced	Found by Ed Pegg in March 2005.
Tans in a tan	4	s = 2	2.121320386	−1.21e-01	-6.066	behind
Tans in a tan	5	s = 2.405+	2.414213610	−9.21e-03	-0.383	behind	Found by David W. Cantrell in May 2005.
Tans in a tan	6	s = (12 + √6 + 5√2)/8 = 2.690+	2.708008426	−1.79e-02	-0.667	behind	Found by Maurizio Morandi in October 2007.
Tans in a tan	7	s = 2.82434+	2.854060736	−2.97e-02	-1.052	behind	Found by Maurizio Morandi in August 2007.
Tans in a tan	8	s = 2√2 = 2.828+	3.000149976	−1.72e-01	-6.072	behind
Tans in a tan	9	s = 3	3.038239476	−3.82e-02	-1.275	behind
Tans in a tan	10	s = 3.30743+	3.413039485	−1.06e-01	-3.193	behind	Found by Maurizio Morandi in August 2007.
Tans in a tan	11	s = 2 + √2 = 3.414+	3.665634546	−2.51e-01	-7.364	behind	Found by Erich Friedman in March 2005.
Tans in a tan	12	s = 3.53106+	3.752654870	−2.22e-01	-6.276	behind	Found by Maurizio Morandi in August 2007.
Tans in a tan	13	s = 3 + √2/2 = 3.707+	4.095535336	−3.88e-01	-10.478	behind	Found by Erich Friedman in March 2005.
Tans in a tan	14	s = 1 + 2√2 = 3.828+	4.010060739	−1.82e-01	-4.745	behind	Found by Erich Friedman in March 2005.
Tans in a tan	15	s = 5/2 + √2 = 3.914+	4.047702897	−1.33e-01	-3.411	behind	Found by Maurizio Morandi in August 2007.
Tans in a tan	16	s = 4	4.069311884	−6.93e-02	-1.733	behind
Tans in a tan	17	s = 4.181+	4.371183055	−1.90e-01	-4.549	behind	Found by Maurizio Morandi in August 2007.
Tans in a tan	18	s = 3√2 = 4.242+	4.508189761	−2.66e-01	-6.260	behind
Tans in a tan	19	s = 4.413+	4.734706665	−3.22e-01	-7.290	behind	Found by David W. Cantrell in May 2005.
Tans in a tan	20	s = 4.535+	4.784964858	−2.50e-01	-5.512	behind	Found by Maurizio Morandi in August 2007.
Tans in a tan	21	s = (6 + 9√2)/4 = 4.681+	4.959368900	−2.77e-01	-5.926	behind	Found by Maurizio Morandi in October 2007.
Tans in a tan	22	s = 3 + 5√2/4 = 4.767+	4.995243624	−2.27e-01	-4.772	behind	Found by Maurizio Morandi in July 2009.
Tans in a tan	23	s = 4.886+	5.166397479	−2.80e-01	-5.739	behind	Found by Maurizio Morandi in November 2007.
Tans in a tan	24	s = 4.947+	5.105939860	−1.59e-01	-3.213	behind	Found by Maurizio Morandi in October 2007.
Tans in a tan	25	s = 5	5.011449527	−1.14e-02	-0.229	behind
Tans in a tan	26	s = 3 + 3/√2 = 5.121+	5.801776469	−6.80e-01	-13.288	behind	Found by Maurizio Morandi in July 2009.
Tans in a tan	27	s = 5.241+	5.842092553	−6.01e-01	-11.469	behind	Found by Maurizio Morandi in July 2009.
Tans in a triangle	2	s = (1+√3)/√2 = 1.93185+	1.931851653	−7.73e-10	-0.000	reproduced
Tans in a triangle	3	s = 3/√2 = 2.12132+	2.121320344	−8.49e-10	-0.000	reproduced
Tans in a triangle	4	s = 2.53732+	2.542382915	−5.06e-03	-0.200	behind	Found by Jonathan Viquerat in May 2026.
Tans in a triangle	5	s = 2.74147+	2.777939226	−3.65e-02	-1.330	behind	Found by Jonathan Viquerat in May 2026.
Tans in a triangle	6	s = 2.93781+	2.975496728	−3.77e-02	-1.283	behind	Found by Jonathan Viquerat in May 2026.
Tans in a triangle	7	s = 3.17427+	3.216732358	−4.25e-02	-1.338	behind	Found by Jonathan Loyd in June 2026.
Tans in a triangle	8	s = 3.35224+	3.432106183	−7.99e-02	-2.382	behind	Found by Jonathan Viquerat in May 2026.
Tans in a triangle	9	s = 3.51439+	3.652427543	−1.38e-01	-3.928	behind	Found by Jonathan Loyd in June 2026.
Tans in a triangle	10	s = 3.69367+	3.957766211	−2.64e-01	-7.150	behind	Found by Aapo Lipponen in July 2026.
Tans in a triangle	11	s = 3.82731+	4.141753754	−3.14e-01	-8.216	behind	Found by Jonathan Loyd in June 2026.
Tans in a triangle	12	s = 4	4.048090182	−4.81e-02	-1.202	behind	Found by Jonathan Loyd in June 2026.
Tans in a triangle	13	s = 4.14927+	4.506795877	−3.58e-01	-8.617	behind	Found by Jonathan Loyd in June 2026.
Tans in a triangle	14	s = 4.29538+	4.853863666	−5.58e-01	-13.002	behind	Found by Jonathan Loyd in June 2026.
Tans in a triangle	15	s = 4.41143+	5.208837878	−7.97e-01	-18.076	behind	Found by Haowei Lin in July 2026.
Tans in a triangle	16	s = 4.60690+	5.176505225	−5.70e-01	-12.364	behind	Found by Haowei Lin in July 2026.
Tans in a triangle	17	s = 4.72627+	4.953290246	−2.27e-01	-4.803	behind	Found by Jonathan Loyd in June 2026.
Tans in a triangle	18	s = 4.84346+	5.399196137	−5.56e-01	-11.474	behind	Found by Jonathan Loyd in June 2026.
Tans in a triangle	19	s = 4.96765+	5.674645515	−7.07e-01	-14.232	behind	Found by Thomas Greenleaf in June 2026.
Tans in a triangle	20	s = 5.06562+	5.759684374	−6.94e-01	-13.701	behind	Found by Thomas Greenleaf in June 2026.
Tans in a triangle	21	s = 5.23033+	5.515514513	−2.85e-01	-5.453	behind	Found by Jonathan Loyd in June 2026.
Tans in a triangle	22	s = 5.33580+	5.493114885	−1.57e-01	-2.948	behind	Found by Jonathan Loyd in June 2026.
Tans in an L	2	s = 1/√2 = .707+	0.707106781	−2.83e-10	-0.000	reproduced
Tans in an L	3	s = (1+√7) / 4 = .911+	0.911437844	−1.63e-08	-0.000	reproduced	Found by Erich Friedman in July 2011.
Tans in an L	4	s = (√6 + √2) / 4 = .965+	0.996805449	−3.09e-02	-3.200	behind	Found by Maurizio Morandi in July 2012.
Tans in an L	5	s = 1	0.999915808	+8.42e-05	0.008	beaten
Tans in an L	6	s = 1	1.000000000	−4.00e-10	-0.000	reproduced
Tans in an L	7	s = (2 + √2) / 3 = 1.138+	1.237772787	−9.97e-02	-8.761	behind	Found by David W. Cantrell in July 2012.
Tans in an L	8	s = (1 + 2√2) / 3 = 1.276+	1.381696585	−1.06e-01	-8.272	behind	Found by Maurizio Morandi in July 2012.
Tans in an L	9	s = 4/3 = 1.333+	1.401007779	−6.77e-02	-5.077	behind	Found by Maurizio Morandi in July 2012.
Tans in an L	10	s = 1.400+	1.506999839	−1.07e-01	-7.643	behind	Found by Maurizio Morandi in July 2012.
Tans in an L	11	s = √2 = 1.414+	1.499986693	−8.58e-02	-6.066	behind
Tans in an L	12	s = √2 = 1.414+	1.569539715	−1.55e-01	-10.985	behind
Tans in an L	13	s = 1.499+	1.802710992	−3.04e-01	-20.261	behind	Found by Maurizio Morandi in July 2012.
Tans in an L	14	s = 1.607+	1.823063981	−2.16e-01	-13.445	behind	Found by Maurizio Morandi in August 2012.
Tans in an L	15	s = 1.680+	1.712804130	−3.28e-02	-1.953	behind	Found by Maurizio Morandi in August 2012.
Tans in an L	16	s = 1 + 1/√2 = 1.70711+	1.942331421	−2.35e-01	-13.779	behind	Found by Edoardo Gnaldi in September 2026.
Tans in an L	17	s = (4 + √2) / 3 = 1.804+	1.982366601	−1.78e-01	-9.846	behind	Found by Maurizio Morandi in August 2012.
Tans in an octagon	2	s = 1/√(2+√2) = .54119+	0.541196100	−2.16e-10	-0.000	reproduced
Tans in an octagon	3	s = .72389+	0.723891057	−1.06e-06	-0.000	reproduced	Found by Thomas Greenleaf in June 2026.
Tans in an octagon	4	s = √(2–√2) = .76536+	0.823112557	−5.77e-02	-7.545	behind	Found by Thomas Greenleaf in June 2026.
Tans in an octagon	5	s = .88072+	0.885270198	−4.55e-03	-0.517	behind	Found by Thomas Greenleaf in June 2026.
Tans in an octagon	6	s = √(2+√2)/2 = .92387+	0.959126328	−3.52e-02	-3.815	behind	Found by Thomas Greenleaf in June 2026.
Tans in an octagon	7	s = .98623+	1.050704068	−6.45e-02	-6.537	behind	Found by Thomas Greenleaf in June 2026.
Tans in an octagon	8	s = 1	1.086166119	−8.62e-02	-8.617	behind
Tans in an octagon	9	s = 1.08295+	1.137769909	−5.48e-02	-5.062	behind	Found by Jake Loyd in June 2026.
Tans in an octagon	10	s = 1.09348+	1.229694279	−1.36e-01	-12.457	behind	Found by Jake Loyd in June 2026.
Tans in an octagon	11	s = 1.15384+	1.255356939	−1.02e-01	-8.798	behind	Found by Jake Loyd in June 2026.
Tans in an octagon	12	s = 4–2√2 = 1.17157+	1.250630211	−7.91e-02	-6.748	behind	Found by Thomas Greenleaf in June 2026.
Tans in an octagon	13	s = 1.21868+	1.428886384	−2.10e-01	-17.249	behind	Found by Jake Loyd in June 2026.
Tans in an octagon	14	s = 3(√2–1) = 1.24264+	1.416268352	−1.74e-01	-13.972	behind	Found by Maurizio Morandi in June 2026.
Tans in an octagon	15	s = 1.31145+	1.426752889	−1.15e-01	-8.792	behind	Found by Jake Loyd in June 2026.
Tans in an octagon	16	s = 9/√2–5 = 1.36396+	1.447148527	−8.32e-02	-6.099	behind	Found by Jake Loyd in June 2026.
Tans in an octagon	17	s = 1.39954+	1.486068871	−8.65e-02	-6.183	behind	Found by Jake Loyd in June 2026.
Tans in an octagon	18	s = √2 = 1.41421+	1.509219859	−9.50e-02	-6.718	behind	Found by Jake Loyd in June 2026.
Tans in an octagon	19	s = 1.48829+	1.733095857	−2.45e-01	-16.449	behind	Found by Jake Loyd in June 2026.
Tans in an octagon	20	s = 35/3–43/3√2 = 1.53146+	1.757936323	−2.26e-01	-14.788	behind	Found by Jake Loyd in June 2026.
Triangles in a circle	2	r = √3/2 = .866+	0.866025415	−1.07e-08	-0.000	reproduced
Triangles in a circle	3	r = 3√3 – 3√2 = .953+	0.953511750	−1.48e-08	-0.000	reproduced	Found by Erich Friedman in 1997.
Triangles in a circle	4	r = .980+	0.980597945	−5.98e-04	-0.061	reproduced	Found by Erich Friedman in 1997.
Triangles in a circle	5	r = 1	1.000000000	−4.00e-10	-0.000	reproduced
Triangles in a circle	6	r = 1	1.000015329	−1.53e-05	-0.002	behind
Triangles in a circle	7	r = 1.152+	1.153231878	−1.23e-03	-0.107	behind	Found by Erich Friedman in 1997.
Triangles in a circle	8	r = 1.263+	1.265692129	−2.69e-03	-0.213	behind	Found by Maurizio Morandi in April 2008.
Triangles in a circle	9	r = 1.314+	1.314752945	−7.53e-04	-0.057	reproduced	Found by David W. Cantrell in July 2002.
Triangles in a circle	10	r = 1.38468+	1.385680061	−1.00e-03	-0.072	behind	Found by Jonathan Viquerat in June 2026.
Triangles in a circle	11	r = 1.466+	1.507265477	−4.13e-02	-2.815	behind	Found by David W. Cantrell in August 2012.
Triangles in a circle	12	r = 1.507+	1.511536071	−4.54e-03	-0.301	behind	Found by David W. Cantrell in October 2005.
Triangles in a circle	13	r = √(7/3) = 1.527+	1.530500836	−2.98e-03	-0.195	behind	Found by Erich Friedman in 1997.
Triangles in a circle	14	r = 1.60448+	1.607206958	−2.73e-03	-0.170	behind	Found by Jake Loyd in June 2026.
Triangles in a circle	15	r = 1.636+	1.714286578	−7.83e-02	-4.785	behind	Found by David W. Cantrell in July 2002.
Triangles in a circle	16	r = 1.687+	1.744892910	−5.79e-02	-3.432	behind	Found by Maurizio Morandi in April 2008.
Triangles in a circle	17	r = 1.730+	1.981617862	−2.52e-01	-14.544	behind	Found by David W. Cantrell in July 2005.
Triangles in a circle	18	r = 1.80176+	1.806601968	−4.84e-03	-0.269	behind	Found by Jake Loyd in June 2026.
Triangles in a circle	19	r = √(10/3) = 1.825+	1.853852175	−2.81e-02	-1.540	behind	Found by Haym Hirsh in August 2019.
Triangles in a circle	20	r = 1.874+	1.935507862	−6.15e-02	-3.282	behind	Found by Erich Friedman in 1997.
Triangles in a circle	21	r = 1.910+	1.914916747	−4.92e-03	-0.257	behind	Found by Maurizio Morandi in May 2008.
Triangles in a circle	22	r = 1.943+	2.012362967	−6.94e-02	-3.570	behind	Found by Maurizio Morandi in June 2008.
Triangles in a circle	23	r = 1.98467+	1.989521196	−4.85e-03	-0.244	behind	Found by Jake Loyd in June 2026.
Triangles in a circle	24	r = 2	2.017174420	−1.72e-02	-0.859	behind
Triangles in a circle	25	r = 2.055+	2.293554876	−2.39e-01	-11.609	behind	Found by David W. Cantrell in July 2005.
Triangles in a circle	26	r = 2.10664+	2.123819166	−1.72e-02	-0.815	behind	Found by Thomas Schadt in August 2026.
Triangles in a circle	27	r = 2.138+	2.297639709	−1.60e-01	-7.467	behind	Found by David W. Cantrell in July 2005.
Triangles in a circle	28	r = 2.18805+	2.291934827	−1.04e-01	-4.748	behind	Found by Thomas Schadt in August 2026.
Triangles in a circle	29	r = 2.20935+	2.378622597	−1.69e-01	-7.662	behind	Found by Jake Loyd in June 2026.
Triangles in a circle	30	r = 2.25124+	2.373894060	−1.23e-01	-5.448	behind	Found by Thomas Schadt in August 2026.
Triangles in a circle	31	r = 2.272+	2.297979887	−2.60e-02	-1.143	behind	Found by Maurizio Morandi in July 2008.
Triangles in a circle	32	r = 2.31295+	2.500492563	−1.88e-01	-8.108	behind	Found by Thomas Schadt in August 2026.
Triangles in a circle	33	r = 2.34169+	2.503360719	−1.62e-01	-6.904	behind	Found by Thomas Schadt in August 2026.
Triangles in a circle	34	r = 2.37504+	2.528099896	−1.53e-01	-6.445	behind	Found by Thomas Schadt in August 2026.
Triangles in a circle	35	r = 2.39906+	2.526071254	−1.27e-01	-5.294	behind	Found by Thomas Schadt in August 2026.
Triangles in a circle	36	r = 2.43969+	2.455129665	−1.54e-02	-0.633	behind	Found by Thomas Schadt in August 2026.
Triangles in a circle	37	r = 2.46349+	2.520059271	−5.66e-02	-2.296	behind	Found by Thomas Schadt in August 2026.
Triangles in a circle	38	r = 2.49003+	2.659013293	−1.69e-01	-6.786	behind	Found by Thomas Schadt in August 2026.
Triangles in a circle	39	r = 2.51938+	2.558120738	−3.87e-02	-1.538	behind	Found by Thomas Schadt in August 2026.
Triangles in a circle	40	r = 2.55675+	2.652385735	−9.56e-02	-3.741	behind	Found by Thomas Schadt in August 2026.
Triangles in a circle	41	r = 2.58629+	2.604958107	−1.87e-02	-0.722	behind	Found by Thomas Schadt in August 2026.
Triangles in a circle	42	r = 2.61145+	2.653029967	−4.16e-02	-1.592	behind	Found by Thomas Schadt in August 2026.
Triangles in a circle	43	r = 2.63998+	2.807165647	−1.67e-01	-6.333	behind	Found by Thomas Schadt in August 2026.
Triangles in a circle	44	r = 2.66620+	2.698836825	−3.26e-02	-1.224	behind	Found by Thomas Schadt in August 2026.
Triangles in a circle	45	r = 2.69809+	2.739751352	−4.17e-02	-1.544	behind	Found by Thomas Schadt in August 2026.
Triangles in a circle	46	r = 2.72457+	2.842261741	−1.18e-01	-4.320	behind	Found by Thomas Schadt in August 2026.
Triangles in a circle	47	r = 2.75037+	2.785123760	−3.48e-02	-1.264	behind	Found by Thomas Schadt in August 2026.
Triangles in a circle	48	r = 2.77672+	2.800826813	−2.41e-02	-0.868	behind	Found by Thomas Schadt in August 2026.
Triangles in a circle	49	r = 2.80521+	2.827161756	−2.20e-02	-0.783	behind	Found by Thomas Schadt in August 2026.
Triangles in a circle	50	r = 2.82736+	2.854818307	−2.75e-02	-0.971	behind	Found by Thomas Schadt in August 2026.
Triangles in a domino	2	s = √3/2	0.866025404	−3.46e-10	-0.000	reproduced
Triangles in a domino	3	s = .96796+	0.967967141	−7.14e-06	-0.001	reproduced	Found by Jonathan Viquerat in April 2026.
Triangles in a domino	4	s = 1.12036+	1.120369428	−9.43e-06	-0.001	reproduced	Found by Jonathan Viquerat in April 2026.
Triangles in a domino	5	s = 1.26315+	1.263157874	−7.87e-06	-0.001	reproduced	Found by Jonathan Viquerat in April 2026.
Triangles in a domino	6	s = 1.37629+	1.376305026	−1.50e-05	-0.001	behind	Found by Jonathan Viquerat in April 2026.
Triangles in a domino	7	s = 1.49076+	1.492220203	−1.46e-03	-0.098	behind	Found by Jonathan Viquerat in April 2026.
Triangles in a domino	8	s = 1.56293+	1.577894780	−1.50e-02	-0.957	behind	Found by Jonathan Viquerat in April 2026.
Triangles in a domino	9	s = 1.64882+	1.693300468	−4.45e-02	-2.698	behind	Found by Bhavithran Ananthan in July 2026.
Triangles in a domino	10	s = 1.68302+	1.719108930	−3.61e-02	-2.144	behind	Found by Aapo Lipponen in July 2026.
Triangles in a domino	11	s = 1.72971+	1.730010548	−3.01e-04	-0.017	behind	Found by Jonathan Viquerat in September 2026.
Triangles in a domino	12	s = 1.74022+	1.745279466	−5.06e-03	-0.291	behind	Found by Jonathan Viquerat in September 2026.
Triangles in a domino	13	s = 1.85319+	1.858381558	−5.19e-03	-0.280	behind	Found by Jonathan Viquerat in April 2026.
Triangles in a domino	14	s = 3(3–√3)/2 = 1.90192+	1.930064476	−2.81e-02	-1.480	behind	Found by Jonathan Viquerat in April 2026.
Triangles in a domino	15	s = 1.97950+	1.980796737	−1.30e-03	-0.066	behind	Found by Jonathan Viquerat in April 2026.
Triangles in a domino	16	s = 2	2.083207026	−8.32e-02	-4.160	behind	Found by Jonathan Viquerat in April 2026.
Triangles in a domino	17	s = 2.10306+	2.108552105	−5.49e-03	-0.261	behind	Found by Jonathan Viquerat in April 2026.
Triangles in a domino	18	s = 2.14913+	2.185604024	−3.65e-02	-1.697	behind	Found by Jonathan Viquerat in April 2026.
Triangles in a domino	19	s = 2.24322+	2.424977651	−1.82e-01	-8.103	behind	Found by Thomas Greenleaf in June 2026.
Triangles in a domino	20	s = 2.29729+	2.501300032	−2.04e-01	-8.880	behind	Found by Aapo Lipponen in July 2026.
Triangles in a domino	21	s = 2.36328+	2.537266136	−1.74e-01	-7.362	behind	Found by Thomas Greenleaf in June 2026.
Triangles in a domino	22	s = 2.42155+	2.600596702	−1.79e-01	-7.394	behind	Found by Jonathan Viquerat in September 2026.
Triangles in a domino	23	s = 2.45562+	2.601639619	−1.46e-01	-5.946	behind	Found by Jonathan Viquerat in September 2026.
Triangles in a domino	24	s = 2.48387+	2.493522297	−9.65e-03	-0.389	behind	Found by Jonathan Viquerat in September 2026.
Triangles in a domino	25	s = 2.52126+	2.619869549	−9.86e-02	-3.911	behind	Found by Jonathan Viquerat in September 2026.
Triangles in a hexagon	2	s = √3/2 = .866+	0.866025415	−1.14e-08	-0.000	reproduced
Triangles in a hexagon	3	s = √((6+√33)/12) = .989+	0.989299542	−1.53e-08	-0.000	reproduced	Found by Erich Friedman in April 2005.
Triangles in a hexagon	4	s = 1	1.000000000	−4.00e-10	-0.000	reproduced
Triangles in a hexagon	5	s = 1	1.000000000	−4.00e-10	-0.000	reproduced
Triangles in a hexagon	6	s = 1	1.000000000	−4.00e-10	-0.000	reproduced
Triangles in a hexagon	7	s = 1.277+	1.323873211	−4.69e-02	-3.671	behind	Found by David W. Cantrell in May 2005.
Triangles in a hexagon	8	s = 1.356+	1.359291669	−3.29e-03	-0.243	behind	Found by David W. Cantrell in July 2012.
Triangles in a hexagon	9	s = 1.434+	1.435739443	−1.74e-03	-0.121	behind	Found by Erich Friedman in April 2005.
Triangles in a hexagon	10	s = 1.497+	1.497049622	−4.96e-05	-0.003	reproduced	Found by Timo Berthold et al in January 2026.
Triangles in a hexagon	11	s = 3/2 = 1.500	1.538675402	−3.87e-02	-2.578	behind	Found by Erich Friedman in April 2005.
Triangles in a hexagon	12	s = 1.623+	1.629500260	−6.50e-03	-0.401	behind	Found by Timo Berthold et al in January 2026.
Triangles in a hexagon	13	s = √(587+51√17)/12√2 = 1.663829+	1.682474252	−1.86e-02	-1.121	behind	Found by Ian Watson in April 2026.
Triangles in a hexagon	14	s = 1.725+	1.736203802	−1.12e-02	-0.649	behind	Found by David W. Cantrell in August 2012.
Triangles in a hexagon	15	s = 7/4 = 1.750	1.833334030	−8.33e-02	-4.762	behind	Found by Erich Friedman in April 2005.
Triangles in a hexagon	16	s = 9/5 = 1.800	1.984239492	−1.84e-01	-10.236	behind	Found by Maurizio Morandi in April 2008.
Triangles in a hexagon	17	s = 11/6 = 1.833+	1.936298188	−1.03e-01	-5.617	behind	Found by Maurizio Morandi in April 2008.
Triangles in a hexagon	18	s = 17/9 = 1.888+	2.013486653	−1.25e-01	-6.599	behind	Found by Maurizio Morandi in April 2008.
Triangles in a hexagon	19	s = 1.953+	2.030463535	−7.75e-02	-3.966	behind	Found by Alex Adrián Nieto in April 2026.
Triangles in a hexagon	20	s = 1.97591+	2.014862326	−3.90e-02	-1.971	behind	Found by Aaden Abraham in April 2026.
Triangles in a hexagon	21	s = 1.99869+	2.037276498	−3.86e-02	-1.931	behind	Found by Haowei Lin in July 2026.
Triangles in a hexagon	22	s = 2	2.024941852	−2.49e-02	-1.247	behind
Triangles in a hexagon	23	s = 2	2.024886606	−2.49e-02	-1.244	behind
Triangles in a hexagon	24	s = 2	2.005069320	−5.07e-03	-0.253	behind
Triangles in a hexagon	25	s = 13/6 = 2.16666+	2.369602526	−2.03e-01	-9.366	behind	Found by Ignacio Vallejo in April 2026.
Triangles in a hexagon	26	s = 2.21991+	2.488956045	−2.69e-01	-12.120	behind	Found by Ian Watson in April 2026.
Triangles in a hexagon	27	s = 2.29540+	2.321522476	−2.61e-02	-1.138	behind	Found by Haowei Lin in July 2026.
Triangles in a hexagon	28	s = 2.32251+	2.509760049	−1.87e-01	-8.062	behind	Found by Jake Loyd in June 2026.
Triangles in a hexagon	29	s = 7/3 = 2.33333+	2.505569767	−1.72e-01	-7.382	behind	Found by Ignacio Vallejo in April 2026.
Triangles in a hexagon	30	s = 19/8 = 2.375	2.425186837	−5.02e-02	-2.113	behind	Found by Ignacio Vallejo in April 2026.
Triangles in a hexagon	31	s = 12/5 = 2.4	2.525110655	−1.25e-01	-5.213	behind	Found by Emerson Connelly in April 2026.
Triangles in a hexagon	32	s = 2.46104+	2.476981290	−1.59e-02	-0.648	behind	Found by Haowei Lin in July 2026.
Triangles in a hexagon	33	s = 2.49038+	2.674458587	−1.84e-01	-7.392	behind	Found by Jake Loyd in June 2026.
Triangles in a hexagon	34	s = 5/2 = 2.5	2.588930502	−8.89e-02	-3.557	reproduced	Found by Emerson Connelly in April 2026.
Triangles in a hexagon	35	s = 5/2 = 2.5	2.687681247	−1.88e-01	-7.507	behind	Found by Emerson Connelly in April 2026.
Triangles in a hexagon	36	s = 2.58307+	2.680097390	−9.70e-02	-3.756	behind	Found by Aristotle Papowitz in July 2026.
Triangles in a hexagon	37	s = 2.61436+	2.624780359	−1.04e-02	-0.399	behind	Found by Jake Loyd in June 2026.
Triangles in a hexagon	38	s = 2.65998+	2.721247662	−6.13e-02	-2.303	behind	Found by Jake Loyd in June 2026.
Triangles in a hexagon	39	s = 8/3 = 2.66666+	2.749739466	−8.31e-02	-3.115	behind	Found by Emerson Connelly in April 2026.
Triangles in a hexagon	40	s = 2.71131+	2.747496175	−3.62e-02	-1.335	behind	Found by Jake Loyd in June 2026.
Triangles in a hexagon	41	s = 2.73692+	2.803784243	−6.69e-02	-2.443	behind	Found by Jake Loyd in June 2026.
Triangles in a hexagon	42	s = 11/4 = 2.75	2.921976356	−1.72e-01	-6.254	behind	Found by Maurizio Morandi in May 2026.
Triangles in a hexagon	43	s = 14/5 =2.8	2.887427464	−8.74e-02	-3.122	reproduced	Found by Thomas Greenleaf in June 2026.
Triangles in a hexagon	44	s = 17/6 = 2.833+	2.934083891	−1.01e-01	-3.556	behind	Found by Emerson Connelly in May 2026.
Triangles in a hexagon	45	s = 17/6 = 2.833+	2.928084457	−9.48e-02	-3.345	behind	Found by Emerson Connelly in May 2026.
Triangles in a hexagon	46	s = 2.88830+	2.962396157	−7.41e-02	-2.565	behind	Found by Jake Loyd in June 2026.
Triangles in a hexagon	47	s = 35/12 = 2.917+	2.944404609	−2.77e-02	-0.951	behind	Found by Emerson Connelly in May 2026.
Triangles in a hexagon	48	s = 47/16 =2.9375	3.016661043	−7.92e-02	-2.695	behind	Found by Thomas Greenleaf in June 2026.
Triangles in a hexagon	49	s = 2.97693+	3.020148007	−4.32e-02	-1.452	behind	Found by Thomas Greenleaf in June 2026.
Triangles in a hexagon	50	s = 3	2.999355618	+6.44e-04	0.021	beaten
Triangles in a hexagon	51	s = 3	3.008688413	−8.69e-03	-0.290	behind
Triangles in a hexagon	52	s = 3	3.033233800	−3.32e-02	-1.108	behind
Triangles in a hexagon	53	s = 3	3.011346630	−1.13e-02	-0.378	behind
Triangles in a hexagon	54	s = 3	3.016921735	−1.69e-02	-0.564	behind
Triangles in a pentagon	2	s = √(6/(3+√5)) s = 1.070+	1.070466283	−1.36e-08	-0.000	reproduced
Triangles in a pentagon	3	s = 1.143+	1.143516936	−5.17e-04	-0.045	reproduced	Found by Maurizio Morandi in August 2012.
Triangles in a pentagon	4	s = 1.199+	1.199266482	−2.66e-04	-0.022	reproduced	Found by Maurizio Morandi in July 2012.
Triangles in a pentagon	5	s = 1 + 2sin(12°)/√3 s = 1.240+	1.240075764	−7.58e-05	-0.006	reproduced	Found by Erich Friedman in March 2012.
Triangles in a pentagon	6	s = 1.393+	1.393620342	−6.20e-04	-0.045	reproduced	Found by Dominik Kamp in April 2026.
Triangles in a pentagon	7	s = 1.581+	1.633913311	−5.29e-02	-3.347	behind	Found by David W. Cantrell in July 2012.
Triangles in a pentagon	8	s = 1.659+	1.659337866	−3.38e-04	-0.020	reproduced	Found by Maurizio Morandi in July 2012.
Triangles in a pentagon	9	s = 1.767+	1.769616105	−2.62e-03	-0.148	behind	Found by Maurizio Morandi in July 2012. Improved slightly by David W. Cantrell in August 2012.
Triangles in a pentagon	10	s = 1.815+	1.852813440	−3.78e-02	-2.083	behind	Found by Timo Berthold et al in January 2026.
Triangles in a pentagon	11	s = 1.871+	1.873483094	−2.48e-03	-0.133	behind	Found by Timo Berthold et al in January 2026.
Triangles in a pentagon	12	s = 1.973+	2.001972361	−2.90e-02	-1.468	behind	Found by Ignacio Vallejo in March 2026.
Triangles in a pentagon	13	s = 2.017+	2.021738631	−4.74e-03	-0.235	behind	Found by Timo Berthold et al in January 2026.
Triangles in a pentagon	14	s = 2.088+	2.092245507	−4.25e-03	-0.203	behind	Found by Ignacio Vallejo in April 2026.
Triangles in a pentagon	15	s = 2.123+	2.177914918	−5.49e-02	-2.587	behind	Found by Ignacio Vallejo in March 2026.
Triangles in a pentagon	16	s = 2.17596+	2.180115810	−4.16e-03	-0.191	behind	Found by Jake Loyd in June 2026.
Triangles in a pentagon	17	s = 2.23656+	2.457135273	−2.21e-01	-9.862	behind	Found by Jake Loyd in June 2026.
Triangles in a pentagon	18	s = 2.29381+	2.500196039	−2.06e-01	-8.998	behind	Found by Jake Loyd in June 2026.
Triangles in a pentagon	19	s = 2.344+	2.357099469	−1.31e-02	-0.559	behind	Found by Ignacio Vallejo in March 2026.
Triangles in a pentagon	20	s = 2.43345+	2.638116294	−2.05e-01	-8.411	behind	Found by Jake Loyd in June 2026.
Triangles in a pentagon	21	s = 2.479+	2.724816658	−2.46e-01	-9.916	behind	Found by Ignacio Vallejo in March 2026.
Triangles in a pentagon	22	s = 2.56740+	2.747701985	−1.80e-01	-7.023	behind	Found by Ian Watson in April 2026.
Triangles in a pentagon	23	s = 2.61825+	2.819142309	−2.01e-01	-7.673	behind	Found by Jake Loyd in June 2026.
Triangles in a pentagon	24	s = 2.66641+	2.716604520	−5.02e-02	-1.882	behind	Found by Ian Watson in April 2026.
Triangles in a pentagon	25	s = 2.71860+	2.761110703	−4.25e-02	-1.564	behind	Found by Jake Loyd in June 2026.
Triangles in a pentagon	26	s = 2.76865+	3.005496731	−2.37e-01	-8.555	behind	Found by Jake Loyd in June 2026.
Triangles in a pentagon	27	s = 2.81741+	3.065796954	−2.48e-01	-8.816	behind	Found by Jake Loyd in June 2026.
Triangles in a pentagon	28	s = 2.86636+	3.107115287	−2.41e-01	-8.399	behind	Found by Aristotle Papowitz in July 2026.
Triangles in a pentagon	29	s = 2.90240+	2.939073459	−3.67e-02	-1.264	behind	Found by Aristotle Papowitz in July 2026.
Triangles in a pentagon	30	s = 2.95014+	3.135604733	−1.85e-01	-6.287	behind	Found by Aristotle Papowitz in July 2026.
Triangles in a pentagon	31	s = 2.98366+	3.209763990	−2.26e-01	-7.578	behind	Found by Jake Loyd in June 2026.
Triangles in a pentagon	32	s = 3.02686+	3.220653002	−1.94e-01	-6.402	behind	Found by Jake Loyd in June 2026.
Triangles in a pentagon	33	s = 3.06583+	3.284466901	−2.19e-01	-7.131	behind	Found by Jake Loyd in June 2026.
Triangles in a pentagon	34	s = 3.11073+	3.423547553	−3.13e-01	-10.056	behind	Found by Aristotle Papowitz in July 2026.
Triangles in a pentagon	35	s = 3.14843+	3.214641893	−6.62e-02	-2.103	behind	Found by Aristotle Papowitz in July 2026.
Triangles in a pentagon	36	s = 3.17473+	3.493379847	−3.19e-01	-10.037	behind	Found by Aristotle Papowitz in July 2026.
Triangles in a pentagon	37	s = 3.21120+	3.313209733	−1.02e-01	-3.177	behind	Found by Jake Loyd in June 2026.
Triangles in a pentagon	38	s = 3.24851+	3.529893689	−2.81e-01	-8.662	behind	Found by Jake Loyd in June 2026.
Triangles in a pentagon	39	s = 3.29219+	3.380625198	−8.84e-02	-2.686	behind	Found by Jake Loyd in June 2026.
Triangles in a pentagon	40	s = 3.32605+	3.569264393	−2.43e-01	-7.312	behind	Found by Jake Loyd in June 2026.
Triangles in a pentagon	41	s = 3.36740+	3.719539891	−3.52e-01	-10.457	behind	Found by Thomas Greenleaf in June 2026.
Triangles in a pentagon	42	s = 3.42505+	3.510178518	−8.51e-02	-2.485	behind	Found by Aristotle Papowitz in July 2026.
Triangles in a pentagon	43	s = 3.46433+	3.560719198	−9.64e-02	-2.782	behind	Found by Aristotle Papowitz in July 2026.
Triangles in a pentagon	44	s = 3.51261+	3.567905542	−5.53e-02	-1.574	behind	Found by Emerson Connelly in May 2026.
Triangles in a pentagon	45	s = 3.51261+	3.835661562	−3.23e-01	-9.197	behind	Found by Emerson Connelly in May 2026.
Triangles in a pentagon	46	s = 3.61491+	3.819481681	−2.05e-01	-5.659	behind	Found by Emerson Connelly in May 2026.
Triangles in a pentagon	47	s = 3.65879+	3.731906191	−7.31e-02	-1.998	behind	Found by Aapo Lipponen in July 2026.
Triangles in a pentagon	48	s = 3.67605+	3.910834665	−2.35e-01	-6.387	behind	Found by Thomas Greenleaf in June 2026.
Triangles in a pentagon	49	s = 3.72296+	3.805205449	−8.22e-02	-2.209	behind	Found by Emerson Connelly in May 2026.
Triangles in a pentagon	50	s = 3.75988+	3.845433192	−8.56e-02	-2.275	behind	Found by Emerson Connelly in May 2026.
Triangles in a square	2	s = √6/2 = 1.224+	1.224744896	−2.48e-08	-0.000	reproduced
Triangles in a square	3	s = √3/2+√6/4 = 1.478+	1.478397856	−1.67e-08	-0.000	reproduced	Found by Erich Friedman in 1996.
Triangles in a square	4	s = 1+1/√3 = 1.577+	1.577350270	−6.31e-10	-0.000	reproduced	Found by Erich Friedman in 1996.
Triangles in a square	5	s = 1.803+	1.803169109	−1.69e-04	-0.009	reproduced	Found by Erich Friedman in 1996.
Triangles in a square	6	s = 9/2–3√3/2 = 1.901+	1.919465812	−1.75e-02	-0.923	behind	Found by Erich Friedman in 1996.
Triangles in a square	7	s = 2	2.000000036	−3.58e-08	-0.000	reproduced	Found by Erich Friedman in 1996.
Triangles in a square	8	s = 3√3/2–1/2 = 2.098+	2.224624559	−1.27e-01	-6.032	behind	Found by Erich Friedman in 1996.
Triangles in a square	9	s = 2.287+	2.289266167	−2.27e-03	-0.099	behind	Found by Maurizio Morandi in July 2008.
Triangles in a square	10	s = 2.377+	2.463731018	−8.67e-02	-3.649	behind	Found by David W. Cantrell in July 2002.
Triangles in a square	11	s = 2.490+	2.498910774	−8.91e-03	-0.358	behind	Found by Maurizio Morandi in June 2008.
Triangles in a square	12	s = 2.558+	2.569612422	−1.16e-02	-0.454	behind	Found by Dominik Kamp in April 2026.
Triangles in a square	13	s = 2.595+	2.598870074	−3.87e-03	-0.149	behind	Found by David W. Cantrell in July 2002.
Triangles in a square	14	s = 2.726+	2.731820858	−5.82e-03	-0.214	behind	Found by David W. Cantrell in July 2002.
Triangles in a square	15	s = 2.82989+	2.839786596	−9.90e-03	-0.350	behind	Found by Jake Loyd in June 2026.
Triangles in a square	16	s = 2.9000+	2.944314789	−4.43e-02	-1.528	behind	Found by Ian Watson in April 2026.
Triangles in a square	17	s = 2.982+	3.025526130	−4.35e-02	-1.460	behind	Found by Maurizio Morandi in July 2008.
Triangles in a square	18	s = 3.051+	3.302796281	−2.52e-01	-8.253	behind	Found by Maurizio Morandi in July 2008.
Triangles in a square	19	s = 3.12929+	3.411704712	−2.82e-01	-9.025	behind	Found by Jake Loyd in June 2026.
Triangles in a square	20	s = 3.2305+	3.381776958	−1.51e-01	-4.683	behind	Found by Ian Watson in April 2026.
Triangles in a square	21	s = 3.31102+	3.505678971	−1.95e-01	-5.879	behind	Found by Thomas Schadt in June 2026.
Triangles in a square	22	s = 3.3757+	3.554802921	−1.79e-01	-5.306	behind	Found by Ian Watson in April 2026.
Triangles in a square	23	s = 3.4311+	3.548703081	−1.18e-01	-3.428	behind	Found by Ian Watson in April 2026.
Triangles in a square	24	s = 3.46780+	3.513278815	−4.55e-02	-1.311	behind	Found by Thomas Schadt in June 2026.
Triangles in a square	25	s = 3.537+	3.893713646	−3.57e-01	-10.085	behind	Found by David W. Cantrell in August 2012.
Triangles in a square	26	s = 3.575+	3.984607941	−4.10e-01	-11.458	behind	Found by Maurizio Morandi in September 2008.
Triangles in a square	27	s = 3.6726+	4.014139333	−3.42e-01	-9.300	behind	Found by Ian Watson in April 2026.
Triangles in a square	28	s = 3.75707+	4.019373683	−2.62e-01	-6.982	behind	Found by Jake Loyd in June 2026.
Triangles in a square	29	s = 3.81711+	4.315022684	−4.98e-01	-13.044	behind	Found by Jake Loyd in June 2026.
Triangles in a square	30	s = 3.86619+	4.269536507	−4.03e-01	-10.433	behind	Found by Jake Loyd in June 2026.
Triangles in a square	31	s = 3.93107+	4.033466368	−1.02e-01	-2.605	behind	Found by Jake Loyd in June 2026.
Triangles in a square	32	s = 3.97880+	4.342155148	−3.63e-01	-9.132	behind	Found by Jake Loyd in June 2026.
Triangles in a square	33	s = 4.05164+	4.290365125	−2.39e-01	-5.892	behind	Found by Jake Loyd in June 2026.
Triangles in a square	34	s = 4.09088+	4.192091411	−1.01e-01	-2.474	behind	Found by Jake Loyd in June 2026.
Triangles in a square	35	s = 4.14123+	4.331232354	−1.90e-01	-4.588	behind	Found by Jake Loyd in June 2026.
Triangles in a square	36	s = 4.20791+	4.261177864	−5.33e-02	-1.266	behind	Found by Jake Loyd in June 2026.
Triangles in a square	37	s = 4.26872+	4.508744211	−2.40e-01	-5.623	behind	Found by Thomas Schadt in July 2026.
Triangles in a square	38	s = 4.32008+	4.419880603	−9.98e-02	-2.310	behind	Found by Thomas Schadt in July 2026.
Triangles in a square	39	s = 4.36792+	4.440336806	−7.24e-02	-1.658	behind	Found by Jake Loyd in June 2026.
Triangles in a square	40	s = 4.41057+	4.452001968	−4.14e-02	-0.939	behind	Found by Thomas Schadt in July 2026.
Triangles in a square	41	s = 4.46431+	4.567511644	−1.03e-01	-2.312	behind	Found by Thomas Schadt in July 2026.
Triangles in a square	42	s = 4.51172+	4.615238222	−1.04e-01	-2.294	behind	Found by Thomas Schadt in July 2026.
Triangles in a square	43	s = 4.55033+	4.714954195	−1.65e-01	-3.618	behind	Found by Thomas Schadt in June 2026.
Triangles in a square	44	s = 4.60023+	5.010070027	−4.10e-01	-8.909	behind	Found by Thomas Schadt in June 2026.
Triangles in a square	45	s = 4.67745+	4.774855941	−9.74e-02	-2.082	behind	Found by Thomas Schadt in June 2026.
Triangles in a square	46	s = 4.72960+	5.195973433	−4.66e-01	-9.861	behind	Found by Thomas Schadt in June 2026.
Triangles in a square	47	s = 4.78204+	5.197357023	−4.15e-01	-8.685	behind	Found by Thomas Schadt in June 2026.
Triangles in a square	48	s = 4.82632+	5.080159701	−2.54e-01	-5.259	behind	Found by Thomas Schadt in June 2026.
Triangles in a square	49	s = 4.87132+	5.198058629	−3.27e-01	-6.707	behind	Found by Thomas Schadt in June 2026.
Triangles in a square	50	s = 4.92191+	5.066031565	−1.44e-01	-2.928	behind	Found by Thomas Schadt in June 2026.
Triangles in a tan	2	s = √3 = 1.73205+	1.732050808	−6.93e-10	-0.000	reproduced
Triangles in a tan	3	s = (√3+1)/√2 = 1.93185+	1.931851653	−7.73e-10	-0.000	reproduced
Triangles in a tan	4	s = (3+√3)/2 = 2.36602+	2.366025422	−1.78e-08	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Triangles in a tan	5	s = (3√2+√6+2√3)/4 = 2.53905+	2.539058053	−4.13e-08	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Triangles in a tan	6	s = √2+√(3/2) = 2.63895+	2.638958446	−1.21e-08	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Triangles in a tan	7	s = 2.78972+	2.789728398	−8.40e-06	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Triangles in a tan	8	s = 3.07313+	3.156596587	−8.35e-02	-2.716	behind	Found by Jonathan Viquerat in May 2026.
Triangles in a tan	9	s = 3.18252+	3.267161840	−8.46e-02	-2.660	behind	Found by Jonathan Viquerat in May 2026.
Triangles in a tan	10	s = 3.34084+	3.345955845	−5.12e-03	-0.153	behind	Found by Jonathan Viquerat in May 2026.
Triangles in a tan	11	s = 3.46951+	3.575877864	−1.06e-01	-3.066	behind	Found by Jonathan Viquerat in May 2026.
Triangles in a tan	12	s = 3.62487+	3.635081021	−1.02e-02	-0.282	behind	Found by Bhavithran Ananthan in July 2026.
Triangles in a tan	13	s = 3.71163+	4.009754605	−2.98e-01	-8.032	behind	Found by Jonathan Viquerat in May 2026.
Triangles in a tan	14	s = 3.88268+	4.137265158	−2.55e-01	-6.557	behind	Found by Jonathan Viquerat in May 2026.
Triangles in a tan	15	s = 3.98382+	3.994828458	−1.10e-02	-0.276	behind	Found by Thomas Greenleaf in June 2026.
Triangles in a tan	16	s = 4.03901+	4.500073861	−4.61e-01	-11.415	behind	Found by Thomas Greenleaf in June 2026.
Triangles in a tan	17	s = 4.20066+	4.240875133	−4.02e-02	-0.957	behind	Found by Jonathan Viquerat in September 2026.
Triangles in a tan	18	s = 4.27120+	4.504224902	−2.33e-01	-5.456	behind	Found by Thomas Greenleaf in June 2026.
Triangles in a tan	19	s = 4.45701+	4.709635512	−2.53e-01	-5.668	behind	Found by Thomas Greenleaf in June 2026.
Triangles in a tan	20	s = 4.56124+	4.569023563	−7.78e-03	-0.171	behind	Found by Bhavithran Ananthan in July 2026.
Triangles in a tan	21	s = 4.64141+	5.049009415	−4.08e-01	-8.782	behind	Found by Akshaj Shandilya in July 2026.
Triangles in a tan	22	s = 4.73276+	4.748527409	−1.58e-02	-0.333	behind	Found by Akshaj Shandilya in July 2026.
Triangles in a tan	23	s = 4.82958+	5.301254194	−4.72e-01	-9.766	behind	Found by Jonathan Viquerat in September 2026.
Triangles in a tan	24	s = 4.88409+	5.389725707	−5.06e-01	-10.353	behind	Found by Jonathan Viquerat in September 2026.
Triangles in a tan	25	s = 5.02418+	5.121649609	−9.75e-02	-1.940	behind	Found by Jonathan Viquerat in September 2026.
Triangles in a tan	26	s = 5.10960+	5.660837548	−5.51e-01	-10.788	behind	Found by Akshaj Shandilya in July 2026.
Triangles in a tan	27	s = 5.19773+	5.344982967	−1.47e-01	-2.833	behind	Found by Akshaj Shandilya in July 2026.
Triangles in a tan	28	s = 5.32367+	5.886567004	−5.63e-01	-10.573	behind	Found by Akshaj Shandilya in July 2026.
Triangles in a tan	29	s = 5.39194+	5.895520742	−5.04e-01	-9.340	behind	Found by Found by Jonathan Viquerat in September 2026.
Triangles in a tan	30	s = 5.46057+	5.555979684	−9.54e-02	-1.747	behind	Found by Found by Jonathan Viquerat in September 2026.
Triangles in a triangle	2	s = 2	2.000000001	−8.00e-10	-0.000	reproduced
Triangles in a triangle	3	s = 2	2.000000001	−8.00e-10	-0.000	reproduced
Triangles in a triangle	4	s = 2	2.000000001	−8.00e-10	-0.000	reproduced
Triangles in a triangle	6	s = 13/8 + 3√13/8 = 2.977+	2.977081784	−5.58e-08	-0.000	reproduced	Found by Maurizio Morandi in August 2008.
Triangles in a triangle	7	s = 3	3.000000001	−1.20e-09	-0.000	reproduced
Triangles in a triangle	8	s = 3	3.000000001	−1.20e-09	-0.000	reproduced
Triangles in a triangle	9	s = 3	3.019078613	−1.91e-02	-0.636	behind
Triangles in a triangle	10	s = 7/2 = 3.5	3.500000660	−6.60e-07	-0.000	reproduced	Found by Erich Friedman in 1997.
Triangles in a triangle	11	s = 9/4 + 9√21/28 = 3.722+	3.914702802	−1.92e-01	-5.151	behind	Found by Erich Friedman in 1997.
Triangles in a triangle	12	s = 2 + 2cos(π/9) = 3.879+	4.000006947	−1.21e-01	-3.120	behind	Found by David W. Cantrell in July 2007.
Triangles in a triangle	13	s = 3.992+	4.034847136	−4.28e-02	-1.073	behind	Found by Maurizio Morandi in May 2008.
Triangles in a triangle	14	s = 4	4.000000002	−1.61e-09	-0.000	reproduced
Triangles in a triangle	15	s = 4	4.004188237	−4.19e-03	-0.105	behind
Triangles in a triangle	16	s = 4	4.000705785	−7.06e-04	-0.018	behind
Triangles in a triangle	17	s = 4.465+	4.907462936	−4.42e-01	-9.910	behind	Found by Maurizio Morandi in May 2008.
Triangles in a triangle	18	s = 9/2 = 4.5	4.509380491	−9.38e-03	-0.208	reproduced	Found by Erich Friedman in 1997.
Triangles in a triangle	19	s = 14/3 = 4.666+	5.037444734	−3.71e-01	-7.946	behind	Found by Maurizio Morandi in May 2008.
Triangles in a triangle	20	s = 33/8 + 9√21/56 = 4.861+	5.052836292	−1.91e-01	-3.936	behind	Found by Maurizio Morandi in May 2008.
Triangles in a triangle	21	s = 4.923+	5.083722668	−1.61e-01	-3.265	behind	Found by Maurizio Morandi in May 2008.
Triangles in a triangle	22	s = 4.996+	5.009693136	−1.37e-02	-0.274	behind	Found by Maurizio Morandi in May 2008.
Triangles in a triangle	23	s = 5	5.001214387	−1.21e-03	-0.024	behind
Triangles in a triangle	24	s = 5	5.074434771	−7.44e-02	-1.489	behind
Triangles in a triangle	25	s = 5	5.000834280	−8.34e-04	-0.017	behind
Triangles in a triangle	26	s = 5.406+	6.056733033	−6.51e-01	-12.037	behind	Found by Joah Frenzley in April 2026.
Triangles in a triangle	27	s = 11/2 = 5.5	6.082965347	−5.83e-01	-10.599	behind	Found by Erich Friedman in 1997.
Triangles in a triangle	28	s = 11/2 = 5.5	6.088161692	−5.88e-01	-10.694	behind	Found by Erich Friedman in 1997.
Triangles in a triangle	29	s = 17/3 = 5.666+	6.064777230	−3.98e-01	-7.026	behind	Found by David W. Cantrell in July 2007.
Triangles in a triangle	30	s = 23/4 = 5.75	6.088493934	−3.38e-01	-5.887	behind	Found by Maurizio Morandi in May 2008.
Triangles in a triangle	31	s = 5.90766+	6.115278619	−2.08e-01	-3.514	behind	Found by Thomas Schadt in June 2026.
Triangles in a triangle	32	s = 5.94593+	6.046561339	−1.01e-01	-1.692	behind	Found by Maurizio Morandi in May 2026.
Triangles in a triangle	33	s = 5.99759+	6.011781171	−1.42e-02	-0.237	behind	Found by Maurizio Morandi in June 2026.
Triangles in a triangle	34	s = 6	6.014282296	−1.43e-02	-0.238	behind
Triangles in a triangle	35	s = 6	6.160243934	−1.60e-01	-2.671	behind
Triangles in a triangle	36	s = 6	6.171116757	−1.71e-01	-2.852	behind
Triangles in a triangle	37	s = 19/3 = 6.333+	7.023639648	−6.90e-01	-10.900	behind	Found by Ian Watson in April 2026.
Triangles in a triangle	38	s = 6.42823+	6.564569889	−1.36e-01	-2.121	behind	Found by Thomas Schadt in June 2026.
Triangles in a triangle	39	s = 13/2 = 6.5	7.058360002	−5.58e-01	-8.590	behind	Found by Erich Friedman in April 2026.
Triangles in a triangle	40	s = 13/2 = 6.5	6.862321792	−3.62e-01	-5.574	behind	Found by Erich Friedman in April 2026.
Triangles in a triangle	41	s = 20/3 = 6.666+	7.013992339	−3.47e-01	-5.210	behind	Found by Emerson Connelly in May 2026.
Triangles in a triangle	42	s = 27/4 = 6.75	6.793316114	−4.33e-02	-0.642	behind	Found by Emerson Connelly in May 2026.
Triangles in a triangle	43	s = 34/5 = 6.8	7.053915075	−2.54e-01	-3.734	behind	Found by Emerson Connelly in May 2026.
Triangles in a triangle	44	s = 6.93076+	7.020707187	−8.99e-02	-1.298	behind	Found by Thomas Schadt in June 2026.
Triangles in a triangle	45	s = 6.95922+	7.021285800	−6.21e-02	-0.892	behind	Found by Maurizio Morandi in May 2026.
Triangles in a triangle	46	s = 6.99837+	7.022019976	−2.36e-02	-0.338	behind	Found by Maurizio Morandi in June 2026.
Triangles in a triangle	47	s = 7	7.020760072	−2.08e-02	-0.297	behind
Triangles in a triangle	48	s = 7	7.026659126	−2.67e-02	-0.381	behind
Triangles in a triangle	49	s = 7	7.205708941	−2.06e-01	-2.939	behind
Triangles in a triangle	50	s = 7 + √21/14 = 7.32732+	8.020720352	−6.93e-01	-9.463	behind	Found by Maurizio Morandi in May 2026.
Triangles in an L	2	s = √3/2 = .86602+	0.866025404	−3.46e-10	-0.000	reproduced
Triangles in an L	3	s = √3/2 = .86602+	0.866025404	−3.46e-10	-0.000	reproduced
Triangles in an L	4	s = .92423+	0.924231435	−1.44e-06	-0.000	reproduced	Found by Jonathan Viquerat in June 2026.
Triangles in an L	5	s = 1	1.000000018	−1.79e-08	-0.000	reproduced	Found by Jonathan Viquerat in June 2026.
Triangles in an L	6	s = 1.12037+	1.125906072	−5.54e-03	-0.494	behind	Found by Jonathan Viquerat in June 2026.
Triangles in an L	7	s = 1.17127+	1.223528562	−5.23e-02	-4.462	behind	Found by Jonathan Viquerat in June 2026.
Triangles in an L	8	s = 1.27527+	1.300648725	−2.54e-02	-1.990	behind	Found by Jonathan Viquerat in June 2026.
Triangles in an L	9	s = 1.32893+	1.356526897	−2.76e-02	-2.077	behind	Found by Jonathan Viquerat in June 2026.
Triangles in an L	10	s = 1.39370+	1.396649254	−2.95e-03	-0.212	behind	Found by Jonathan Viquerat in June 2026.
Triangles in an L	11	s = 1.46116+	1.535195347	−7.40e-02	-5.067	behind	Found by Jonathan Viquerat in June 2026.
Triangles in an L	12	s = 3/2 = 1.5	1.501911067	−1.91e-03	-0.127	reproduced	Found by Jonathan Viquerat in June 2026.
Triangles in an L	13	s = 1.56571+	1.705853189	−1.40e-01	-8.951	behind	Found by Jonathan Viquerat in June 2026.
Triangles in an L	14	s = 1.62225+	1.700919893	−7.87e-02	-4.849	behind	Found by Jonathan Viquerat in June 2026.
Triangles in an L	15	s = 1.68012+	1.717661220	−3.75e-02	-2.234	behind	Found by Jonathan Viquerat in June 2026.
Triangles in an L	16	s = 1.72307+	1.728376399	−5.31e-03	-0.308	behind	Found by Jonathan Viquerat in June 2026.
Triangles in an L	17	s = 1.73204+	1.920072632	−1.88e-01	-10.856	behind	Found by Jonathan Viquerat in June 2026.
Triangles in an L	18	s = 1.75029+	1.786626398	−3.63e-02	-2.076	behind	Found by Jonathan Viquerat in June 2026.
Triangles in an L	19	s = 1.82181+	1.977609146	−1.56e-01	-8.552	behind	Found by Jonathan Viquerat in June 2026.
Triangles in an L	20	s = 1.86706+	1.873718913	−6.66e-03	-0.357	behind	Found by Jonathan Viquerat in June 2026.
Triangles in an octagon	2	s = √3/√(4+2√2) = .66282+	0.662827157	−8.60e-09	-0.000	reproduced
Triangles in an octagon	3	s = .73651+	0.736539682	−2.97e-05	-0.004	behind	Found by Ignacio Vallejo in March 2026.
Triangles in an octagon	4	s = .77731+	0.777317157	−7.16e-06	-0.001	reproduced	Found by Timo Berthold et al in May 2026.
Triangles in an octagon	5	s = .80366+	0.803666304	−6.30e-06	-0.001	reproduced	Found by Nicolas Campailla in May 2026.
Triangles in an octagon	6	s = .81574+	0.824455477	−8.72e-03	-1.068	behind	Found by Ignacio Vallejo in March 2026.
Triangles in an octagon	7	s = .92453+	0.969932888	−4.54e-02	-4.911	behind	Found by Ignacio Vallejo in March 2026.
Triangles in an octagon	8	s = .98777+	0.988425486	−6.55e-04	-0.066	behind	Found by Timo Berthold et al in May 2026.
Triangles in an octagon	9	s = 1.00871+	1.066916270	−5.82e-02	-5.770	behind	Found by Grant Mowry in April 2026.
Triangles in an octagon	10	s = 1.07515+	1.134919590	−5.98e-02	-5.559	behind	Found by Jake Loyd in May 2026.
Triangles in an octagon	11	s = 1.14562+	1.146569577	−9.50e-04	-0.083	behind	Found by Grant Mowry in April 2026.
Triangles in an octagon	12	s = 1.19914+	1.228581139	−2.94e-02	-2.455	behind	Found by Timo Berthold et al in May 2026.
Triangles in an octagon	13	s = 1.23726+	1.249880337	−1.26e-02	-1.020	behind	Found by Jake Loyd in June 2026.
Triangles in an octagon	14	s = 1.27629+	1.278947709	−2.66e-03	-0.208	behind	Found by Jake Loyd in June 2026.
Triangles in an octagon	15	s = 1.30240+	1.305677155	−3.28e-03	-0.252	behind	Found by Timo Berthold et al in May 2026.
Triangles in an octagon	16	s = 1.34566+	1.395743971	−5.01e-02	-3.722	behind	Found by Jake Loyd in June 2026.
Triangles in an octagon	17	s = 1.38854+	1.391069779	−2.53e-03	-0.182	behind	Found by Jake Loyd in June 2026.
Triangles in an octagon	18	s = 1.41763+	1.507982700	−9.04e-02	-6.374	behind	Found by Jake Loyd in June 2026.
Triangles in an octagon	19	s = 1.46678+	1.568773516	−1.02e-01	-6.954	behind	Found by Jake Loyd in June 2026.
Triangles in an octagon	20	s = 1.49689+	1.579385911	−8.25e-02	-5.511	behind	Found by Jake Loyd in June 2026.
Triangles in an octagon	21	s = 1.52519+	1.538065539	−1.29e-02	-0.844	behind	Found by Jake Loyd in June 2026.
Triangles in an octagon	22	s = 1.55435+	1.625824716	−7.15e-02	-4.598	behind	Found by Jake Loyd in June 2026.
Triangles in an octagon	23	s = 1.58348+	1.662261376	−7.88e-02	-4.975	behind	Found by Jake Loyd in June 2026.
Triangles in an octagon	24	s = 1.60180+	1.657214572	−5.54e-02	-3.460	behind	Found by Jake Loyd in June 2026.
Triangles in an octagon	25	s = 1.63703+	1.801539545	−1.65e-01	-10.049	behind	Found by Jake Loyd in June 2026.
Triangles in an octagon	26	s = 1.67455+	1.700087511	−2.55e-02	-1.525	behind	Found by Jake Loyd in June 2026.
Triangles in an octagon	27	s = 1.70616+	1.731187639	−2.50e-02	-1.467	behind	Found by Jake Loyd in June 2026.
Triangles in an octagon	28	s = 1.73796+	1.812222981	−7.43e-02	-4.273	behind	Found by Jake Loyd in June 2026.
Triangles in an octagon	29	s = 1.75285+	1.770836712	−1.80e-02	-1.026	behind	Found by Jake Loyd in June 2026.
Triangles in an octagon	30	s = 1.77911+	1.863331625	−8.42e-02	-4.734	behind	Found by Jake Loyd in June 2026.
Triangles in an octagon	31	s = 1.80338+	1.913852407	−1.10e-01	-6.126	behind	Found by Aristotle Papowitz in July 2026.
Triangles in an octagon	32	s = 1.82994+	1.839199819	−9.26e-03	-0.506	behind	Found by Aristotle Papowitz in July 2026.
Triangles in an octagon	33	s = 1.84789+	1.939430314	−9.15e-02	-4.954	behind	Found by Aristotle Papowitz in July 2026.
Triangles in an octagon	34	s = 1.86454+	1.889661587	−2.51e-02	-1.347	behind	Found by Aristotle Papowitz in July 2026.
Triangles in an octagon	35	s = 1.89051+	1.924680673	−3.42e-02	-1.807	behind	Found by Aristotle Papowitz in July 2026.
Triangles in an octagon	36	s = 1.92667+	1.974396302	−4.77e-02	-2.477	behind	Found by Aristotle Papowitz in July 2026.
Triangles in an octagon	37	s = 1.95615+	1.995255032	−3.91e-02	-1.999	behind	Found by Aristotle Papowitz in July 2026.
No cases match this filter.

Data as of 2026-09-13 17:36 UTC. Every value is certified by an independent validator; none is a claim of optimality. Nothing has been submitted to the page.