Tans in Triangles

The following pictures show n tans (with short side 1) packed inside the smallest known equilateral triangle (with side s).

1.

s = √2 = 1.41421+
Trivial. 		           2.

s = (1+√3)/√2 = 1.93185+
Trivial. 		           3.

s = 3/√2 = 2.12132+
Trivial.

4.

s = 2.53732+
Found by Jonathan Viquerat
in May 2026. 		           5.

s = 2.74147+
Found by Jonathan Viquerat
in May 2026. 		           6.

s = 2.93781+
Found by Jonathan Viquerat
in May 2026.
7.

s = 3.17427+
Found by Jonathan Loyd
in June 2026. 		           8.

s = 3.35224+
Found by Jonathan Viquerat
in May 2026. 		           9.

s = 3.51439+
Found by Jonathan Loyd
in June 2026.
10.

s = 3.69367+
Found by Aapo Lipponen
in July 2026. 		           11.

s = 3.82731+
Found by Jonathan Loyd
in June 2026. 		           12.

s = 4
Found by Jonathan Loyd
in June 2026.
13.

s = 4.14927+
Found by Jonathan Loyd
in June 2026. 		           14.

s = 4.29538+
Found by Jonathan Loyd
in June 2026. 		           15.

s = 4.41075+
Found by Joshua Wolk
in September 2026.
16.

s = 4.57988+
Found by Joshua Wolk
in September 2026. 		           17.

s = 4.70881+
Found by Yanis Gomes
in October 2026. 		           18.

s = 4.82316+
Found by Yanis Gomes
in October 2026.
19.

s = 4.94492+
Found by Joshua Wolk
in September 2026. 		           20.

s = 5.06281+
Found by Joshua Wolk
in September 2026. 		           21.

s = 5.18862+
Found by Yanis Gomes
in October 2026.
22.

s = 5.31277+
Found by Yanis Gomes
in October 2026. 		           23.

s = 5.40625+
Found by Yanis Gomes
in October 2026. 		           24.

s = 5.54013+
Found by Joshua Wolk in September 2026.
25.

s = 5.62896+
Found by Yanis Gomes
in October 2026. 		           26.

s = 5.74813+
Found by Yanis Gomes
in October 2026. 		           27.

s = 5.84200+
Found by Yanis Gomes
in October 2026.
28.

s = 5.94881+
Found by Yanis Gomes
in October 2026. 		           29.

s = 6.07057+
Found by Yanis Gomes
in October 2026. 		           30.

s = 6.16017+
Found by Yanis Gomes
in October 2026.
31.

s = 6.26346+
Found by Yanis Gomes
in October 2026. 		           32.

s = 6.34145+
Found by Yanis Gomes
in October 2026. 		           33.

s = 8/11+75√2/22+√(4422–2880√2)/22
s = 6.39769+
Found by Yanis Gomes
in October 2026.
34.

s = 6.54412+
Found by Yanis Gomes
in October 2026. 		           35.

s = 6.65367+
Found by Joshua Wolk
in September 2026. 		           36.

s = 6.75069+
Found by Yanis Gomes
in October 2026.
37.

s = 6.80779+
Found by Yanis Gomes
in October 2026. 		           38.

s = 6.91794+
Found by Yanis Gomes
in October 2026. 		           39.

s = 7.00960+
Found by Yanis Gomes
in October 2026.
40.

s = 7.10140+
Found by Joshua Wolk in September 2026. 		           41.

s = 7.19804+
Found by Yanis Gomes
in October 2026. 		           42.

s = 7.28688+
Found by Yanis Gomes
in October 2026.
43.

s = 7.36614+
Found by Yanis Gomes
in October 2026. 		           44.

s = 7.44739+
Found by Yanis Gomes
in October 2026. 		           45.

s = 7.53766+
Found by Yanis Gomes
in October 2026.
46.

s = 7.61743+
Found by Yanis Gomes
in October 2026. 		           47.

s = 7.68191+
Found by Yanis Gomes
in October 2026. 		           48.

s = 7.73924+
Found by Yanis Gomes
in October 2026.
49.

s = 7.82011+
Found by Yanis Gomes
in October 2026. 		           50.

s = 7.90406+
Found by Yanis Gomes
in October 2026.