Tans in Triangles

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 = 1.41420+
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 = 3.69368+
Found by Thomas Greenleaf
in June 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 = 4.45985+
Found by Jonathan Loyd
in June 2026.

16.

s = 4.61687+
Found by Jonathan Loyd
in June 2026.

17.

s = 4.72627+
Found by Jonathan Loyd
in June 2026.

18.

s = 4.84346+
Found by Jonathan Loyd
in June 2026.

19.

s = 4.96765+
Found by Thomas Greenleaf
in June 2026.

20.

s = 5.06562+
Found by Thomas Greenleaf
in June 2026.

21.

s = 5.23033+
Found by Jonathan Loyd
in June 2026.

22.

s = 5.33580+
Found by Jonathan Loyd
in June 2026.