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 = 3.17613+
Found by Jonathan Viquerat
in May 2026.

8.

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

9.

s = 3.51839+
Found by Jonathan Viquerat
in May 2026.

10.

s = 3.72991+
Found by Jonathan Viquerat
in May 2026.

11.

s = 3.91311+
Found by Jonathan Viquerat
in May 2026.

12.

s = 4.09786+
Found by Jonathan Viquerat
in May 2026.

13.

s = 4.25039+
Found by Jonathan Viquerat
in May 2026.

14.

s = 4.39199+
Found by Jonathan Viquerat
in May 2026.

15.

s = 4.61827+
Found by Jonathan Viquerat
in May 2026.

16.

s = 4.68645+
Found by Jonathan Viquerat
in May 2026.

17.

s = 4.93130+
Found by Jonathan Viquerat
in May 2026.

18.

s = 5.02326+
Found by Jonathan Viqueratl
in May 2026.

19.

s = 5.21782+
Found by Jonathan Viquerat
in May 2026.

20.

s = 5.30029+
Found by Jonathan Viquerat
in May 2026.