Triangles in Tans

The following pictures show n unit equilateral triangles packed inside the smallest known tan (with short side length s).

1.

s = 1.22474+
Trivial. 		           2.

s = √3 = 1.73205+
Trivial. 		           3.

s = 1.93185+
Trivial.

4.

s = 2.36602+
Found by Jonathan Viquerat
in May 2026 		           5.

s = 2.53905+
Found by Jonathan Viquerat
in May 2026 		           6.

s = 2.63896+
Found by Jonathan Viquerat
in May 2026
7.

s = 2.78972+
Found by Jonathan Viquerat
in May 2026 		           8.

s = 3.07313+
Found by Jonathan Viquerat
in May 2026 		           9.

s = 3.18252+
Found by Jonathan Viquerat
in May 2026
10.

s = 3.34084+
Found by Jonathan Viquerat
in May 2026 		           11.

s = 3.46951+
Found by Jonathan Viquerat
in May 2026 		           12.

s = 3.62500+
Found by Jonathan Viquerat
in May 2026
13.

s = 3.71163+
Found by Jonathan Viquerat
in May 2026 		           14.

s = 3.88268+
Found by Jonathan Viquerat
in May 2026 		           15.

s = 3.98382+
Found by Thomas Greenleaf
in June 2026
16.

s = 4.03901+
Found by Thomas Greenleaf
in June 2026 		           17.

s = 4.20273+
Found by Jonathan Viquerat
in May 2026 		           18.

s = 4.27120+
Found by Thomas Greenleaf
in June 2026
19.

s = 4.45701+
Found by Thomas Greenleaf
in June 2026 		           20.

s = 4.56124+
Found by Thomas Greenleaf
in June 2026 		           21.-22.

s = 4.73304+
Found by Thomas Greenleaf
in June 2026
23.

s = 4.85921+
Found by Thomas Greenleaf
in June 2026