Tans in Hexagons

Tans in Hexagons

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

1.

s = .74062+
Trivial.
2.

s = (3+√3)/6 = .78867+
Found by Jonathan Viquerat
in May 2026. 3.

s = .98883+
Found by Jonathan Viquerat
in May 2026.

4.

s = 1.05845+
Found by Jonathan Viquerat
in May 2026.

5.

s = 1.13976+
Found by Jonathan Viquerat
in May 2026.

6.

s = 1.20610+
Found by Jonathan Viquerat
in May 2026.

7.

s = 1.30322+
Found by Thomas Greenleaf
in June 2026.

8.

s = 1.37728+
Found by Thomas Greenleaf
in June 2026.

9.

s = 1.44631+
Found by Thomas Greenleaf
in June 2026.

10.

s = 1.51366+
Found by Thomas Greenleaf
in June 2026.

11.

s = 1.59198+
Found by Jake Loyd
in June 2026.

12.

s = 1.65076+
Found by Jake Loyd
in June 2026.

13.

s = 1.70429+
Found by Jake Loyd
in June 2026.

14.

s = 1.76680+
Found by Jake Loyd
in June 2026.

15.

s = 1.82658+
Found by Jake Loyd
in June 2026.

16.

s = 1.88728+
Found by Jake Loyd
in June 2026.

17.

s = 1.93877+
Found by Jake Loyd
in June 2026.

18.

s = 1.99031+
Found by Jake Loyd
in June 2026.

19.

s = 2.03182+
Found by Jake Loyd
in June 2026.

20.

s = 2.1029+
Found by Jake Loyd
in June 2026.

21.

s = 2.14048+
Found by Jake Loyd
in June 2026.

22.

s = 2.19278+
Found by Jake Loyd
in June 2026.