Hexagons in Tans

Hexagons in Tans

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

1.

s = 3.15659+
Trivial. 2.

s = 4.46410+
Trivial. 3.

s = 4.94974+
Trivial.

4.

s = 5.75097+
Found by Jonathan Viquerat
in May 2026.

5.

s = 6.50265+
Found by Jonathan Viquerat
in May 2026.

6.

s = 6.74289+
Found by Jonathan Viquerat
in May 2026.

7.

s = 7.39923+
Found by Jonathan Viquerat
in May 2026.

8.

s = 7.83340+
Found by Jonathan Viquerat
in May 2026.

9.

s = 8.28267+
Found by Jonathan Viquerat
in May 2026.

10.

s = 8.53604+
Found by Jonathan Viquerat
in May 2026.

11.

s = 9.06093+
Found by Jonathan Viquerat
in May 2026.

12.

s = 9.41319+
Found by Jonathan Viquerat
in May 2026.

13.

s = 9.70132+
Found by Jonathan Viquerat
in May 2026.

14.

s = 10.03836+
Found by Jonathan Viquerat
in May 2026.

15.

s = 10.32919+
Found by Jonathan Viquerat
in May 2026.

16.

s = 10.71469+
Found by Jonathan Viquerat
in May 2026.

17.

s = 10.97884+
Found by Jonathan Viquerat
in May 2026.

18.

s = 11.27299+
Found by Jonathan Viqueratl
in May 2026.

19.

s = 11.49013+
Found by Jonathan Viquerat
in May 2026.

20.

s = 11.77041+
Found by Jonathan Viquerat
in May 2026.