Octagons in Tans

Octagons in Tans

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

1.

s = 2+3/√2 = 4.12132+
Trivial. 2.

s = 3+2√2 = 5.82842+
Trivial. 3.

s = 3+5/√2 = 6.53553+
Trivial.

4.

s = 4+5/√2 = 7.53553+
Trivial.

5.

s = 9/2+3√2 = 8.74263+
Found by Jonathan Viquerat
in May 2026.

6.

s = 4+7/√2 = 8.94974+
Trivial.

7.

s = 5+7/√2 = 9.94974+
Found by Jonathan Viquerat
in May 2026.

8.

s = 10.65684+
Found by Jonathan Viquerat
in May 2026.

9.

s = 6+7/√2 = 10.94974+
Trivial.

10.

s = 5+9/√2 = 11.36395+
Trivial.

11.

s = 12.33328+
Found by Jonathan Viquerat
in May 2026.

12.

s = 12.65684+
Found by Jonathan Viquerat
in May 2026.

13.

s = 13.21750+
Found by Jonathan Viquerat
in May 2026.

14.

s = 13/2+5√2 = 13.57106+
Found by Jonathan Viquerat
in May 2026.

15.

s = 6+11/√2 = 13.77816+
Trivial.

16.

s = 8+9/√2 = 14.36395+
Trivial.

17.

s = 14.77816+
Found by Jonathan Viquerat
in May 2026.

18.

s = 15.34720+
Found by Jonathan Viqueratl
in May 2026.

19.

s = 15.68053+
Found by Jonathan Viquerat
in May 2026.

20.

s = 15/2+6√2 = 15.98527+
Found by Jonathan Viquerat
in May 2026.