Pentagons in Tans

Pentagons in Tans

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

1.

s = 2.48911+
Trivial. 2.

s = 3.52014+
Trivial. 3.

s = 3.97792+
Trivial.

4.

s = 4.63338+
Found by Jonathan Viquerat
in May 2026.

5.

s = 5.16518+
Found by Jonathan Viquerat
in May 2026.

6.

s = 5.48233+
Found by Jonathan Viquerat
in May 2026.

7.

s = 6.03679+
Found by Jonathan Viquerat
in May 2026.

8.

s = 6.30671+
Found by Jonathan Viquerat
in May 2026.

9.

s = 6.69536+
Found by Jonathan Viquerat
in May 2026.

10.

s = 6.98078+
Found by Jonathan Viquerat
in May 2026.

11.

s = 7.34729+
Found by Jonathan Viquerat
in May 2026.

12.

s = 7.54006+
Found by Jonathan Viquerat
in May 2026.

13.

s = 7.82906+
Found by Jonathan Viquerat
in May 2026.

14.

s = 8.16823+
Found by Joshua Wolk
in September 2026.

15.

s = 8.45665+
Found by Joshua Wolk
in September 2026.

16.

s = 8.66023+
Found by Jonathan Viquerat
in May 2026.

17.

s = 8.89679+
Found by Jonathan Viquerat
in September 2026.

18.

s = 9.08709+
Found by Joshua Wolk
in September 2026.

19.

s = 9.38475+
Found by Joshua Wolk
in September 2026.

20.

s = 9.61257+
Found by Joshua Wolk
in September 2026.

21.

s = 9.78840+
Found by Joshua Wolk
in September 2026.

22.

s = 10.00563+
Found by Joshua Wolk
in September 2026.

23.

s = 10.24859+
Found by Jonathan Viquerat
in September 2026.

24.

s = 10.43710+
Found by Joshua Wolk
in September 2026.

25.

s = 10.63197+
Found by Jonathan Viquerat
in September 2026.