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 = 9.70087+
Found by Bhavithran Ananthan
in July 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 = 10.71239+
Found by Yanis Gomes
in October 2026. 		           17.

s = 10.97884+
Found by Jonathan Viquerat
in May 2026. 		           18.

s = 11.27248+
Found by Joshua Wolk
in September 2026.
19.

s = 11.49001+
Found by Yanis Gomes
in October 2026. 		           20.

s = 11.77041+
Found by Jonathan Viquerat
in May 2026. 		           21.

s = 12.07183+
Found by Joshua Wolk
in September 2026.
22.

s = 12.35653+
Found by Yanis Gomes
in October 2026. 		           23.

s = 12.62391+
Found by Joshua Wolk
in September 2026. 		           24.

s = 12.77726+
Found by Joshua Wolk
in September 2026.
25.

s = 13.08599+
Found by Joshua Wolk
in September 2026. 		           26.

s = 13.27477+
Found by Yanis Gomes
in October 2026. 		           27.

s = 13.51849+
Found by Joshua Wolk
in September 2026.

28.

s = 59/2–10√3+3√(2–√3) = 13.73240+
Found by Yanis Gomes
in October 2026. 		           29.

s = 31√3/3–9/2+√(2–√3) = 13.91549+
Found by Yanis Gomes
in October 2026. 		           30.

s = 14.20342+
Found by Joshua Wolk
in September 2026.

31.

s = 14.40252+
Found by Joshua Wolk
in September 2026. 		           32.

s = 14.56835+
Found by Joshua Wolk
in September 2026. 		           33.

s = 14.83322+
Found by Joshua Wolk
in September 2026.

34.

s = 15.04413+
Found by Joshua Wolk
in September 2026. 		           35.

s = 15.20957+
Found by Joshua Wolk
in September 2026. 		           36.

s = 15.38850+
Found by Joshua Wolk
in September 2026.

37.

s = 15.58897+
Found by Yanis Gomes
in October 2026. 		           38.

s = 2+37√3/6+√(122–65√3) = 15.74964+
Found by Yanis Gomes
in October 2026. 		           39.

s = 15.94094+
Found by Joshua Wolk
in September 2026.

40.

s = 16.15503+
Found by Joshua Wolk
in September 2026. 		           41.

s = 16.30437+
Found by Joshua Wolk
in September 2026. 		           42.

s = 16.51457+
Found by Yanis Gomes
in October 2026.

43.

s = 16.69095+
Found by Yanis Gomes
in October 2026. 		           44.

s = 16.88432+
Found by Joshua Wolk
in September 2026. 		           45.

s = 17.05504+
Found by Joshua Wolk
in September 2026.

46.

s = 17.21966+
Found by Joshua Wolk
in September 2026. 		           47.

s = 17.38105+
Found by Joshua Wolk
in September 2026. 		           48.

s = 17.55164+
Found by Joshua Wolk
in September 2026.

49.

s = 17.70714+
Found by Joshua Wolk
in September 2026. 		           50.

s = 17.88827+
Found by Joshua Wolk
in September 2026.