Tans in Octagons

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

1.-2.

s = 1/√(2+√2) = .54119+
Trivial.
  		           3.

s = .72389+
Found by Thomas Greenleaf
in June 2026. 		           4.

s = √(2–√2) = .76536+
Found by Thomas Greenleaf
in June 2026.

5.

s = .88072+
Found by Thomas Greenleaf
in June 2026. 		           6.

s = √(2+√2)/2 = .92387+
Found by Thomas Greenleaf
in June 2026. 		           7.

s = .98622+
Found by Yanis Gomes
in October 2026.
8.

s = 1
Trivial.
  		           9.

s = 1.08295+
Found by Jake Loyd
in June 2026. 		           10.

s = 1.09348+
Found by Jake Loyd
in June 2026.
11.

s = 1.15384+
Found by Jake Loyd
in June 2026. 		           12.

s = 4–2√2 = 1.17157+
Found by Thomas Greenleaf
in June 2026. 		           13.

s = 1.21868+
Found by Jake Loyd
in June 2026.
14.

s = 3(√2–1) = 1.24264+
Found by Maurizio Morandi
in June 2026. 		           15.

s = 1.31145+
Found by Jake Loyd
in June 2026. 		           16.

s = 1.36380++
Found by Yanis Gomes
in October 2026.
17.

s = 1.39954+
Found by Jake Loyd
in June 2026. 		           18.

s = √2 = 1.41421+
Found by Jake Loyd
in June 2026. 		           19.

s = 1.47759+
Found by Yanis Gomes
in October 2026.
20.

s = 1.51210+
Found by Yanis Gomes
in October 2026. 		           21.

s = 1.55762+
Found by Yanis Gomes
in October 2026. 		           22.

s = 1.58542+
Found by Joshua Wolk
in September 2026.
23.

s = 1.61495+
Found by Yanis Gomes
in October 2026. 		           24.

s = 1.63944+
Found by Yanis Gomes
in October 2026. 		           25.

s = 1.67606+
Found by Yanis Gomes
in October 2026.
26.

s = 1.70406+
Found by Yanis Gomes
in October 2026. 		           27.

s = 1.73499+
Found by Yanis Gomes
in October 2026. 		           28.

s = 6–3√2 = 1.75735+
Found by Yanis Gomes
in October 2026.
29.

s = (5–√2)/2 = 1.79289+
Found by Maurizio Morandi
in October 2026. 		           30.

s = 2√2–1 = 1.82842+
Found by Maurizio Morandi
in October 2026. 		           31.

s = 1.84927+
Found by Yanis Gomes
in October 2026.
32.

s = 1.87653+
Found by Yanis Gomes
in October 2026. 		           33.

s = 7√2–8 = 1.89949+
Found by Maurizio Morandi
in October 2026. 		           34.

s = 1.92893+
Found by Joshua Wolk
in September 2026.
35.

s = 1.95837+
Found by Joshua Wolk
in September 2026. 		           36.

s 1.98857+
Found by Joshua Wolk
in September 2026. 		           37.

s = 1.99877+
Found by Joshua Wolk
in September 2026.
38.

s = 2.02716+
Found by Joshua Wolk
in September 2026. 		           39.

s = 2.06177+
Found by Yanis Gomes
in October 2026. 		           40.

s = 2.09678+
Found by Yanis Gomes
in October 2026.
41.

s = 2.12213+
Found by Joshua Wolk
in September 2026. 		           42.

s = 2.14501+
Found by Yanis Gomes
in October 2026. 		           43.

s = 2.16577+
Found by Yanis Gomes
in October 2026.
44.

s = 2.18804+
Found by Yanis Gomes
in October 2026. 		           45.

s = 2.21935+
Found by Yanis Gomes
in October 2026. 		           46.

s = 2.24291+
Found by Yanis Gomes
in October 2026.
47.

s = 2.26171+
Found by Yanis Gomes
in October 2026. 		           48.

s = 2.29636+
Found by Yanis Gomes
in October 2026. 		           49.

s = 2.31923+
Found by Yanis Gomes
in October 2026.
50.

s = 2.34184+
Found by Yanis Gomes
in October 2026.