Octagons in Squares

The following pictures show n unit octagons packed inside the smallest known square (of side s).

1.

s = 1 + √2 = 2.41421+
Trivial.
  		           2.

s = 2 + 3√2/2 = 4.12132+
Found by Jonathan Viquerat
in May 2026. 		           3.-4.

s = 2 + 2√2 = 4.82842+
Trivial.
 

5.

s = 3 + 2√2 = 5.82842+
Found by Jonathan Viquerat
in May 2026. 		           6.

s = (11√2+17)/5 = 6.51126+
Found by Jonathan Viquerat
in May 2026. 		           7.

s = (5√2+7)/2 = 7.03553+
Found by Jonathan Viquerat
in May 2026.
8.-9.

s = 3 + 3√2 = 7.24264+
Trivial.
  		           10.

s = 4+3√2 = 8.24264+
Found by Jonathan Viquerat
in May 2026. 		           11.

s = 8.57596+
Found by Jonathan Viquerat
in May 2026.
12.

s = (23√2+38)/8 = 8.81586+
Found by Jonathan Viquerat
in May 2026. 		           13.

s = 9.19909+
Found by Jonathan Viquerat
in May 2026. 		           14.

s = (7√2+9)/2 = 9.44974+
Found by Jonathan Viquerat
in May 2026.
15.-16.

s = 4 + 4√2 = 9.65685+
Trivial. 		           17.

s = 10.44973+
Found by Jonathan Viquerat
in May 2026. 		           18.

s = (17√2+29)/5 = 10.60832+
Found by Jonathan Viquerat
in May 2026.
19.

s = 10.96620+
Found by Haowei Lin
in July 2026. 		           20.

s = (39√2+67)/11 = 11.10493+
Found by Jonathan Viquerat
in May 2026. 		           21.

s = 11.47891+
Found by Grigory Merzon
in August 2026.
22.

s = 11.63403+
Found by Grigory Merzon
in August 2026. 		           23.

s = 11.86396+
Found by Joshua Wolk
in September 2026. 		           24.-25.

s = 5 + 5√2 = 12.07106+
Trivial.
26.

s = 12.75167+
Found by Joshua Wolk
in September 2026. 		           27.

s = 12.91949+
Found by Joshua Wolk
in September 2026. 		           28.

s = 13.11977+
Found by Joshua Wolk
in September 2026.
29.

s = 13.30840+
Found by Joshua Wolk
in September 2026. 		           30.

s = 13.38847+
Found by Joshua Wolk
in September 2026. 		           31.

s = 13.73323+
Found by Joshua Wolk
in September 2026.
32.

s = 13.94285+
Found by Joshua Wolk
in September 2026. 		           33.

s = 14.05624+
Found by Joshua Wolk
in September 2026. 		           34.

s = 14.27818+
Found by Joshua Wolk
in September 2026.
35.-36.

s = 6 + 6√2 = 14.48528+
Trivial. 		           37.

s = 14.97438+
Found by Joshua Wolk
in September 2026. 		           38.

s = 15.10712+
Found by Joshua Wolk
in September 2026.
39.

s = 15.20118+
Found by Joshua Wolk
in September 2026. 		           40.

s = 15.51710+
Found by Joshua Wolk
in September 2026. 		           41.

s = 15.66801+
Found by Joshua Wolk
in September 2026.
42.

s = 15.68731+
Found by Joshua Wolk
in September 2026. 		           43.

s = 16.03641+
Found by Joshua Wolk
in September 2026. 		           44.

s = 16.22423+
Found by Joshua Wolk
in September 2026.
45.

s = 16.38335+
Found by Joshua Wolk
in September 2026. 		           46.

s = 16.47425+
Found by Joshua Wolk
in September 2026. 		           47.

s = 16.69239+
Found by Joshua Wolk
in September 2026.
48.-49.

s = 7 + 7√2 = 16.89950+
Trivial. 		           50.

s = 17.29153+
Found by Joshua Wolk
in September 2026.