Squares in Octagons

The following pictures show n unit squares packed inside the smallest known octagon (with side s).

1.
           2.
           3.
s = 1/√(2+√2) = .54119+
Trivial.
  		s = .87667+
Found by Ignacio Vallejo
in March 2026. 		s = 1.02940+
Found by Ignacio Vallejo
in March 2026.

4.
           5.
           6.
s = √(4–2√2) = 1.08239+
Trivial.
  		s = 3√2 – 3 = 1.24261+
Trivial.
  		s 1.34312+
Found by Ignacio Vallejo
in March 2026.

7.
           8.
           9.
s = 1.43691+
Found by Ignacio Vallejo
in March 2026. 		s = 1.56967+
Found by Ignacio Vallejo
in March 2026. 		s = 3/√(2+√2) = 1.62358+
Trivial.
 

10.
           11.
           12.
s = 1.68262+
Found by Ignacio Vallejo
in March 2026. 		s = 1.73180+
Found by Ignacio Vallejo
in March 2026. 		s = 1.75364+
Found by Ignacio Vallejo
in March 2026.

13.
           14.
           15.
s = 1.89760+
Found by Ignacio Vallejo
in March 2026. 		s = 1.98350+
Found by Ignacio Vallejo
in March 2026. 		s = 2.03259+
Found by Ignacio Vallejo
in March 2026.

16.
           17.
           18.
s = 5√2 – 5 = 2.07106+
Trivial.
  		s = 5√2 – 5 = 2.07106+
Trivial.
  		s = 2.16778+
Found by Ignacio Vallejo
in March 2026.

19.
           20.
s = 2.22823+
Found by Ignacio Vallejo
in March 2026. 		s = 2.28730+
Found by Ignacio Vallejo
in March 2026.