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 = √(6–√2–√(20√2–26))/2 = 0.87669+
Found by Maurizio Morandi
in December 2013. 		s = 18 – 12√2 = 1.02940+
Found by Erich Friedman
in December 2013.

4.
           5.
           6.
s = √(4–2√2) = 1.08239+
Trivial.
  		s = 3√2 – 3 = 1.24261+
Trivial.
  		s = 7 – 4√2 = 1.34314+
Found by Maurizio Morandi
in December 2013.

7.
           8.
           9.
s = √(5–√2–√(8√2–9)) = 1.43690+
Found by Maurizio Morandi
in December 2013. 		s = 1.56962+
Found by Grant Mowry
in May 2026. 		s = 3/√(2+√2) = 1.62358+
Trivial.
 

10.
           11.
           12.
s = 2^(3/4) = 1.68179+
Found by Maurizio Morandi
in December 2013. 		s = 1.73159+
Found by Jake Loyd
in May 2026. 		s = √(6–√2–√(20√2–26)) = 1.75339+
Found by Maurizio Morandi
in December 2013.

13.
           14.
           15.
s = 1.89674+
Found by Grant Mowry
in May 2026. 		s = 1.98314+
Found by Jake Loyd
in May 2026. 		s = 2.03174+
Found by Jake Loyd
in May 2026.

16.
           17.
           18.
s = 5√2 – 5 = 2.07106+
Trivial.
  		s = 5√2 – 5 = 2.07106+
Trivial.
  		s = 2.16743+
Found by Jake Loyd
in May 2026.

19.
           20.
           21.
s = 2.22498+
Found by Jake Loyd
in May 2026. 		s = 2.28622+
Found by Jake Loyd
in May 2026. 		s = 2.31855+
Found by Jake Loyd
in May 2026.

22.
           23.
           24.
s = 2.41603+
Found by Jake Loyd
in May 2026. 		s = 2.46952+
Found by Jake Loyd
in May 2026. 		s = 6√2 – 6 = 2.48528+
Trivial.

25.
           26.
           27.
s = 2.48975+
Found by Jake Loyd
in May 2026. 		s = 2.52755+
Found by Jake Loyd
in May 2026. 		s = 2.58615+
Found by Jake Loyd
in May 2026.

28.
           29.
           30.
s = 2.63037+
Found by Jake Loyd
in May 2026. 		s = 2.70639+
Found by Jake Loyd
in May 2026. 		s = 2.73900+
Found by Jake Loyd
in May 2026.