Octagons in Circles

Octagons in Circles

The following pictures show n unit octagons packed inside the smallest known circles (with radius r).

1.

r = √(1+1/√2) = 1.30656+
Trivial.
2.

r = √(13/4+2√2) = 2.46544+
Trivial.
3.

r = 2.71611+
Found by Jonathan Viquerat
in June 2026.

4.

r = √(9/2+3√2) = 2.95679+
Trivial.

5.

r = 3.37974+
Found by Jonathan Viquerat
in June 2026.

6.

r = 3.69797+
Found by Jonathan Viquerat
in June 2026.

7.

r = 3.77329+
Found by Jonathan Viquerat
in June 2026.

8.

r = 4.12460+
Found by Jonathan Viquerat
in June 2026.

9.

r = 4.46088+
Found by Jonathan Viquerat
in June 2026.

10.

r = 4.72215+
Found by Jonathan Viquerat
in June 2026.

11.

r = 4.88201+
Found by Jonathan Viquerat
in June 2026.

12.

r = 5.00001+
Found by Jonathan Viquerat
in June 2026.

13.

r = 5.23457+
Found by Jonathan Viquerat
in June 2026.

14.

r = 5.34131+
Found by Jonathan Viquerat
in June 2026.

15.

r = 5.60687+
Found by Jonathan Viquerat
in June 2026.

16.

r = 5.73298+
Found by Jonathan Viquerat
in June 2026.

17.

r = 5.94448+
Found by Jonathan Viquerat
in June 2026.

18.

r = 6.05968+
Found by Jonathan Viquerat
in June 2026.

19.

r = 6.07328+
Found by Jonathan Viquerat
in June 2026.

20.

r = 6.36903+
Found by Jonathan Viquerat
in June 2026.