Hexagons in Circles

Hexagons in Circles
The following pictures show n unit hexagons packed inside the smallest known circle (with radius r).

1.
2.
3.

r = 1
Trivial. r = √13/2 = 1.802+
Trivial. s = 2
Trivial.

4.
5.
6.-7.

r = (21–√145)/4 = 2.239+
Found by Maurizio Morandi
in March 2026. r = 2.471+
Found by Maurizio Morandi
in March 2026. r = √7 = 2.645+
Trivial.

8.
9.
10.

r = 2.984+
Found by Maurizio Morandi
in March 2026. r = 3.301+
Found by Maurizio Morandi
in March 2026. r = 7/2 = 3.5
Found by Maurizio Morandi
in March 2026.

11.-12.
13.
14.

r = √13 = 3.605+
Found by Maurizio Morandi
in March 2026. r = 3.823+
Found by Maurizio Morandi
in March 2026. r = √(109–9√109) = 3.877+
Found by Maurizio Morandi
in March 2026.

1.		2.		3.
r = 1 Trivial.		r = √13/2 = 1.802+ Trivial.		s = 2 Trivial.

4.		5.		6.-7.
r = (21–√145)/4 = 2.239+ Found by Maurizio Morandi in March 2026.		r = 2.471+ Found by Maurizio Morandi in March 2026.		r = √7 = 2.645+ Trivial.

8.		9.		10.
r = 2.984+ Found by Maurizio Morandi in March 2026.		r = 3.301+ Found by Maurizio Morandi in March 2026.		r = 7/2 = 3.5 Found by Maurizio Morandi in March 2026.

11.-12.		13.		14.
r = √13 = 3.605+ Found by Maurizio Morandi in March 2026.		r = 3.823+ Found by Maurizio Morandi in March 2026.		r = √(109–9√109) = 3.877+ Found by Maurizio Morandi in March 2026.