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. 		r = 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 = 3.82298+
Found by Jonathan Viquerat
in April 2026. 		r = √(109–9√109) = 3.877+
Found by Maurizio Morandi
in March 2026.

15.
           16.
           17.
r = 4.08174+
Found by Jonathan Viquerat
in April 2026. 		r = 4.13966+
Found by Jonathan Viquerat
in April 2026. 		r = 4.30170+
Found by Jonathan Viquerat
in April 2026.

18.-19.
           20.
r = √19 = 4.35889+
Trivial. 		r = 4.62598+
Found by Jonathan Viquerat
in April 2026.