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 = 3.48172+
Found by Jake Loyd
in June 2026.

11.
           12.
           13.
r = 3.59003+
Found by Jake Loyd
in June 2026. 		r = √13 = 3.605+
Found by Maurizio Morandi
in March 2026. 		r = 3.82289+
Found by Jake Loyd
in June 2026.

14.
           15.
           16.
r = 3.87755+
Found by Jake Loyd
in June 2026. 		r = 4.08154+
Found by Jake Loyd
in June 2026. 		r = 4.13960+
Found by Jake Loyd
in June 2026.

17.
           18.-19.
           20.
r = 4.30158+
Found by Jake Loyd
in June 2026. 		r = √19 = 4.35889+
Trivial. 		r = 4.62527+
Found by Jake Loyd
in June 2026.

21.
           22.
           23.
r = 4.68305+
Found by Jake Loyd
in June 2026. 		r = 4.89204+
Found by Jake Loyd
in June 2026. 		r = 4.98608+
Found by Jake Loyd
in June 2026.

24.
           25.
           26.-27.
r = 5.08387+
Found by Jake Loyd
in June 2026. 		r = 5.18816+
Found by Jake Loyd
in June 2026. 		r = 5.28194+
Found by Thomas Greenleaf
in June 2026.