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 = √(7/2 + √5/10 + √(3+6/√5))
r = 2.47134+
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.
r = 5.08385+
Found by Joshua Wolk
in September 2026. 		r = 5.18804+
Found by Haowei Lin
in June 2026. 		r = 5.25746+
Found by Haowei Lin
in June 2026.

27.
           28.
           29.
r = 5.28167+
Found by Haowei Lin
in June 2026. 		r = 5.40413+
Found by Joshua Wolk
in September 2026. 		r = 5.51357+
Found by Joshua Wolk
in September 2026.

30.
           31.
           32.
r = 5.56425+
Found by Joshua Wolk
in September 2026. 		r = 5.56776+
Found by Joshua Wolk
in September 2026. 		r = 5.73225+
Found by Joshua Wolk
in September 2026.

33.
           34.
           35.
r = 5.81018+
Found by Joshua Wolk
in September 2026. 		r = 5.88849+
Found by Joshua Wolk
in September 2026. 		r = 6.00084+
Found by Joshua Wolk
in September 2026.

36.-37.
           38.
           39.
r = 6.08276+
Trivial. 		r = 6.26102+
Found by Joshua Wolk
in September 2026. 		r = 6.31089+
Found by Joshua Wolk
in September 2026.

40.
           41.
           42.
r = 6.39323+
Found by Joshua Wolk
in September 2026. 		r = 6.46920+
Found by Joshua Wolk
in September 2026. 		r = 6.55744+
Found by Joshua Wolk
in September 2026.

43.
           44.
           45.
r = 6.61753+
Found by Joshua Wolk
in September 2026. 		r = 6.66848+
Found by Joshua Wolk
in September 2026. 		r = 6.73801+
Found by Joshua Wolk
in September 2026.

46.
           47.
           48.
r = 6.80188+
Found by Joshua Wolk
in September 2026. 		r = 6.91122+
Found by Joshua Wolk
in September 2026. 		r = 6.96072+
Found by Joshua Wolk
in September 2026.

49.
           50.
r = 7.04206+
Found by Joshua Wolk
in September 2026. 		r = 7.08208+
Found by Joshua Wolk
in September 2026.