Triangles in Circles

The following pictures show n equilateral triangles packed inside a unit circle, so that the total sum of the sides of the triangles is as large as possible.

1.
           2.
           3.
Σ s = √3 = 1.73205+
Trivial.
  		Σ s = 4/√3 = 2.30940+
Trivial.
A continuum of solutions. 		Σ s = 3.18767+
Found by Jonathan Viquerat
in June 2026.

4.
           5.
           6.
Σ s = 3+2/√3 = 4.15470+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 5
Trivial.
  		Σ s = 6
Trivial.
 

7.
           8.
           9.
Σ s = 5+2/√3 = 6.15470+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 6.62452+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 7.00636+
Found by Haowei Lin
in July 2026.

10.
           11.
           12.
Σ s = 7.39853+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 7.77426+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 8.09500+
Found by Jonathan Viquerat
in June 2026.

13.
           14.
           15.
Σ s = 8.53190+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 8.83315+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 9.25219+
Found by Jonathan Viquerat
in June 2026.

16.
           17.
           18.
Σ s = 9.57822+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 9.93206+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 10.23592+
Found by Jonathan Viquerat
in June 2026.

19.
           20.
           21.
Σ s = 10.55247+
Found by Haowei Lin
in July 2026. 		Σ s = 10.86683+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 11.16682+
Found by Jonathan Viquerat
in September 2026.

22.
           23.
           24.
Σ s = 11.44887+
Found by Jonathan Viquerat
in September 2026. 		Σ s = 11.73932+
Found by Jonathan Viquerat
in September 2026. 		Σ s = 12
Found by Joost de Winter
in September 2026.

25.
           26.
           27.
Σ s = 12.24607+
Found by Jonathan Viquerat
in September 2026. 		Σ s = 12.57733+
Found by Jonathan Viquerat
in September 2026. 		Σ s = 12.81014+
Found by Jonathan Viquerat
in September 2026.

28.
           29.
           30.
Σ s = 13.02990+
Found by Jonathan Viquerat
in September 2026. 		Σ s = 13.33746+
Found by Jonathan Viquerat
in September 2026. 		Σ s = 13.58712+
Found by Jonathan Viquerat
in September 2026.

31.
           32.
           33.
Σ s = 13.85140+
Found by Joost de Winter
in September 2026. 		Σ s = 14.08063+
Found by Jonathan Viquerat
in September 2026. 		Σ s = 14.32516+
Found by Jonathan Viquerat
in September 2026.

34.
           35.
           36.
Σ s = 14.52204+
Found by Jonathan Viquerat
in September 2026. 		Σ s = 14.78382+
Found by Joost de Winter
in September 2026. 		Σ s = 15.02816+
Found by Joost de Winter
in September 2026.

37.
           38.
           39.
Σ s = 15.25425+
Found by Joost de Winter
in September 2026. 		Σ s = 15.30323+
Found by Joost de Winter
in September 2026. 		Σ s = 15.52737+
Found by Joost de Winter
in September 2026.

40.
           41.
           42.
Σ s = 15.75346+
Found by Joost de Winter
in September 2026. 		Σ s = 15.86072+
Found by Joost de Winter
in September 2026. 		Σ s = 16.08311+
Found by Joost de Winter
in September 2026.

43.
           44.
           45.
Σ s = 16.28881+
Found by Joost de Winter
in September 2026. 		Σ s = 16.50305+
Found by Joost de Winter
in September 2026. 		Σ s = 16.69049+
Found by Joost de Winter
in September 2026.

46.
           47.
           48.
Σ s = 16.97489+
Found by Joost de Winter
in October 2026. 		Σ s = 17.24606+
Found by Joost de Winter
in October 2026. 		Σ s = 17.51723+
Found by Joost de Winter
in October 2026.

49.
           50.
Σ s = 17.73917+
Found by Joost de Winter
in October 2026. 		Σ s = 17.95325+
Found by Joost de Winter
in October 2026.