Triangles in Triangles

The following pictures show n equilateral triangles with side 1 packed inside the smallest known equilateral triangles (of side length s ). Most of these have not been proven.

1.
           2.-4.
           5.
s = 1
Trivial. 		s = 2
Trivial. 		s = 1 + √3 = 2.732+
Proved by Erich Friedman
in 1997.

6.
           7.-9.
           10.
s = 13/8 + 3√13/8 = 2.977+
Found by Maurizio Morandi
in August 2008. 		s = 3
Trivial. 		s = 7/2 = 3.500
Found by Erich Friedman
in 1997.

11.
           12.
           13.
s = 9/4 + 9√21/28 = 3.722+
Found by Erich Friedman
in 1997. 		s = 2 + 2cos(π/9) = 3.879+
Found by David W. Cantrell
in July 2007. 		s = 3.992+
Found by Maurizio Morandi
in May 2008.

14.-16.
           17.
           18.
s = 4
Trivial. 		s = 4.465+
Found by Maurizio Morandi
in May 2008. 		s = 9/2 = 4.500
Found by Erich Friedman
in 1997.

19.
           20.
           21.
s = 14/3 = 4.666+
Found by Maurizio Morandi
in May 2008. 		s = 33/8 + 9√21/56 = 4.861+
Found by Maurizio Morandi
in May 2008. 		s = 4.923+
Found by Maurizio Morandi
in May 2008.

22.
           23.-25.
           26.
s = 4.996+
Found by Maurizio Morandi
in May 2008. 		s = 5
Trivial. 		s = 5.406+
Found by Joah Frenzley
in April 2026.

27.-28.
           29.
           30.
s = 11/2 = 5.500
Found by Erich Friedman
in 1997. 		s = 17/3 = 5.666+
Found by David W. Cantrell
in July 2007. 		s = 23/4 = 5.75
Found by Maurizio Morandi
in May 2008.

31.
           32.
           33.
s = 5.90766+
Found by Thomas Schadt
in June 2026. 		s = 5.94593+
Found by Maurizio Morandi
in May 2026. 		s = 5.99759+
Found by Maurizio Morandi
in June 2026.

34.-36.
           37.
           38.
s = 6
Trivial.
  		s = 19/3 = 6.333+
Found by Ian Watson
in April 2026. 		s = 6.42823+
Found by Thomas Schadt
in June 2026.

39.-40.
           41.
           42.
s = 13/2 = 6.500
Found by Erich Friedman
in April 2026. 		s = 20/3 = 6.666+
Found by Emerson Connelly
in May 2026. 		s = 27/4 = 6.750
Found by Emerson Connelly
in May 2026.

43.
           44.
           45.
s = 41/6 = 6.833+
Found by Emerson Connelly
in May 2026. 		s = 6.93076+
Found by Thomas Schadt
in June 2026. 		s = 6.95922+
Found by Maurizio Morandi
in May 2026.

46.
           47.-49.
           50.
s = 6.99837+
Found by Maurizio Morandi
in June 2026. 		s = 7
Trivial.
  		s = 7 + √21/14 = 7.32732+
Found by Maurizio Morandi
in May 2026.