Tans in Tans

The following pictures show n tans with leg 1 packed inside the smallest known tan (of leg length s).

1.
           2.
           3.
s = 1
Trivial. 		s = √2 = 1.414+
Trivial. 		s = (4+√2+2√(2+2√2))/5 = 1.96179+
Found by Ed Pegg
in March 2005.

4.
           5.
           6.
s = 2
Trivial. 		s = 2.405+
Found by David W. Cantrell
in May 2005. 		s = (12 + √6 + 5√2)/8 = 2.690+
Found by Maurizio Morandi
in October 2007.

7.
           8.
           9.
s = 2.82434+
Found by Maurizio Morandi
in August 2007. 		s = 2√2 = 2.828+
Trivial. 		s = 3
Trivial.

10.
           11.
           12.
s = 3.30742+
Found by Joshua Wolk
in September 2026. 		s = 2 + √2 = 3.414+
Found by Erich Friedman
in March 2005. 		s = 3.53106+
Found by Maurizio Morandi
in August 2007.

13.
           14.
           15.
s = 3 + √2/2 = 3.707+
Found by Erich Friedman
in March 2005. 		s = 3.82807+
Found by Yanis Gomes
in October 2026. 		s = 5/2 + √2 = 3.914+
Found by Maurizio Morandi
in August 2007.

16.
           17.
           18.
s = 4
Trivial. 		s = 4.181+
Found by Maurizio Morandi
in August 2007. 		s = 3√2 = 4.242+
Trivial.

19.
           20.
           21.
s = 4.41299+
Found by Yanis Gomes
in October 2026. 		s = 4.535+
Found by Maurizio Morandi
in August 2007. 		s = (6 + 9√2)/4 = 4.681+
Found by Maurizio Morandi
in October 2007.

22.
           23.
           24.
s = 3 + 5√2/4 = 4.767+
Found by Maurizio Morandi
in July 2009. 		s = 4.82843+
Found by Yanis Gomes
in October 2026. 		s = 4.947+
Found by Maurizio Morandi
in October 2007.

25.
           26.
           27.
s = 5
Trivial. 		s = 3 + 3/√2 = 5.121+
Found by Maurizio Morandi
in July 2009. 		s = 5.241+
Found by Maurizio Morandi
in July 2009.

28.
           29.
           30.
s = 5.36947+
Found by Yanis Gomes
in October 2026. 		s = 5.44952+
Found by Maurizio Morandi
in October 2026. 		s = 5.53530+
Found by Yanis Gomes
in October 2026.

31.
           32.
           33.
s = 5.61622+
Found by Maurizio Morandi
in October 2026. 		s = 4√2 = 5.65685+
Trivial. 		s = 5.78559+
Found by Yanis Gomes
in October 2026.

34.
           35.
           36.
s = 5.88566+
Found by Yanis Gomes
in October 2026. 		s = 5.95710+
Found by Joshua Wolk
in September 2026. 		s = 6
Trivial.

37.
           38.
           39.
s = 6.12105+
Found by Maurizio Morandi
in October 2026. 		s = 6.23774+
Found by Joshua Wolk
in September 2026. 		s = 6.30325+
Found by Maurizio Morandi
in October 2026.

40.
           41.
           42.
s = 9/√2 = 6.36396+
Trivial. 		s = 5 + √2 = 6.41421+
Found by Maurizio Morandi
in October 2026. 		s = 3 + 5/√2 = 6.53553+
Found by Maurizio Morandi
in October 2026.

43.
           44.
           45.
s = 3(3 + √2)/2 = 6.62132+
Found by Maurizio Morandi
in October 2026. 		s = 6.69032+
Found by Maurizio Morandi
in October 2026. 		s = 6.77087+
Found by Maurizio Morandi
in October 2026.

46.
           47.
           48.
s = 6.85339+
Found by Maurizio Morandi
in October 2026. 		s = 6.91405+
Found by Maurizio Morandi
in October 2026. 		s = 6.98311+
Found by Beckett Kaplinski
in October 2026.

49.
           50.
s = 7
Trivial. 		s = 5√2 = 7.07107+
Trivial.