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 = 1.961+
Found by Ed Pegg
in March 2005.

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

7.            8.            9.
s = 2.824+
Found by Maurizio Morandi
in August 2007. 		s = 2√2 = 2.828+
Trivial. 		s = 3
Trivial.

10.            11.            12.
s = 3.307+
Found by Maurizio Morandi
in November 2007. 		s = 2 + √2 = 3.414+
Found by Erich Friedman
in March 2005. 		s = 3.531+
Found by Maurizio Morandi
in August 2007.

13.            14.            15.
s = 3 + √2/2 = 3.707+
Found by Erich Friedman
in March 2005. 		s = 1 + 2√2 = 3.828+
Found by Erich Friedman
in March 2005. 		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 = 4.413+
Found by David Cantrell
in May 2005. 		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 = 4.799+
Found by Maurizio Morandi
in October 2007. 		s = 4.886+
Found by Maurizio Morandi
in November 2007. 		s = 4.947+
Found by Maurizio Morandi
in October 2007.

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