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


7.
           8.
           9.
s = 2.824+
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 W. 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 = 3 + 5√2/4 = 4.767+
Found by Maurizio Morandi
in July 2009.
s = 4.886+
Found by Maurizio Morandi
in November 2007.
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.


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