Squares in Tans

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


1.            2.            3.
s = 2
Trivial.
s = 2√2 = 2.828+
Trivial.
s = 3
Trivial.


4.            5.            6.
s = 5 / √2 = 3.535
Found by Erich Friedman
in March 2005.
s = 4
Found by Erich Friedman
in March 2005.
s = 4
Trivial.


7.            8.            9.
s = 3 + √2 = 4.414+
Found by Erich Friedman
in March 2005.
s = 2 + 2√2 = 4.828+
Found by Erich Friedman
in March 2005.
s = 7 / √2 = 4.949+
Found by Erich Friedman
in March 2005.


10.            11.            12.
s = 5
Trivial.
s = 4 + √2 = 5.414+
Found by Erich Friedman
in March 2005.
s = 4√2 = 5.656+
Found by Erich Friedman
in March 2005.


13.            14.            15.
s = 3 + 2√2 = 5.828+
Found by Erich Friedman
in March 2005.
s = 6
Found by Erich Friedman
in March 2005.
s = 6
Trivial.


16.            17.            18.
s = 9 / √2 = 6.363+
Found by Erich Friedman
in March 2005.
s = 5 + √2 = 6.414+
Found by Erich Friedman
in March 2005.
s = 4 + 2√2 = 6.828+
Found by Erich Friedman
in March 2005.


19.            20.            21.
s = 2 + 7 / √2 = 6.949+
Found by David W. Cantrell
in May 2005.
s = 7
Found by Erich Friedman
in March 2005.
s = 7
Trivial.


22.            23.            24.
s = 1 + 9 / √2 = 7.363+
Found by Erich Friedman
in March 2005.
s = 6 + √2 = 7.414+
Found by Erich Friedman
in March 2005.
s = 7 + 1 / √2 = 7.707+
Found by David W. Cantrell
in May 2005.


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