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.