Squares in Circles

The following pictures show n squares packed inside a unit circle, so that the total sum of the sides of the squares is as large as possible.


1.            2.            3.
s = √2 = 1.414+
Trivial.
s = 4 / √5 = 1.788+
Trivial.
s = 2.331+
Found by Erich Friedman
in June 2011.


4.            5.            6.
s = 2√2 = 2.828+
Found by Erich Friedman
in June 2011.
s = 3.204+
Found by Maurizio Morandi
in July 2011.
s = 3.597+
Found by Maurizio Morandi
in July 2011.


7.            8.            9.
s = (2√10 + √190) / 5 = 4.021+
Found by Erich Friedman
in June 2011.
s = (10√2 + 5√10 + √190) / 10 = 4.373+
Found by Erich Friedman
in June 2011.
s = (10√2 + 3√10) / 5 = 4.725+
Found by Erich Friedman
in June 2011.


10.            11.            12.
s = 4.970+
Found by Erich Friedman
in June 2011.
s = 5.185+
Found by Maurizio Morandi
in July 2011.
s = 5.419+
Found by Maurizio Morandi
in August 2011.


13.            14.            15.
s = 5.720+
Found by Maurizio Morandi
in August 2011.
s = 6.005+
Found by Erich Friedman
in June 2011.
s = 6.218+
Found by Maurizio Morandi
in July 2011.


16.            17.            18.
s = 6.435+
Found by Maurizio Morandi
in July 2011.
s = 6.595+
Found by Maurizio Morandi
in July 2011.
s = 6.816+
Found by Maurizio Morandi
in July 2011.


19.            20.            21.
s = 7.069+
Found by David W. Cantrell
in July 2011.
s = 7.271+
Found by Maurizio Morandi
in July 2011.
s = 7.473+
Found by Maurizio Morandi
in July 2011.


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