Squares in Pentagons

The following pictures show n unit squares packed inside the smallest known pentagon (with side s).


1.
           2.
           3.
s = cos(27°) / cos(18°)
s = .936+
Trivial.
 
s = 4√(1-2/√5)+√5-2
s = 1.535+
Found by Erich Friedman
in March 2012.
s = 1.695+
Found by David W. Cantrell
in July 2012.
 


4.
           5.
           6.
s = 1.861+
Found by Maurizio Morandi
in July 2012.
 
s = 1 + cos(18°)
s = 1.951+
Found by Erich Friedman
in March 2012.
s = 6√(1-2/√5)+√5-2
s = 2.185+
Found by Erich Friedman
in March 2012.


7.
           8.
           9.
s = 6√(1-2/√5)+2√5-4
s = 2.421+
Found by Erich Friedman
in July 2012.
s = 2.565+
David W. Cantrell
in July 2012.
 
s = 2.770+
Found by David W. Cantrell
in July 2012.
 


10.
           11.
           12.
s = 2.809+
Found by David W. Cantrell
in July 2012.
s = 2.921+
Found by David W. Cantrell
in July 2012.
s = 2.973+
Found by David W. Cantrell
in July 2012.


13.
           14.
           15.
s = 2√(1-2/√5)+2√5-2
s = 3.121+
Found by David W. Cantrell
in July 2012.
s = 3.187+
Found by David W. Cantrell
in July 2012.
 
s = (√(125-38√5)+8-2√5)/3
s = 3.284+
Found by David W. Cantrell
in July 2012.


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