Triangles in Pentagons

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


1.
           2.
           3.
s = cos(42°) / cos(18°)
s = .781+
Trivial.
 
s = √(6/(3+√5))
s = 1.070+
Found by Erich Friedman
in March 2012.
s = 1.143+
Found by Maurizio Morandi
in August 2012.
 


4.
           5.
           6.
s = 1.199+
Found by Maurizio Morandi
in July 2012.
 
s = 1 + 2sin(12°)/√3
s = 1.240+
Found by Erich Friedman
in March 2012.
s = 3+3/√5-√(6+6/√5)
s = 1.394+
Found by Maurizio Morandi
in July 2012.


7.
           8.
           9.
s = 1.581+
Found by David W. Cantrell
in July 2012.
s = 1.659+
Found by Maurizio Morandi
in July 2012.
s = 1.767+
Found by DC after MM
in August 2012.


10.
           11.
           12.
s = 30/(3+3√5+√(6(5+√5)) = 1.840+
Found by David W. Cantrell
in July 2012.
s = 1.906+
Found by David W. Cantrell
in July 2012.
s = 1.991+
Found by David W. Cantrell
in August 2012.


13.
           14.
s = 2.040+
Found by David W. Cantrell
in August 2012.
s = (3+√(15–6√5))/2 = 2.129+
Found by Maurizio Morandi
in September 2012.


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