Squares Covering Triangles
The following pictures show n unit squares covering the largest known equilateral triangle of side s.


1.            2.            3.
s = √6 - √2 = 1.035+
Trivial.
s = 1.322+
Found by Maurizio Morandi
in March 2009.
s = 2.108+
Found by David Cantrell
in August 2002.


4.            5.            6.
s = 4/√3 = 2.309+
Found by David Cantrell
in August 2002.
s = 2.534+
Found by Maurizio Morandi
in April 2009.
s = 3.168+
Found by David Cantrell
in August 2002.


7.            8.            9.
s = 3.327+
Found by Maurizio Morandi
in May 2009.
s = 3.495+
Found by Maurizio Morandi
in April 2009.
s = 3.711+
Found by Maurizio Morandi
in May 2009.


10.            11.            12.
s = 4.197+
Found by Maurizio Morandi
in April 2009.
s = 4.351+
Found by Maurizio Morandi
in May 2009.
s = 2√3 + √6 - √2 = 4.499+
Found by Maurizio Morandi
in May 2009.


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