Squares Covering Triangles

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.

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.