Squares Covering Circles

The following pictures show n unit squares covering the largest known circle (of radius r).


1. 2. 3.
r = 1/2 = .500
Trivial.
r = 2 - √2 = .585+
Proved by Trevor Green
in August 1999.
r = .794+
Proved by Trevor Green
in August 1999.

4. 5. 6.
r = 1
Proved by Trevor Green
in August 1999.
r = 1.028+
Found by Maurizio Morandi
in April 2009.
r = 1.126+
Found by Erich Friedman
in August 1999.

7. 8. 9.
r = 1.239+
Found by David Cantrell
in July 2002.
r = 1.375+
Found by Maurizio Morandi
in March 2009.
r = 3/2 =1.500
Trivial.

10. 11. 12.
r = 1.546+
Found by Trevor Green
in August 1999.
r = 1.608+
Found by Maurizio Morandi
in March 2009.
r = 1.701+
Found by David Cantrell
in August 2002.

13. 14. 15.
r = 1.779+
Found by Maurizio Morandi
in April 2009.
r = 1.883+
Found by David Cantrell
in July 2002.
r = 1.991+
Found by Maurizio Morandi
in April 2009.

16. 17. 18.
r = 2.007+
Found by Maurizio Morandi
in May 2009.
r = 2.042+
Found by Maurizio Morandi
in June 2009.
r = 2.116+
Found by Maurizio Morandi
in June 2009.

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