Trivial.
Proved by Trevor Green
in August 1999.
Proved by Trevor Green
in August 1999.
The following pictures show n unit squares covering the largest known circle (of radius r).
| 1.
| 2.
| 3.
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| 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. 
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| 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. 
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| 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. 
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| 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. 
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| 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. 
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| 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. |