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. |