In "Covering a circle" you were to cover a unit circle with 3 squares as small as possible.

I would like instead to cover a circle of maximum radius with n non-overlapping unit squares.

The n=3 problem is solved. Try 4, 5, 6, 7, and 8. (Feel free to keep going. I've done up to 36, but that's a bit excessive.)

unit         circle

squares radius

3              5/8

4              1

5              1

6              17/16 *

7              SQRT(5)/2

8              5/4

9              3/2

 

 

*confirmed with the help of the Circle Calculator I found at the following link:  http://www.1728.com/circsect.htm 

 

I used the following unit square layouts to help determine the radius sizes. Where n=5, it mattered not where the fifth square was placed. The orientation, of course, also does not matter.

 ___

|   |___

|___|   |

|   |___| 

|___|

 ___ ___

|   |   |

|___|___|

|   |   | 

|___|___|

 ___ ___

|   |   |___

|___|___|   |

|   |   |___| 

|___|___|

 ___ ___

|   |   |___

|___|___|   |

|   |   |___| 

|___|___|

  |   |

  |___|

     ___

 ___|   |___

|   |___|   |

|___|   |___|

|   |___|   |

|___|   |___|

    |___|

 ___ ___ ___

|   |   |   |

|___|___|___|

|   |   |   | 

|___|___|___|

  |   |   |

  |___|___|

 ___ ___ ___

|   |   |   |

|___|___|___|

|   |   |   | 

|___|___|___|

|   |   |   |

|___|___|___|

 

Edited on June 23, 2006, 7:52 am

Posted by Dej Mar on 2006-06-23 07:51:46