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Cutting planes with polygons (Posted on 2006-09-06) Difficulty: 3 of 5
Into how many regions can you partition the plane with m n-sided regular polygons?

For example, with two squares you can achieve up to 10 regions by choosing the right size and position of your squares.

See The Solution Submitted by JLo    
Rating: 4.0000 (2 votes)

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Solution an equation | Comment 3 of 17 |

I believe the equation, where P is the number of regions the plane is partitioned, is: 

P = n*(m)*(m-1) + 2

For two squares this is 4*(2)*(2-1)+2 = 10.

 

Edited on September 6, 2006, 3:13 pm
  Posted by Dej Mar on 2006-09-06 15:08:19

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