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.

Hmmm, it seems that you would be able to do 2n+2 regions with 2 n-sided polygons, in the same way as with squares (putting them on top of each other and then rotating one slightly).

For three squares, i'm guesstimating from a sketch that you can get 22 regions.

Posted by vswitchs on 2006-09-06 13:24:27