Describe how every simple polygon can be tranformed into any other simple polygon with the same area by dissecting it with straight cuts and rearranging the pieces.

These are the steps to transform a simple polygon into a square. Then the second polygon can be constructed by reversing the steps.

1. Dissect polygon into triangles
2. Transform each triangle into a rectangle
3. Transform each rectangle into a square
4. Combine all squares into one by joining two at a time

Steps 3 and 4 are themselves interesting problems.

Edited on September 25, 2006, 11:36 pm

Posted by Art M on 2006-09-25 23:35:03