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.

(In reply to re: spoiler by brianjn)

Use Art M's procedure to convert simple polygon P_1
into square S_1 and simple polygon P_2 into square S_2.

The squares are congruent by definition. 

Apply the cuts making up square S_1 to square S_2.

Now square S_2 is made up of pieces that can form
simple polygon P_1 or simple polygon P_2.

To convert a rectangle into a square see

  www.cut-the-knot.org/Curriculum/Geometry/SquareRectangle.shtml

To combine two squares into one see Proof #2 under

  www.cut-the-knot.org/pythagoras/index.shtml

Edited on September 26, 2006, 4:14 pm

Posted by Bractals on 2006-09-26 16:11:24