Make your own dissection puzzle

Just take any rectangle and draw approximate squares in it. Do the algebra to find the sizes. The only problem is that if your squares are very inaccurately drawn, you might find that some of them have zero or even negative sides!

Here's an example with some very nonsquare squares. In order to square them up, some have to be set to size zero. The figure on the left is a rectangle dissected into rectangles, and the sizes computed if they're to be squares. Note that there are two red rectangles labelled 0. The figure on the right has those two zeroed rectangles removed and the remaining rectangles squared off.

3 4
2 1
1 0
1 3
2 0
2
  
3 4
2 1
1 1 3
2 2

It can also happen that some of the rectangles are assigned negative sizes. I'll leave it to you to figure out how to adjust the drawing to make them positive.

To Puzzle 7.

1999. This page may be printed for classroom use.
David E. Joyce

Department of Mathematics and Computer Science
Clark University
Worcester, MA 01610

The address of this file is http://aleph0.clarku.edu/~djoyce/puzzles/square1.html