This is a small programm that I wrote to demonstrate the Wallace-Bolyai-Gerwien theorem. You can create an arbitrary polygon (by clicking with the mouse) which will then be transformed (by cutting along straight lines and moving and rotating of the resulting pieces) into a rectangle of the same area and with a predetermined fixed width. More detailed instructions can be found below.
The program was created using the Common Lisp
compiler from LispWorks.
You can download it from
http://weitz.de/files/Polygons.dmg (OS X).
You are free to use this software for private or educational purposes.
(But you are of course using it at your own risk.) However, redistribution of any kind is not allowed without
If you want to give this program to someone else, point them to the
original download location
When you start the program, you'll see a pane that's mostly white and a gray rectangle to the right which occupies about 30% of the window's area. The gray rectangle is the "target" and the aim of the program is to cut your (still-to-be-constructed) polygon into pieces that will fit exactly into this target (up to a specific height which can only be determined once you've actually created a polygon).
Click in the white area to specify the corners of your polygon, either clockwise or counterclockwise. Once you click on your first corner for the second time, your polygon is finished. At this point you'll notice that the corners aren't emphasized as circles anymore. You'll also see a dashed horizontal line in the target rectangle: The program has computed your polygon's area and the pieces it is about to create will have to fit exactly into the gray area below the dashed line.
Everything in this program (except for clicking to add polygon
corners) is done with the context menu. You can for example always
undo the last corner by right-clicking and selecting "
Remove last point".
(In this case, you can also type
Or you can select "
Restart from scratch" to remove
everything you've done so far.
Once you're happy with your polygon, select "
Transform the entire polygon"
and you can then watch an animation that should end with your
polygon neatly chopped into pieces which are stacked in the target
rectangle occupying just the right height. You'll notice that the
program will cut away triangles from the polygon until it is
finished. If you select "
Transform only one triangle", only
one of these steps is shown. In both cases the program won't accept
mouse input while the animation is running. This is on purpose.
Should you encounter a bug, please be so kind to send me an email with
information about the problem. In this case it'd be very helpful if you could call "
Dump all polygons"
from the context menu while the program is still running and send me
the file that was written. (It will contain a list of all polygons
you entered in your session so that I'll have a chance to reproduce
the error you've seen.)
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