Divide a circular disk into seven parts with a straightedge and compass such that each part has the same area and perimeter.

(In reply to re(2): Solution (picture) by owl)

Thanks, and it was intuitive because I immediately discounted the idea of creating a regular heptagon. Classical geometry doesn't allow this because it requires angle trisection, which is known to be impossible. There are a bunch of approximations for regular heptagons but nothing exact with a compass and straightedge. (My first mathematics teacher was an absolute genius and turned me on to much of this.)

Once you start thinking about other things, the first thing I thought of in non-conventional shapes was a yin-yang. From there it wasn't a stretch to use symmetry - I really only worked on half of the circle.

And that picture is so much nicer than the sloppy, smudged graph paper I have.

Posted by Eric on 2004-12-10 13:19:06