Re: [math-fun] What's your proof?

At 09:26 AM 6/11/03, John McCarthy wrote:

A polygon can be scaled to have vertices at lattice points if and only if all its angles have rational tangents.

I don't think so. That would mean there was a lattice-point regular octagon, but there isn't, as JHC has just confirmed. For another example, consider a parallelogram with angles that are alternately arctan(2) and arctan(-2), and with sides alternately 1 and pi. The tangents are rational, but lattice-point distances can't be in the ratio 1:pi. -- Fred W. Helenius <fredh@ix.netcom.com>