Dan Coby writes:
Thanks. I took a look at the postings on r.c.woodturning. From DJ's
equations I see that there are additional issues with N = 3 that I had
not considered.

At N=3 the angles are all leaning the "other way" so the sin/cos stuff
doesn't work out, plus you measure off the other side of each segment.
I tested N=2 also but there were infinities. I suppose if you can't
figure out the math for N=2, you probably shouldn't be using heavy
equipment with sharp objects.