From: chenrich@monmouth.com (Christopher J. Henrich) Newsgroups: sci.math Subject: Re: Angle trisection Date: Sat, 11 Jan 1997 13:12:02 -0500 In article <5b0nhs\$c0s@corn.cso.niu.edu>, grubb@math.niu.edu wrote: > Robin Chapman (rjc@maths.ex.ac.uk) writes: > > In the recent "The Book of Numbers" (Springer 1996) Conway and Guy > > give constructions for regular 7, 9 and 13-gons using straightedge, > > compass and angle trisector. The heptagon construction is amazingly > > neat. > > > I am curious if there is a characterization of the regular polygons > that can be constructed with compass and *marked* straight-edge. > Since this gives an angle trisector, we can solve cubics, so those > whose number of sides is 2^n 3^m p_1 p_2 ...p_k where each p_i is > a prime of the form (2^a 3^b +1) should be possible. Are there others? > In particular, can an 11-gon be constructed in this way? How about > a 25-gon? > > ---Dan Grubb See the article "Angle Trisection, the Heptagon, and the Triskaidekagon", by Andrew M. Gleason, in _The American Mathematical Monthly_ vol. 95 #3 (March 1988), pp. 185-194. I think 11 -gons and 25-gons are not constructible with a trisector. You need a quinsector. (Anybody got one?) -- Christopher J. Henrich chenrich@monmouth.com