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