From: wcw@math.psu.edu (William C Waterhouse)
Subject: Re: hyperbolic constructions
Date: 15 Oct 1999 19:21:49 GMT
Newsgroups: sci.math.research
Keywords: trisect an angle there? (no)

In article <38053B40.917E9BF4@math.utexas.edu>, lewis bowen <lbowen@fireant.ma.utexas.edu> writes:
> Is it possible to trisect a (geodesic) segment in the hyperbolic plane
> using only a straightedge and compass?

The answer is no. This is stated as an exercise on p. 294 of 
R. Hartshorne, Companion to Euclid  (AMS, 1997). There are
no hints given, but the context shows that you are expected
to use the Poincare model of the hyperbolic plane with only
constructible points (in the usual sense) allowed.

William C. Waterhouse
Penn State