From: Gerry Myerson <gerry@mpce.mq.edu.au>
Subject: Re: trisecting an angle = 135 degrees
Date: Mon, 10 Apr 2000 16:56:48 +1000
Newsgroups: sci.math
Summary: Angles that can be trisected but not constructed

In article <5qqqescq0ev17tlb039q8v7pjht7p8v81g@4ax.com>, Fred W. 
Helenius <fredh@ix.netcom.com> wrote:

=> Gerry Myerson <gerry@mpce.mq.edu.au> wrote:
=> 
=> >It has been noted that there are angles that can be constructed 
=> >(with compass & unmarked straightedge) but not trisected, e.g., 
=> >pi/3 (a.k.a. 60 degrees). 
=> 
=> >Has it been noted that there are angles that can be trisected 
=> >but not constructed? 
=> 
=> If you mean angles like m*Pi/n, m,n integers, n not a multiple
=> of 3, the answer is yes, on this newsgroup, about a year and a
=> half ago, by the poster who goes by spamless@nil.nil:
=> 
=> http://www.deja.com/getdoc.xp?AN=401658676&fmt=text

I like this. 

Another example is given by Hadlock, in Field Theory and its Classical 
Problems. Let x be the angle whose cosine is half the cube root of 2. 
Then the cosine of 3x is 1 - (3/2)cuberoot2, so 3x is trisectable 
but not constructible. 

Gerry Myerson (gerry@mpce.mq.edu.au)