Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP
Path: utzoo!watmath!clyde!burl!ulysses!bellcore!decvax!decwrl!amdcad!amd!pesnta!hplabs!hao!seismo!umcp-cs!aplcen!jhunix!ins_ampm
From: ins_ampm@jhunix.UUCP (Michael P McKenna)
Newsgroups: net.puzzle
Subject: Re: A New Trigonometrical puzzle.
Message-ID: <2130@jhunix.UUCP>
Date: Sat, 8-Mar-86 21:55:57 EST
Article-I.D.: jhunix.2130
Posted: Sat Mar  8 21:55:57 1986
Date-Received: Thu, 13-Mar-86 07:46:28 EST
References: <35@rtgvax.UUCP>
Reply-To: ins_ampm@jhunix.ARPA (Michael P McKenna)
Organization: Johns Hopkins Univ. Computing Ctr.
Lines: 25

In article <35@rtgvax.UUCP> smjw@rtgvax.UUCP writes:
>
>
>Here is a puzzle I was told about many years ago but have
>not seen since. I have not been able to solve it so am not
>sure it can be.
>
>Take any triangle and trisect its internal angles. The points
>at which the trisecting lines first intersect each other form 
>another triangle.
>Prove that that triangle is alway equilateral.
>
>I would be very grateful to anyone who can simply prove
>(or disprove) the above statement.
>

You can find a proof of this in _Introduction to Geometry_ by
H.S.M. Coxeter.  This is a WONDERFUL book that explores many aspects
of geometry (introduction is something of a misnomer).  If you can't
find it in your library COMPLAIN VERY LOUDLY!

                                                     Dwight S. Wilson

P.S.  For anyone interested in buying this book:  The publisher
      is John Wiley, & Sons, Inc.