From: "Clive Tooth" <clive@pisquaredoversix.force9.co.uk>
Subject: Re: tools for trisection of angle ?
Date: Thu, 28 Jan 1999 15:58:06 -0000
Newsgroups: sci.math

Charles Mulks wrote in message <78q04k$9s2$1@msunews.cl.msu.edu>...
>
>I know you can't trisect an angle using only a compass
>and straightedge (at least I think I know it - my high
>school geometry is pushing 40 years old).
>
>What other simple tool(s) would I need to do it -
>assuming that it can be done.
>
>I can imagine drawing a circular arc, laying a string
>along the arc, straighten the string, trisect it, and
>lay it back along the arc - in which case all I need
>is a piece of string - but this seems more like a
>"close enough" approach.
>
>I'm looking for a "geometrically exact" method.
>
>TIA
>Charlie Mulks

Your method is not "close enough", it is exact!

Anyway, I have become interested in linkages lately and there are many
instruments which trisect an angle. One of them is called Pascal's
Trisector. It is described on page 228 of my (old) copy of "Mathematical
Models" by Cundy and Rollett.

Imagine a rod PAB, where B is free to slide along the rod. Imagine two other
rods AO and OB, each equal in length to AP. Imagine this placed down on a
line POC. As B slides along the rod the angle BPO is one third of the angle
BOC.

There is also another thing called a Tomahawk, which is a combination of a
T-square and a semicircle. I will leave you to research that. :)

Clive