Date: Jul 19, 2002 9:54 AM
Author: Steve Gray
Subject: Re: Trisection
Mark Stark wrote:

> Steve wrote:

>

> > I just did a 5-minute check with Geometer's Sketchpad. In one

> >iteration (original directions only) it didn't do too well. My angle

> >was 75 degrees. My guess for placing D was BD/BA=0.292.

> >The angle E'OB comes out to be 25.562 degrees, 2% high.

> > I think my construction is correct because as the first guess

> >approaches 25 degrees, the construction result does also.

> > But I agree that further tweaks might make it much better.

>

> Steve:

>

> I think there is something wrong with your construction.

> I am assuming you were using 75 degrees as your unknown angle at point

> A,(this is the original lettering), intended length AB=AC=1 and the

> first guess radius from step 4 to be CD=.292 (I'm not sure why you

> call it BD). My results using the above yield 24.996 deg.

> Even if I do use BD=.292, (which is outside the first guess parameters

> of the construction) I get 25.174 deg.

>

> Please try again.

>

> Mark.

You're right. My error was putting F down such that AF=2*AC instead of

3*AC. Now I get 24.999 degrees! Much better!

Have you tried to find under what conditions this procedure makes its

worst error?

One could require that the first guess for point D to be CD/CB=3/8.

Mathematica

would be useful for solving the algebra.

Very nice construction.

Steve.