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Re: Trisection
Posted:
Jul 19, 2002 9:54 AM
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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.
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