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


Mark Stark wrote:
> Steve wrote: > > > I just did a 5minute 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.



