With the angle to trisect equal to 75 degrees, suppose your initial
guess is 25+e (e given in degrees), then the construction will give
an angle 25+e' (e' in degrees is the new error), with the approximation:
e' == 0.00000 63462 * e^3
Exact values are (we are always in degrees):
e = 1, e' = 0.00000 63462
e = 10, e' = 0.00634 61824
e = 20, e' = 0.05076 78055
e = 30, e' = 0.17131 72068
These values are the result of exact algebraic computations carried
out using Maple. I checked them numerically using Cabri-Geometry.
However, for the specific case of 75 degrees, the degree 8 polynomial
giving the result has two close roots near 25 degrees (25 and 24.207). It
means that choosing another set of intersection points than the one described
may lead to this wrong position.
At 13:44 18/07/2002 -0400, Mark Stark 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.
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.