Re: Trisecting an arbitrary angle


quasi wrote:
> On Tue, 19 Jul 2005 12:37:14 +0200, "Jutta Gut"
> <gut.jutta.gerhard@xxxxxxxxx> wrote:
> >
> >If I understand correctly, you have shown that in an triangle with
> >the sides a^3 , a*(b^2-a^2) , b*(b^2-2*a^2) one angle is three times
> >another one.
> >
> >The more interesting question would be: given an angle, how to
> >construct a triangle with the sides a^3 , a*(b^2-a^2) , b*(b^2-2*a^2)
> >and the given angle?
> >
> >Jutta
>
> Contructing the triangle effectively trisects the given angle which in
> general has been shown to not be possible using straight edge and
> compass. There are only countably many angles for which trisection by
> straight edge and compass is possible.

The OP isn't requiring that an arbitrary angle be trisected.

Maybe, during the construction process, the smaller angle will be
tripled, which _is_ allowed using straightedge and compass.

--- Christopher Heckman

.

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