Re: Math Trek: Trisecting an Angle with Origami

In article <d79173tnh69r8p5nenr3hb12akihpj4qkk@xxxxxxx>,
quasi <quasi@xxxxxxxx> wrote:

Let's define a "3D straightedge" as a device capable of drawing a
great circle between any 2 distinct points which are not polar
opposites. As far as a compass, stay with an ordinary 2D compass.

The simple question is, starting with the point (0,0,1) on the
standard unit sphere, what are all the constructible points?

All your 2D circles & great circles are given by quadratics,
so it seems to me you still only get points whose co-ordinates
are in quadratics extensions of quadratic extensions of ...
quadratic extensions of the rationals. If you can take square roots,
you should be able to get all such points.

--
Gerry Myerson (gerry@xxxxxxxxxxxxxxx) (i -> u for email)
.

Relevant Pages

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