trisect

You can't trisect an arc using only a compass and a straightedge.

There's a construction in the plane for trisecting a segment.

You are correct, but you can trisect that piece of wood an infinite number of ways.

Yup - they're the same thing... you trisect the angle from the corner, and end up with an edge neatly in thirds.

If you're starting from nothing, all you need is a square of paper; origami can trisect an angle.

" How come geometry classes never prove that it's impossible to trisect the angle?

This is actually quite similar to the reason you can't trisect an angle, square a circle, or double a cube.

If you can put the points of the compass against the straightedge, which gives you a marked straightedge, you can trisect an angle.

Then, at the end of class, he mentioned that no one had ever succeeded in figuring out a method to trisect angles.

This stuff is all 200 years old, or so, but you'll still find cranks who think they can trisect angles using classical greek construction techniques.

Especially when all you need to trisect an angle is a straightedge marked to measure a single fixed distance.

For example you can trisect an arbitrary angle if allowed an infinite number of steps.

If there were something special, one ought to observe endless failure, much like trying to trisect the angle or prove the parallel axiom; but instead, one observes remarkably rapid progress.

I’ll share one I’ve been pondering for 30 years since my geometry teacher told me it’s impossible: It’s not possible to trisect an arbitrary angle using only a straightedge and compass.

An important aspect of this isn't that you cant trisect any particular angle, its that you cant trisect any arbitrary angle, plenty of angles, like 90 degrees, are trivial to trisect.

It is not obvious that you can't trisect the angle, and there is a minimally complex way to obtain the result which is certainly more complex than, say, the impossibility of 1 = 2 in the integers.

Trisecting this segment, and connecting the trisection back to the angle, will trisect the angle.