Question:
How can you trisect an angle using a compass and straight edge? I am taking
tenth grade geometry.

Replies:
I do not remember anything about the proof, but trisecting an angle using
compass and straightedge is not possible. Likewise, "squaring the circle"
is also not possible. It may have to do with irrational (or even transcen-
dental) numbers.

hawley
It depends on the angle. For example, since it is possible to construct a
30 degree angle, a right angle is trisectable. In general trisection is not
possible. For a nice discussion, see Felix Klein's Famous Problems of
Elementary Geometry (Chelsea 1955 and 1962 2nd ed.). Therein it states that
since general trisection is related to cubic equations, and only those
related to equations that may be solved using square roots are generally
constructable, we cannot trisect the angle or duplicate the cube.

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