Community Mathematics Centre, CoMaC
(2013)
An impossible construction.
At Right Angles, 2 (1).
p. 65.
Abstract
It is well known that there is no general procedure
for trisecting an angle using only a compass and
unmarked ruler (naturally, we must stick to the
rules governing geometric constructions).
In particular, a 60° angle cannot be so trisected.
This implies that a 20° angle cannot be constructed
using such means. However, here is a construction
which appears to do the impossible! Throughout,
the notation ‘Circle(P,Q)’ means: “circle with
centre P, passing through Q” (for a given pair of
points P, Q). We start with any two points O and A
(see Figure 1) and follow the steps given below.
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