An impossible construction

Community Mathematics Centre, CoMaC (2013) An impossible construction. At Right Angles, 2 (1). p. 65.

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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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Articles in APF Magazines

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Community Mathematics Centre, CoMaC

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