Retorts

Circling a Pentagon

With reference to Dr Taylor's letter concerning the construction of a regular pentagon [Retorts, November], there are a number of ways this can be done, indeed, Euclid gave a method in the last book of his Elements.

Perhaps the simplest way to draw a regular pentagon within a circle is to draw the circle, centre O, with perpendicular diameters AB, CD as shown. Bisect OB at M. Draw an arc centre M, of radius length CM, cutting AO at N. Draw an arc centre C, radius CN, cutting the circle at P and Q. CP and CQ are two sides of the required regular pentagon. Step out the other sides around the circle.

Russell Dear, Invercargill