Similar Figures

Extract

If it was required to divide the area in Fig. 1 into n equal parts—say, for simplicity, three equal parts—how should we proceed?

There is a method, given in books on geometry, of constructing a figure similar to a given figure and n times its area. This method pivots on a property of similar figures as follows: if ABCDE and

FGHKL are similar figures on bases AE and FL respectively, then

A₁: A₂ = AE²: FL²

For purposes of comparison with what follows, the solution by this method is here recalled.