Geometric Constructions Using Hinged Mirrors

The debate over what geometry to teach has raged without resolution or respite for years, with nearly any position having its proponents and detractors. However, in all these exchanges I have yet to hear the suggestion that the teaching of geometric constructions be replaced by something better, for a number of possible reasons. Most of the constructions we teach are actually quite useful. They give the secondary school student, starved for a Piagetian concrete-operational experience, something tangible. The constructions offer an opportunity for problem solving if properly presented. Probably most significant, however, is the simple fact that they are inherently interesting, as an extensive literature on the problems attests.