Mechanical advantage: The Archimedean tradition of acquiring geometric insight from mechanical metaphor

Abstract

Archimedes’ genius was derived in no small part from his ability to effortlessly interpret problems in both geometric and mechanical ways. We explore, in a modern context, the application of mechanical reasoning to geometric problem solving. The general form of this inherently Archimedean approach is described and it’s specific use is demonstrated with regard to the problem of finding the geodesics of a surface. Archimedes’ approach to thinking about problems may be his greatest contribution, and in that spirit we present some work related to teaching Archimedes’ ideas at an elementary level. The aim is to cultivate the same sort of creative problem solving employed by Archimedes, in young students with nascent mechanical reasoning skills.