ABSTRACT
This chapter unveils the psychological basis for one of the most famous theorems in mathematics: the Pythagorean theorem. The ancient Greek mathematician, Euclid, proved the Pythagorean theorem through a sequence of 47 propositions, based on five axioms (postulates), which themselves are based on Plato’s rules for construction. In developing the first axiomatic system, Euclid provided a rigorous method for proof and proving. Looking closer at the Pythagorean theorem and Euclid’s proof of it, we can find evidence of these actions, which include sweeps and shears that produce and transform area. On one hand, axiomatization provides for rigorous (rule-based) methods of communicating arguments. On the other hand, it masks the dynamic nature of mathematics. A dynamic investigation of the Pythagorean theorem leads to a more intuitive proof and a generalization of the theorem.
