Overview

Ancient Greek mathematicians systematized their knowledge about geometry, with the compendium by Euclid providing definitions, axioms, theorems, and proofs in final form. His Elements dictated the standard for communicating mathematical results and served as the basis for elementary mathematics education for centuries.

Background

Traditionally, Thales of Miletus (c. 624-547 B.C.) is credited with bringing geometry to Greece from Egypt. Stories about him relate that he proved such theorems as the equality of base angles in an isosceles triangle, the equality of vertical angles, and the angle-side-angle criterion for triangle congruence. These stories are important not because they are incontrovertibly true, which is impossible to ascertain, but because they demonstrate that Greeks of several hundred years later saw themselves as approaching geometry in a new way after Thales's contributions.

For example, the Pythagoreans...