The Pythagorean Theorem as a Rooted In-tree Dependency Graph

Jesse Atkinson
Proceedings of Bridges 2016: Mathematics, Music, Art, Architecture, Education, Culture (2016)
Pages 503–506 Short Papers


We look back to concept and dependency graphs of Euclid’s Elements, Book 1, that show the deductive relationships among its propositions. We claim that Book 1 does not have one overall coherent structure but rather is organized around two propositions—1.45 and 1.47. In other words, Book 1 has a dual core. For the latter proposition, the Pythagorean Theorem, we constructed a rooted in-tree graph to help visualize its role and proof.