# Jesse Atkinson, Charles Knight, Phillip Weaver

All three artists are all interested in graphs of mathematical proofs, especially 3-D graphs, which can represent such proofs in a beautiful, unique, and visually exciting manner. As networks, these 3-D graphs have possible isomorphic relations to mammalian brain neural networks. Such relations are part of the on-going investigations of these artists.

3-D rooted tree dependency graph of the proof of the Pythagorean Theorem (I.47), following Euclid's proof in Book 1, Elements. Each node or vertex (wooden ball) is a proposition, common notion, postuate, or definition, and each edge (a 1/8" brass rod) is a deductive edge, except for those connecting definitions to a proposition. All propositions needed to prove I.47 are themselves proven in this structure, some 31 propositions in all. If any proposition appears more than once, then it has its own node, but its proof is not repeated. The larger wooden balls are of mountain myrtle; myrtle leaves were used to crown victors in war and games, along with olive lives. The smaller wooden balls are of pine.