Euclid, the ancient Greek geometer, documented hundreds of geometric proofs in thirteen books known as the Elements.
Their deductive format set the basis for the geometry commonly used today in Euclidean geometry.
Our research over several semesters (sponsored by AMP) involved examining the first book of Euclid's Elements, initially through such propositions as 1.45 and 1.47'the Pythagorean Theorem'and more recently the other 46 propositions.
Through investigating the premises (applica) and the e applicata (propositions needed in proofs) of propositions, we found that proofs are built in a vertex-and-edge structure. This can be presented through dependency graphs and is closely related to the graph theory found in fields such as neuroscience, computer science, and biology.
We have produced several art pieces derived from our data that serve as artistic and visual representations of the graph theory used in the proofs in Euclid's Elements. This helps to bridge the gap from STEM to STEAM and broaden the accessibility of these concepts to those outside of STEM fields.
With these tools in hand, we attempt to rationalize Euclid's Elements, both in terms of itself as well as within the greater intellectual realm.