Euclid’s Elements (c. 300 BCE) has long been held to be an example of minimalist mathematical beauty. As mathematics educators interested in embodied learning, we want to share that beauty with our students (and mainstream dance audiences), to promote understanding and appreciation of Euclidean proofs in visceral, movement-oriented ways. This paper reports on a successful experiment in dancing Euclidean proofs in the context of a university mathematics education class, and explores philosophical, mathematical, and pedagogical dimensions of the process of dancing geometric proofs on the beach.