The Pentagonal Numbers Meet the Choose-4 Numbers

James Morrow
Proceedings of Bridges 2016: Mathematics, Music, Art, Architecture, Education, Culture (2016)
Pages 529–532 Short Papers


The artistic endeavor of visually representing 70 as both a pentagonal number and a combinatorial number raised some questions, conjectures, and then proofs, concerning the relationship between pentagonal numbers and Choose-4 numbers in Pascal's triangle. The proofs, initially failing to give understanding, inspired, through visualization, a deeper mathematical understanding and an interesting and satisfying solution to the initial artistic endeavor.