Olivetti Club

Hazel BrennerCornell University
Optimal point sets determining few distinct triangles

Tuesday, April 6, 2021 - 4:30pm

If I hand you a stack of as many identical paper triangles as you like and tell you to put tacks in a corkboard so that any triple of tacks can pin the corners of one of the triangles, how many tacks can you place? How about if I give you n different types of triangles in d dimensions? It turns out we can prove that this question has unique answers for $n=1$ and $n=2$ for $d>2$ and perhaps more! The proof takes us on a tour of Erdős problems, finite metric spaces, basic graph theory, high school geometry and an obscure enumerative combinatorics paper from the 1950s. I recommend joining us to anyone who thinks triangles and/or counting things are neat! No particular background is needed.