Research Project

Written Proof ( Working File )

Techxpo 2021 Mathematical Sciences Winner

NUMS/PiMUC 2021 4th Place Presentation Winner

Convex Mosaics and Their Applications.

This study looked at convex polygonal mosaics in two and three dimensions. We discuss the combinatorial and averaging properties of certain mosaics and show how they relate. Using a unique topological approach, we prove the existence of a large class of convex planar mosaics within certain natural combinatorial restrictions. We derive corresponding properties of mosaics on the entire plane based on existing results on the average properties of mosaics on finite domains. We expand the existing theory by looking at non-convex, non-polygonal and\or non-normal mosaics and their relation to the Schläli plane. We suggest applications of our theory in understanding mosaics in physical situations. We suggest applications of our theory in understanding mosaics in physical situations.

Designed By: Micheal Bruner, Heidi Steiger, and Marie Steiger