**Advisor**

### Dr. Daniel M Look

### Support

Though each discipline tends to be regarded as the antithesis of the other, mathematics and art intersect often and with fascinating results. This junction appears notably in the works of M.C Escher, a Dutch artist who, despite his incredulity in having any mathematical prowess, developed his own ideas of plane division which would appear in his tessellations. These tessellations would inspire his interest in what mathematicians call plane crystallographic or wallpaper groups, which are classifications of wallpaper patterns, or two dimensional repetitive patterns. This research was done as an investigation into why there are exactly 17 wallpaper groups via a proof based in group theory and M.C Escherâ€™s artistic contribution to the argument. An artistic aspect of the research was also done with the goal of designing and painting a pattern belonging to each of the 17 wallpaper groups.