Math is off the walls : an honors thesis (HONRS 499)

Wallpaper is a household item that to the untrained eye has no apparent mathematical qualities aside from simple geometric symmetries. However, upon further scrutiny, a plethora of deep and beautiful mathematics may be seen hiding among these images. This paper represents my exposition of the results of the work of numerous mathematicians regarding the mathematics of wallpaper. The mathematical topics seen in this paper include, but are not limited to semi-direct products of groups, isometries, orbifolds, non-positive curvature, and Coxeter groups.