Date of Award

2016

Document Type

Thesis

Degree Name

Bachelors

Department

Natural Sciences

First Advisor

Poimenidou, Eirini

Area of Concentration

Applied Mathematics

Abstract

In this thesis we examine methods of tiling using tiles which are subsets of Zn. We start by examining the traditional methods developed by Golomb, then move on to examining more modern techniques such as including methods of group theory, the Conway criterion, and the conversion of tiles to polynomials. We also briefly discuss the incredible proof of the Chalcraft conjecture which states that for any tile T there is some integer d such that T tiles Zd. Using two computer programs we developed to generate images of tilings with chosen tiles, we examine all possible, 79 tiles up to symmetries, contained in a 3 x 3 square to determine which can tile Z2. We then demonstrate how the methods work by using the tiles. We conclude this thesis by examining some of the open problems in tiling.

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