Date of Award


Degree Type


Degree Name

Honors Thesis



First Advisor

Prem Sharma


From the Megalithic Temples of Malta constructed over 5,500 years ago, to the Pyramid of Djoser in Egypt built some 4,700 years ago, to more recent works of architectural wonder such an the Taj Mahal, the testimonials to the innate human genius for creating beauty through symmetry, color, and patterns abound. Evidently, the mathematical underpinnings of many architectural marvels are mostly rooted in the Euclidean Geometry. Now, as marvelous as these monuments are, one may wonder what would be the concepts of beauty and symmetry in a non-Euclidean universe. It turns out that this is not a far-fetched thought. It is now an established fact (implied, for example, by Einstein's theory of relativity) that the space-time we live in is, in fact, non- Euclidea.n (or at least more non-Euclidean than Euclidean). Over the last two hundred years, we have corne to realize that the notion of distance in the universe is far more complex than what we had always believed. The goal of this thesis is to study the the concepts of symmetry and pattern in a purely topologica.l setting that is independent of any notion of distance.