Viz

MATH 395: Surfaces

Instructor: Helen Wong
Mathematics
Spring 2011

Viz Math with Models Webpage
Course Description
Selected topics in the topology and geometry of surfaces, possibly including the classification theorem; the fundamental group and mapping class group of surfaces; gluing construction of surfaces from Euclidean, spherical and hyperbolic polygons; tessellations and their related quotient spaces.

Introduction

Helen Wong taught MATH 395:Surfaces during Spring 2011. Students explored the relationship between topology and geometry in the course, and this exhibit presents some examples of surfaces and a smattering of ideas which were studied. Many of the objects were created by Carleton students both for use in the course and as a result of the course, and all of the labels were written by students in Helen's class.

Topology and geometry are two mathematical subjects that ask questions about shape. A sphere is inherently different from the surface of a doughnut, but how can we describe this in a mathematically precise way? In geometry these types of questions are answered by comparing local measurements--of angles and curvature, of shortest distances between nearby points. In topology, a looser global view is taken that ignores local fluctuations and focuses on more qualitative properties like orientability or genus (whether the surface has any doughnut holes). By their very nature, the two subjects go hand in hand, bound tightly together by many beautiful theorems.

Exhibition and Label Assignment

Exhibition Images and Labels