September 29-November 17, 2011
Gould Library
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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.

This relationship between topology and geometry was the subject of a recent seminar course, and this exhibit presents some examples of surfaces and a smattering of ideas which were studied. To a mathematician, a surface is an object without thickness and which locally has two dimensions of freedom. The theory of surfaces is rich, and because they are relatively simple and easy to visualize, they provide a wonderful first place to begin exploring the ideas of topology and geometry.

Many of the objects were created by Carleton students both for use in the course and as a result of the course. Others--including the beautiful blown-glass Acme Klein Bottle--were made by artists and are part of the Mathematics Department collection. Whether finely crafted or made from simple materials, this collection of objects is designed to facilitate understanding and enhance the meaning of abstract mathematical ideas.