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Course Text Philosophy:

We will be using three principal texts in this course. The first is Beyond the Third Dimension by Thomas Banchoff. This is an introduction to the idea of higher dimensions intended for the non-mathematician; it includes examples from many branches of life, and suggests ways we can investigate four dimensions using analogies from two and three dimensions. We will use it as a starting point for our discussions, and will try to fill in some of the mathematical details as we go.

The second is Jeff Weeks' The Shape of Space. This is intended as an introduction to 3-manifolds (a important topic of current research in mathematics), but it is very readable and includes lots if interesting material pertinent to dimensions, and to the geometric and topological ideas that we will be studying. We will call on it regularly as a reference and source of inspiration in these areas.

The third book is the 19th-century novel Flatland. This is a classic work that must be read by anyone interested in higher dimensions, as it has been an important influence on geometers and other scientists ever since its publication in 1884. It chronicles the adventure of a creature living in a fictitious two-dimensional world, and how he comes to learn ways of understanding a three-dimensional space. We are meant to use this as a pattern for trying to visualize four- and higher-dimensional spaces. In addition to having a mathematical agenda, Flatland is a social commentary on Victorian English society, particularly on the way it treated women and the poor. In good Swiftian tradition, Abbott has exaggerated these oppressive customs in his planar community as a means of satirizing his own society.

In addition to these longer books, we will be reading several short stories or excerpts that address the fourth dimension, and will view mathematical videotapes when appropriate to the subject.

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Created: 24 Mar 2005
Last modified: 24 Mar 2005 10:52:23
Comments to: dpvc@union.edu
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