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Course Text Philosophy:

We will be using two 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 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. In particular, we will watch portions of two recent film versions of Flatland, plus several other movies and quite a few short computer animation sequences.

[HOME] Math 53 (Fall 2015) web pages
Created: 03 Sep 2015
Last modified: 03 Sep 2015 00:00:00
Comments to: dpvc@union.edu
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