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Contribution to Book
A Noneuclidean Universe
Mathematics and Computer Science
  • Frank A. Farris, Santa Clara University
Document Type
Book Chapter
Publication Date
Mathematical Association of America (MAA)
Let us construct a hypothetical universe, if for no other reason than to challenge our preconceptions about space. We call it a noneuclidean universe because it contradicts some of the notions central to euclidean geometry, where, for instance, the angle measures in a triangle add up to 180 degrees. There are many noneuclidean universes; ours is of a type called hyperbolic. This hypothetical universe has been constructed before. It is often called the Poincaré Upper Halfplane, in honor of French mathematician Henri Poincaré (1854-1912). I admire Poincaré because he is said to have been the last person in the world who understood all the mathematics known in his day. In honor of Poincaré, let us call the inhabitants of our hypothetical universe the Poincarites.
Chapter of
Expeditions in Mathematics
Tatiana Shubin
David F. Hayes
Gerald L. Alexanderson

Copyright 2011 Mathematical Association of America. All Rights Reserved.

Citation Information
Farris, Frank A. "A Noneuclidean Universe." Expeditions in Mathematics. Ed. Tatiana Shubin, David F. Hayes, and Gerald L. Alexanderson. Washington, D.C.: Mathematical Association of America, 2011. 153-64.