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The Edge of the Universe-Noneuclidean Wallpaper
Mathematics and Computer Science
  • Frank A. Farris, Santa Clara University
Document Type
Publication Date
Mathematical Association of America (MAA)

A simple mathematical model of a two-dimensional universe, called the Poincaré Upper Halfplane, illustrates the possibility of a universe with an unattainable edge. In this article, I describe this model -a famous example of a noneuclidean geometry-and explain how conversations with an analytic number theorist led me to create wallpaper patterns for its inhabitants. These are interesting not only for their high "Gee whiz!"factor, but also as a window for observing the features of this unusual geometry.


Copyright 2001 Mathematical Association of America. All Rights Reserved. Stable URL

Citation Information
FARRIS, Frank A. "The Edge of the Universe-Noneuclidean Wallpaper."Math Horizons, 8, (September, 2001): 16-23. The MAA honored this article with the Trevor Evans Award in 2002. It later appeared in a volume of selected articles from Math Horizons, which took its title from the title of my article.