If the universe had an edge, you could go there, put your hand through and find something on the other side, right? This reasoning breaks down if you and your measuring devices shrink as you approach the edge, making it infinitely far away. We show a mathematical model of such a universe, called the Poincare Upper Halfplane, and study some of its features. Physics suggests that this turns out to be a cold and lonely place, but we make beautiful wallpaper for the inhabitants. (Hint: in the picture above, all the fan-shapes are exactly the same size!) This is a good chance to think about the shape of space and to apply some classic geometry, such as circle inversion. It is also a chance to see a demonstration with Geometer's Sketchpad.
Frank Farris won the Trevor Evans Award for his article, The Edge of the Universe, in the magazine Math Horizons in 2002. Previously he won the David Logothetti teaching award at Santa Clara University, where he has been a professor since 1984. Professor Farris received his doctorate from MIT in 1981, and is now Editor of Mathematics Magazine, a journal published for college mathematics students and faculty by the Mathematical Association of America (the MAA).
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