I have probably already butchered the correct terminology but what do you call a square that wraps around the sides and the corners? For example, an object can walk east over the right edge, and will show up on the left side, same with the top and bottom. So opposite sides and corners are connected. Thanks!
What do you call this topological object/shape?
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0You might like to read this: http://www.jcu.edu/math/vignettes/Mobius.htm – 2012-12-03
1 Answers
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Topologically speaking, it's a torus, assuming you aren't introducing any "twists" in your identification.
To see how, think of the square as made of some material that will stretch and bend however you like it. Since you want left and right to be effectively joined, simply "glue" them together to get a circular tube. Since you want the top and bottom to be joined, glue the top and bottom edges of the tube together, to get a donut shape--a torus.