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 June 1st, 2009, 02:42 AM #1 Newbie   Joined: Jun 2009 Posts: 2 Thanks: 0 What shape is this? There are many video games where the screen "wraps around" - that is, if you go off the top, you end up at the bottom (and vice versa), and if you go off the left you end up on the right (and vice versa). The arcade classic Asteroids is one example. It occurred to me a while back that the playing area in these games is not a sphere, but rather a torus. Now imagine instead a video game that takes place in a cube, where in addition to the left/right, top/bottom rules above, you can also run out the back and end up in the front, and vice versa. My question is, topologically, what shape does this represent?
 June 24th, 2009, 02:24 AM #2 Member     Joined: Aug 2007 Posts: 42 Thanks: 4 Re: What shape is this? Circle times the torus?
 June 25th, 2009, 09:56 PM #3 Newbie   Joined: Jun 2009 Posts: 5 Thanks: 0 Re: What shape is this? I believe it would just be a next-dimensional torus. Interestingly, here is the idea and application of what you're suggesting. http://www.traipse.com/stereoscopic_display/index.html
 June 27th, 2009, 05:36 AM #4 Member   Joined: Dec 2007 Posts: 43 Thanks: 0 Re: What shape is this? The shape you described is a one-holed torus.
June 27th, 2009, 06:39 AM   #5
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Re: What shape is this?

Quote:
 Originally Posted by computronium There are many video games where the screen "wraps around" - that is, if you go off the top, you end up at the bottom (and vice versa), and if you go off the left you end up on the right (and vice versa). The arcade classic Asteroids is one example. It occurred to me a while back that the playing area in these games is not a sphere, but rather a torus. Now imagine instead a video game that takes place in a cube, where in addition to the left/right, top/bottom rules above, you can also run out the back and end up in the front, and vice versa. My question is, topologically, what shape does this represent?
I would say it is a 3-torus and maybe write $T^3$ ... so the standard torus is a 2-torus $T^2$ and then the 1-torus $T^1$ is a circle

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