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Topic: "real world" uses of topology?
Replies: 15   Last Post: Mar 4, 2001 5:51 PM

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Martin Green

Posts: 116
Registered: 12/8/04
Re: "real world" uses of topology?
Posted: Mar 4, 2001 4:15 PM
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Yes, Kevin, that's what they did. I couldn't understand
how it worked, so I made a meticulous map locating every
square. When I was done. I realized it was the map
of a torus.

Martin Green
Teach yourself Yiddish while you read
the exciting autobiography of Falk Zolf.

"Kevin Foltinek" <> wrote in message
> "Martin Green" <> writes:

> > > Someone once developed a video game that was supposed to be
> > > like a 3-d version of Tetris. It was played on a spherical planet
> > > that was laid out in a checkerboard. You could rotate the sphere
> > > left, right, up, and down, and you always saw this checkerboard
> > > pattern in front of you.Topologically, this is impossible on a shpere!
> > > (Lines of longitude have to meet SOMEWHERE.)
> > > How did the game developers solve this problem???

> I haven't seen the game, so I'm merely speculating.
> Perhaps the spherical planet is not spherical, but toroidal. (Rather
> like the universe in Asteroids, Pac-Man, etc., is a torus.) I think
> it would be easy to give the illusion of a spherical planet, by
> assigning a metric to the torus which has positive Gauss curvature in
> the "visible" portion, and isometrically embedding that portion into
> Euclidean 3-space and performing the obvious projection. (Presumably
> there are ways to do this which make the final mapping (x,y)_{torus}
> -> (x,y)_{display} computationally inexpensive.)
> Kevin.

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