# Infinitie dimensions?

#### waht

here is an interesting link at mathworld that describes a hypersphere and the formula for determining the surface area of a sphere in higher dimensions. If you look at the graph, the maximum area is in 7th dimension and diverges to 0 for higher dimensions.

Although some people speculate the universe might have infinite dimensions, could this be proof that an infinite dimensional universe may not exist.

http://mathworld.wolfram.com/Hypersphere.html

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#### Telos

No, just that a spherical universe with infinite dimensions has surface area 0 (probably because it wouldn't have a surface).

That's interesting, though. Does a surface area max occur with other hyper-shapes, as n approaches infinity?

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#### Timbuqtu

Apart from the hyper-sphere and the hyper-cube (area = 2n, which ofcourse diverges for n going to infinity) I think there are not really a lot of shapes that can be intuitively generalised to an arbitrary number of dimensions.

#### Telos

Mathworld outputs no results and Google isn't much help either. That's too bad... isn't it supposed to be one of the leadings candidates for the shape of the universe?

I know Kaku mentions the hypertorus in "Hyperspace," but I'm not sure he mentioned anything about the surface area in relation to n.

Oh, for those using Mac OS X, I found a http://www.versiontracker.com/dyn/moreinfo/macosx/20105 of a rotating 4D Torus. Trippy!

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#### HallsofIvy

Homework Helper
Mathematics cannot prove anything about physics- it can only prove statements about particular models for physics- perhaps that a particular model is not valid.

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