Weird shape

Discussion of shapes with curves and holes in various dimensions.

Weird shape

Postby Keiji » Sun Jun 11, 2006 11:46 am

Okay, so I thought:

a 2D torus is two concentric circles..
Now what about two concentric torii? Concentric torii being, they both have the same major radius but a different minor radius. What happens if we take the 4D analog of this shape?
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Re: Weird shape

Postby Marek14 » Mon Jun 12, 2006 7:58 am

Rob wrote:Okay, so I thought:

a 2D torus is two concentric circles..
Now what about two concentric torii? Concentric torii being, they both have the same major radius but a different minor radius. What happens if we take the 4D analog of this shape?


That's when you replace all points of a shape with 1D circle - i.e. two points. These shapes show as cross-sections of higher-dimensional torii - concentric circles appear as cross-section of 3D torus, for example.
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