Difference between revisions of "Torus"
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[[Image:Ghdyt.png|right|thumb|300px]] | [[Image:Ghdyt.png|right|thumb|300px]] | ||
| + | A '''Torus''' is the mathematical term for a “doughnut” shape created by rotating a circle around an axis. | ||
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| + | If the “inner radius” (the size of the doughnut hole) is R, and the radius of the circular cross-section is r, then, the surface area of the torus is | ||
| + | :S = 4 π<sup>2</sup> (R+r)r | ||
| + | and the volume is | ||
| + | :V = 2 π<sup>2</sup>(R+r)r<sup>2</sup> | ||
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| + | == Topology == | ||
A '''Torus''' can be defined as the [[cartesian product]] of 2 [[circle]]s. It can be constructed from a [[rectangle]] by identifying its opposite edges. | A '''Torus''' can be defined as the [[cartesian product]] of 2 [[circle]]s. It can be constructed from a [[rectangle]] by identifying its opposite edges. | ||
| + | |||
| + | This means that the torus surface is connected in the same way as the points on a rectangle, where you can “wrap-around” from one side of the rectangle to the other. This was a common topology used in the playing field of older video games. | ||
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[[Category:Geometry]] | [[Category:Geometry]] | ||
Revision as of 18:00, April 6, 2007
A Torus is the mathematical term for a “doughnut” shape created by rotating a circle around an axis.
If the “inner radius” (the size of the doughnut hole) is R, and the radius of the circular cross-section is r, then, the surface area of the torus is
- S = 4 π2 (R+r)r
and the volume is
- V = 2 π2(R+r)r2
Topology
A Torus can be defined as the cartesian product of 2 circles. It can be constructed from a rectangle by identifying its opposite edges.
This means that the torus surface is connected in the same way as the points on a rectangle, where you can “wrap-around” from one side of the rectangle to the other. This was a common topology used in the playing field of older video games.