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| − | WILL the real Osama bin Laden please stand up? The CIA and assorted other spooks on the trail of the world’s most wanted man could give themselves a hand by giving social networking site Facebook a good going over. They would find that he has brazenly signed up to chat with his mates — or rather that 11 people have set up entries under his name.
| + | [[Image:Ghdyt.png|right|thumb|300px]] |
| − | WILL the real Osama bin Laden please stand up? The CIA and assorted other spooks on the trail of the world’s most wanted man could give themselves a hand by giving social networking site Facebook a good going over. They would find that he has brazenly signed up to chat with his mates — or rather that 11 people have set up entries under his name.
| + | A '''Torus''' is the mathematical term for a “doughnut” shape created by rotating a circle around an axis. |
| − | WILL the real Osama bin Laden please stand up? The CIA and assorted other spooks on the trail of the world’s most wanted man could give themselves a hand by giving social networking site Facebook a good going over. They would find that he has brazenly signed up to chat with his mates — or rather that 11 people have set up entries under his name.
| + | |
| − | WILL the real Osama bin Laden please stand up? The CIA and assorted other spooks on the trail of the world’s most wanted man could give themselves a hand by giving social networking site Facebook a good going over. They would find that he has brazenly signed up to chat with his mates — or rather that 11 people have set up entries under his name.
| + | 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 |
| − | WILL the real Osama bin Laden please stand up? The CIA and assorted other spooks on the trail of the world’s most wanted man could give themselves a hand by giving social networking site Facebook a good going over. They would find that he has brazenly signed up to chat with his mates — or rather that 11 people have set up entries under his name.
| + | :S = 4 π<sup>2</sup> (R+r)r |
| − | WILL the real Osama bin Laden please stand up? The CIA and assorted other spooks on the trail of the world’s most wanted man could give themselves a hand by giving social networking site Facebook a good going over. They would find that he has brazenly signed up to chat with his mates — or rather that 11 people have set up entries under his name.
| + | and the volume is |
| − | WILL the real Osama bin Laden please stand up? The CIA and assorted other spooks on the trail of the world’s most wanted man could give themselves a hand by giving social networking site Facebook a good going over. They would find that he has brazenly signed up to chat with his mates — or rather that 11 people have set up entries under his name.
| + | :V = 2 π<sup>2</sup>(R+r)r<sup>2</sup> |
| − | WILL the real Osama bin Laden please stand up? The CIA and assorted other spooks on the trail of the world’s most wanted man could give themselves a hand by giving social networking site Facebook a good going over. They would find that he has brazenly signed up to chat with his mates — or rather that 11 people have set up entries under his name.
| + | |
| − | WILL the real Osama bin Laden please stand up? The CIA and assorted other spooks on the trail of the world’s most wanted man could give themselves a hand by giving social networking site Facebook a good going over. They would find that he has brazenly signed up to chat with his mates — or rather that 11 people have set up entries under his name.
| + | |
| − | WILL the real Osama bin Laden please stand up? The CIA and assorted other spooks on the trail of the world’s most wanted man could give themselves a hand by giving social networking site Facebook a good going over. They would find that he has brazenly signed up to chat with his mates — or rather that 11 people have set up entries under his name.
| + | == Topology == |
| − | WILL the real Osama bin Laden please stand up? The CIA and assorted other spooks on the trail of the world’s most wanted man could give themselves a hand by giving social networking site Facebook a good going over. They would find that he has brazenly signed up to chat with his mates — or rather that 11 people have set up entries under his name.
| + | 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 under the [[quotient topology]]. |
| − | WILL the real Osama bin Laden please stand up? The CIA and assorted other spooks on the trail of the world’s most wanted man could give themselves a hand by giving social networking site Facebook a good going over. They would find that he has brazenly signed up to chat with his mates — or rather that 11 people have set up entries under his name.
| + | |
| − | WILL the real Osama bin Laden please stand up? The CIA and assorted other spooks on the trail of the world’s most wanted man could give themselves a hand by giving social networking site Facebook a good going over. They would find that he has brazenly signed up to chat with his mates — or rather that 11 people have set up entries under his name.
| + | 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. |
| − | WILL the real Osama bin Laden please stand up? The CIA and assorted other spooks on the trail of the world’s most wanted man could give themselves a hand by giving social networking site Facebook a good going over. They would find that he has brazenly signed up to chat with his mates — or rather that 11 people have set up entries under his name.
| + | |
| − | WILL the real Osama bin Laden please stand up? The CIA and assorted other spooks on the trail of the world’s most wanted man could give themselves a hand by giving social networking site Facebook a good going over. They would find that he has brazenly signed up to chat with his mates — or rather that 11 people have set up entries under his name.
| + | The [[genus]] of a one-fold torus is 1. |
| − | WILL the real Osama bin Laden please stand up? The CIA and assorted other spooks on the trail of the world’s most wanted man could give themselves a hand by giving social networking site Facebook a good going over. They would find that he has brazenly signed up to chat with his mates — or rather that 11 people have set up entries under his name.
| + | |
| | + | [[Category:Geometry]] |
| | + | [[category:mathematics]] |
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 under the quotient topology.
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.
The genus of a one-fold torus is 1.
