Difference between revisions of "Torus"

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[[Image:Ghdyt.png|right|thumb|300px]]
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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.  
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A '''Torus''' is the mathematical term for a “doughnut” shape created by rotating a circle around an axis.
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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.  
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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.
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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
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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.
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:S = 4 &pi;<sup>2</sup> (R+r)r
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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.
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and the volume is
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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.
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:V = 2 &pi;<sup>2</sup>(R+r)r<sup>2</sup>
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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.
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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.
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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.
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== Topology ==
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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.
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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]].  
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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.
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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.  
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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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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.
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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.
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The [[genus]] of a one-fold torus is 1.
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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.  
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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.
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[[Category:Geometry]]
 
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[[category:mathematics]]
 

Revision as of 16:28, August 11, 2007

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. 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. 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. 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. 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. 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.

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