Changes

[[Image:Ghdyt.png|right|thumb|300px]]

[[Image:Ghdyt.png|right|thumb|300px]]

A '''Torus''' is the mathematical term for a “[[doughnut]]-like” shape created by rotating a circle around an axis.   

A '''Torus''' is the mathematical term for a “[[doughnut]]-like” shape created by rotating a [[circle]] around the [[x-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

If the “inner [[radius]]” (the width 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

:S = 4 π² (R+r)r

and the volume is

and the [[volume]] is

:V = 2 π²(R+r)r²

:V = 2 π²(R+r)r²

== Topology ==

== 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 under the [[quotient topology]].  

In [[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 [[edge]]s 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.

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.