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Torus in 3-space

32 bytes removed, 08:06, 31 July 2007
Equational descriptions
Let <math>r_1</math> denote the average radius and <math>r_2</math> denote the tube radius. Suppose the base circle is in the <math>xy</math>-plane and the origin of the torus is the origin. Then the parametric equations aer in terms of two angles, <math>\alpha</math> and <math>\beta</math>, where:
<math>\begin{eqnarray*}
x & = & r_1 \cos \alpha + r_2 \cos \alpha \cos \beta\\
y & = & r_1 \sin \alpha + r_2 \sin \alpha \cos \beta\\
z & = & r_2 \sin \beta
\end{eqnarray*}</math>
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