# Changes

Let $r_1$ denote the average radius and $r_2$ denote the tube radius. Suppose the base circle is in the $xy$-plane and the origin of the torus is the origin. Then the parametric equations aer in terms of two angles, $\alpha$ and $\beta$, where:
$\begin{eqnarray*} x & = & r_1 \cos \alpha + r_2 \cos \alpha \cos \beta\\ y & = & r_1 \sin \alpha + r_2 \sin \alpha \cos \beta\\ z & = & r_2 \sin \beta \end{eqnarray*}$