Torus and circles

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One group member will plot a torus with two circles on it.

One group member will produce a plot like this one:

This is a torus with two circles on it where the radius from the center of the torus to the center of the tube is $2$ , and the radius of the tube is $1$ .

As a gesture of friendship, I will tell you that the parametric formula for a torus of radius $R$ is:

$\begin{align*} x(s,t) &= (R + r\cdot \cos(t))\cos(s)\\ y(s,t) &= (R + r\cdot \cos(t))\sin(s)\\ z(s,t) &= r\cdot \sin(t) \end{align*}$

where $R$ is the radius from the center of the torus to the center of the tube, and $r$ is the radius of the tube.

You may color you circles any color you like—though you must make them different colors.