Let be the circle in the x-z plane with radius and center (R,0,0). A torus of revolution is obtained by revolving about the z-axis. Show that the patch is given by .
Ahmmm, a patch is just a mapping x: that defines the whole curve.
I've attached a drawing how to calculate the coordinates of the points of the surface of a torus.
1. The black circle in the x-y-plane is the path of point R. In the picture of the torus I've choosen R=5
2. The red circle has the radius . I've taken r = 3.
With and the angle v you can calculate the x and y-coordinate of the points.
3. The z-coordinate of all points only depends on r and the angle u.