# Parametric Torus

- Author:
- Norm Prokup

- Topic:
- Calculus, Parametric Curves, Surface

The parametric equations and describe a torus. The left graphics window shows a rectangular domain of points (u, t). The right window shows the torus.

Try dragging the corners of the rectangle around to restrict the domain. For example, try moving the green point in the upper left corner closer to the black point in the lower left corner. This narrows the interval of t-values that will be plotted on the surface in the right-hand window. This torus is a surface of revolution: it can be obtained by revolving a circle about the z-axis. Which variable, u or t, draws this circle? Which variable, u or t, rotates the circle around the z-axis?