Math 13 Fall 2004

Calculus of Vector-valued Functions

Examples of Parametrized Surfaces

November 16, 2004

   Define a parametrized surface in the space

>	X := (s, t) -> [2 * cos(s) * sin(t), 2 * sin(s) * sin(t), 2 * cos(t)];

    Let's render it with parameters taking values in some rectangle.

    Looks like a slice of a sphere!

>	plot3d(X(s,t), s = 0 .. 2, t = 0 .. 1);

    Make the parametrizing rectangle larger . . .

>	plot3d(X(s,t), s = 0 .. 4, t = 0 .. 2);

    . . . and larger. It's indeed a sphere!

    Black lines are the coordinate curves. "Meridians" and "latitude circles"

        correspond to s and t being constants, respecively.

>	plot3d(X(s,t), s = 0 .. 2*Pi, t = 0 .. Pi);

>