**level curve**is just a 2D plot of the curve

*f*(

*x*,

*y*) =

*k*, for some constant value

*k*. Thus by plotting a series of these we can get a 2D picture of what the three-dimensional surface looks like.

A **level curve** is just a 2D plot of the curve
*f*(*x*,*y*) = *k*, for some constant value
*k*. Thus by plotting a series of these we can get a 2D picture
of what the three-dimensional surface looks like.

In the following, we demonstrate this. This is essentially an animation that you can go through step by step. As you click through, you'll see a little pop-up window that explains what you want to look for as you step through each frame in the demonstration. Click here to open the pop-up window for the current frame of the demonstration.

Finally, we can graph all of the level curves in a countour plot, as
shown in the figure to the right. Here we've highlighted the level
curve corresponding to *z* = 1 in magenta.

level curves

Last modified: Wed Jan 28 16:11:42 EST 2004

Comments to:glarose@umich.edu

©2004 Gavin LaRose, UM Math Dept.