A Brief Note on Contour Graphs 

Consider a function . For any constant we can look at the graph of . This graph is called 

a contour if and a level surface if . Notice that the level surface of is the sphere of radius 1. 

In fact, we can think of all of the surfaces above as level surfaces. 

Some contours... 

Here is the hyperbolic paraboloid from above along with five planes and . The intersection 

of the surface with the planes gives contours. 

(1)

 

Here are the contours graphed by themselves. 

(2)

 

Here are some more contours.