# Contour plots

A contour plot is a 2-dimensional way to visualize a 3-dimensional surface. It is done by by plotting constant z slices, called contours (a.k.a. level sets). That is, given a value for $z$, points/lines/curves are drawn for the $(x,y)$ coordinates where that $z$ value occurs.

### Near a minimum

This is the contour plot for the function $z = x^2 + y^2$ near $(0,0)$. Noticing the closed contour lines with lower values in the center and higher values on the outside.

### Near a maximum

This is the contour plot for the function $z = 4 - x^2 - y^2$ near $(0,0)$. Noticing the closed contour lines with higher values in the center and lower values on the outside.

This is the contour plot for the function $z = x^2 - y^2$ near $(0,0)$ which is a saddle point.