Contour Plots
Main Concept

A contour line of the function $zequals;f\left(xcomma;y\right)$ is a 2dimensional curve with the equation $f\left(x\,y\right)equals;k$, where k is a constant in the range of f. A contour line can be described as the intersection of the horizontal plane $zequals;k$ with the surface defined by f. Contour lines are also known as level curves.
A contour plot is a plot containing several contour lines, each representing a different magnitude of k. The contour interval is the difference in the value of $k$ between successive contour lines. The regions between contours are often shaded or colored to indicate these differences in the value of k.
In cartography, contour lines are commonly used to illustrate points of equal elevation above a given level, such as mean sea level. A contour map is a map illustrated with contour lines, the most common example of which is a topographic map that shows mountains, hills, valleys, and the steepness of slopes through contour lines representing elevation.



Choose a function from the dropdown menu, or type your own function in the text box below and click "Enter" to plot it. Use the radio buttons to choose the number of contour lines you would like to have in your plot and then click the "Create Contour Plot" button to animate the creation of the contour plot, as k grows from the smallest value displayed to the largest (as is shown by the $z\mathit{}\mathit{equals;}\mathit{}k$ plane moving upwards).

z = f(x, y) =





Number of Contour Lines:



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