We present an applet that combines a contour diagram plotter and a 3D function grapher, and allows the user to toggle between the two. Since both contour maps and 3D graphs are very sensitive to the choice of x and y ranges, it is often very hard to interpret a contour diagram without seeing the corresponding 3D graph. This applet provides an opportunity to compare these two ways of visualizing functions of two variables. Click either of the images below to open the applet.

The image above shows the contour map part, the one below the 3D grapher part.

In the applet, the user can enter a formula for a function f(x,y), x and y ranges and see the corresponding contour diagram. The 3D grapher part draws the 3D graph of a user-defined function f(x,y), in the user-defined x and y ranges. The 3D graph can be rotated in real time. The possibility of comparing the two ways of visualizing functions of two variables gives the applet its pedagogical value.

Note:   The applet is written in ActionScript 3 and requires several of our custom AS3 classes. The complete source code for the applet is available in the AS3 developers section of Flash and Math at: Contour Map Plotter and 3D Function Grapher in Flash Combined.

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We gratefully acknowledge the past support of the National Science Foundation, the Mathematical Association of America, and the Mathematical Sciences Digital Library.