Euler's Elegant Example

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This applet illustrates Euler's Elegant Example: an infinite family of cubic equations that pass through nine fixed points. The equation is

y3 - y = p(x3 - x)

where p is a parameter that may be any real number.

In this applet, you can set particular values of p using the slider control, or put the applet into play mode and observe the curve as p cycles through values between −5 and +5.

This is a Java Applet created using GeoGebra from - it looks like you don't have Java installed, please go to

Bradley and Stemkoski, Created with GeoGebra