### Lemniscate of Bernoulli

**Cartesian equation: **

(*x*^{2} + *y*^{2})^{2} = *a*^{2}(*x*^{2} - *y*^{2})

**Polar equation: **

*r*^{2} = *a*^{2}cos(2*θ*)

Click on the **Curve** menu to choose one of the associated curves. Then click on the diagram to choose a point for the involutes, pedal curve, etc. You can then move the point around and watch the associated curve change.

For the **inverse** (wrt a circle) click the mouse and drag to choose a centre and radius. You can then drag the centre of the circle

Use the buttons on the right to move the graph or the ones in the middle to alter the scale. The buttons on the left can be used to alter the value of the parameter *a*. The two *inc* buttons alter the rate at which you can vary the parameter.

You can see the Java source code, you can go to the Applet Index or you can go to the curve.
BS/JOC/EFR July 1996

The URL of this page is:

http://www-history.mcs.st-andrews.ac.uk/Java/Lemniscate.html