Figure Eight Curve

Cartesian equation:
x4 = a2(x2-y2)
Polar equation:
r2 = a2cos(2θ)sec4(θ)


Click below to see one of the Associated curves.

Definitions of the Associated curves Evolute
Involute 1 Involute 2
Inverse curve wrt origin Inverse wrt another circle
Pedal curve wrt origin Pedal wrt another point
Negative pedal curve wrt origin Negative pedal wrt another point
Caustic wrt horizontal rays Caustic curve wrt another point

If your browser can handle JAVA code, click HERE to experiment interactively with this curve and its associated curves.

This curve is also known as the Lemniscate of Gerono.

Other Web site:

Xah Lee

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JOC/EFR/BS January 1997

The URL of this page is:
http://www-history.mcs.st-andrews.ac.uk/Curves/Eight.html