Pear-shaped Quartic

Cartesian equation:
b2y2 = x3(a-x)


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 was studied by G de Longchamps in 1886.

G de Longchamps has several other curves named after him.

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JOC/EFR/BS January 1997

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