Cayley's Sextic

Cartesian equation:
4(x2 + y2 - ax)3 = 27a2(x2 + y2)2
Polar equation:
r = 4a cos3(θ/3)

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

Click THIS LINK to experiment interactively with this curve and its associated curves.

This was first discovered by Maclaurin but studied in detail by Cayley.

The name Cayley's sextic is due to R C Archibald who attempted to classify curves in a paper published in Strasbourg in 1900.

The evolute of Cayley's Sextic is a nephroid curve.

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JOC/EFR/BS January 1997

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