Cayley's Sextic

Cartesian equation: 4(x^2+y^2-ax)^3 = 27a^2(x^2+y^2)^2

Polar equation: r = 4a cos^3(theta/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
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 February 1996