Kampyle of Eudoxus

Cartesian equation:
a2x4 = b4(x2 + y2)
Polar equation:
r = b2/(a cos2(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

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

A curve studied by Eudoxus also in relation to the classical problem of duplication of the cube.

Eudoxus was a pupil of Plato. His main work was in astronomy. He was the first to describe the constellations and invented the astrolabe. He introduced the study of mathematical astronomy into Greece.

Eudoxus found formulas for measuring pyramids cones and cylinders. His work contains elements of the calculus with a rigorous study of the method of exhaustion.

The word kampyle comes from the Greek καμπύλη meaning curve.

Further information:

J H McCoy

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JOC/EFR/BS January 1997

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