**Cartesian equation: **

*a*^{2}*x*^{4} = *b*^{4}(*x*^{2} + *y*^{2})

**Polar equation: **

*r* = *b*^{2}/(*a* cos^{2}(*θ*))

**Click below to see one of the Associated curves.**

If your browser can handle JAVA code, click HERE 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 κ*α**μ*πύ*λ**η* meaning *curve*.

**Further information:**

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JOC/EFR/BS January 1997

The URL of this page is:

http://www-history.mcs.st-andrews.ac.uk/Curves/Kampyle.html