Definition:Kampyle of Eudoxus

Curve

 * KampyleOfEudoxus.png

The Kampyle of Eudoxus has the Cartesian equation:
 * $$x^4 = x^2 + y^2$$

where the point $$x = y = 0$$ is specifically excluded.

In polar coordinates, it is described by the equation:
 * $$r = \sec^2 \theta$$

He used it in his work relating to the problem of Doubling the Cube.

The word kampyle comes from the Greek καμπύλη (pronounced kam-pill-ee), meaning curve.