Definition:Kampyle of Eudoxus

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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:

$r = \sec^2 \theta$

Source of Name

This entry was named for Eudoxus of Cnidus.

Historical Note

The kampyle of Eudoxus was used by Eudoxus of Cnidus in his work relating to the problem of Doubling the Cube.

Linguistic Note

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