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.

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.