# Definition:Kampyle of Eudoxus

## Definition

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.