# Definition:Kampyle of Eudoxus

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## 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**.