# Kampyle of Eudoxus

The **Kampyle of Eudoxus** (Greek: καμπύλη [γραμμή], meaning simply "curved [line], curve") is a curve with a Cartesian equation of

from which the solution *x* = *y* = 0 is excluded.

## Alternative parameterizationsEdit

In polar coordinates, the Kampyle has the equation

Equivalently, it has a parametric representation as

## HistoryEdit

This quartic curve was studied by the Greek astronomer and mathematician Eudoxus of Cnidus (c. 408 BC – c.347 BC) in relation to the classical problem of doubling the cube.

## PropertiesEdit

The Kampyle is symmetric about both the *x*- and *y*-axes. It crosses the *x*-axis at (±*a*,0). It has inflection points at

(four inflections, one in each quadrant). The top half of the curve is asymptotic to as , and in fact can be written as

where

is the th Catalan number.

## See alsoEdit

## ReferencesEdit

- J. Dennis Lawrence (1972).
*A catalog of special plane curves*. Dover Publications. pp. 141–142. ISBN 0-486-60288-5.