Kampyle of Eudoxus


The Kampyle of Eudoxus is a curve with a Cartesian equation of
from which the solution x = y = 0 is excluded.

Alternative parameterizations

In polar coordinates, the Kampyle has the equation
Equivalently, it has a parametric representation as

History

This quartic curve was studied by the Greek astronomer and mathematician Eudoxus of Cnidus in relation to the classical problem of doubling the cube.

Properties

The Kampyle is symmetric about both the x- and y-axes. It crosses the x-axis at. It has inflection points at
. The top half of the curve is asymptotic to as, and in fact can be written as
where
is the th Catalan number.