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.

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

The Kampyle is symmetric about both the x- and y-axes.

It crosses the x-axis at (±a,0).

The top half of the curve is asymptotic to

Graph of Kampyle of Eudoxus with a = 1