The Kampyle of Eudoxus (Greek: καμπύλη [γραμμή], meaning simply "curved [line], curve") is a curve with a Cartesian equation of
Graph of Kampyle of Eudoxus with a
from which the solution x = y = 0 is excluded.
In polar coordinates, the Kampyle has the equation
Equivalently, it has a parametric representation as
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
is the th Catalan number.