Graph of 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 should be 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 - and -axes. It crosses the -axis at and . 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.