Kampyle of Eudoxus

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Graph of Kampyle of Eudoxus with a = 1

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 parameterizations[edit]

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). 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.

See also[edit]


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

External links[edit]