Kampyle of Eudoxus

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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.

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 (c. 408 BC – c.347 BC) in relation to the classical problem of doubling the cube.

Properties

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

where

is the th Catalan number.

See also

References

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External links

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