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Kampyle of Eudoxus

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KampyleofEudoxus

The Kampyle of Eudoxus is a curve studied by Eudoxus in relation to the classical problem of cube duplication. It is given by the polar equation

r=asec^2theta,
(1)

and the parametric equations

x=asect
(2)
y=atantsect
(3)

with t in [-pi/2,pi/2].

The arc length, curvature, and tangential angle are given by

s(t)=1/4[sin^(-1)(2tant)+2tantsqrt(1+4tan^2t)]
(4)
kappa(t)=(1-3cos(2t))/(2(1+4tan^2t)^(3/2))
(5)
phi(t)=cot^(-1)(2tant).
(6)

See also

Epispiral

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References

Lawrence, J. D. A Catalog of Special Plane Curves. New York: Dover, pp. 141-143, 1972.MacTutor History of Mathematics Archive. "Kampyle of Eudoxus." http://www-groups.dcs.st-and.ac.uk/~history/Curves/Kampyle.html.

Cite this as:

Weisstein, Eric W. "Kampyle of Eudoxus." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/KampyleofEudoxus.html

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