Kampyle of Eudoxus
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) = [画像:(1-3cos(2t))/(2(1+4tan^2t)^(3/2))]
(5)
phi(t) = cot^(-1)(2tant).
(6)
See also
EpispiralExplore with Wolfram|Alpha
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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." https://mathshistory.st-andrews.ac.uk/Curves/Kampyle/.Referenced on Wolfram|Alpha
Kampyle of EudoxusCite this as:
Weisstein, Eric W. "Kampyle of Eudoxus." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/KampyleofEudoxus.html