Steinmetz Curve
SteinmetzCurve
A Steinmetz curve is a curve of intersection of two perpendicularly placed cylinders of radii a and b comprising a Steinmetz solid. If the vertical cylinder has radius a and the horizontal cylinder radius b, then the Steinmetz curves are given by the parametric equations
x(t) = acost
(1)
y(t) = asint
(2)
z(t) = +/-sqrt(b^2-a^2sin^2t)
(3)
(Gray 1997, p. 204).
See also
Cylinder, Steinmetz SolidExplore with Wolfram|Alpha
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References
Gray, A. Modern Differential Geometry of Curves and Surfaces with Mathematica, 2nd ed. Boca Raton, FL: CRC Press, 1997.Referenced on Wolfram|Alpha
Steinmetz CurveCite this as:
Weisstein, Eric W. "Steinmetz Curve." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/SteinmetzCurve.html