TOPICS
Search

Steinmetz Curve

DOWNLOAD Mathematica NotebookDownload Wolfram Notebook
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 Solid

Explore with Wolfram|Alpha

References

Gray, A. Modern Differential Geometry of Curves and Surfaces with Mathematica, 2nd ed. Boca Raton, FL: CRC Press, 1997.

Cite this as:

Weisstein, Eric W. "Steinmetz Curve." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SteinmetzCurve.html

Subject classifications