Steinmetz curve

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Steinmetz curves for various cases Steinmetz-kurve.svg
Steinmetz curves for various cases
Steinmetz solid (intersection of two cylinders) involving Steinmetz curves (purple) Steinmetz-cc.svg
Steinmetz solid (intersection of two cylinders) involving Steinmetz curves (purple)

A Steinmetz curve is the curve of intersection of two right circular cylinders of radii and whose axes intersect perpendicularly. In case of the Steimetz curves are the edges of a Steinmetz solid. If the cylinder axes are the x- and y-axes and , then the Steinmetz curves are given by the parametric equations:

It is named after mathematician Charles Proteus Steinmetz, along with Steinmetz's equation, Steinmetz solids, and Steinmetz equivalent circuit theory.

In the case when the two cylinders have equal radii the curve degenerates to two intersecting ellipses.

See also

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References

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  1. Abbena, Elsa; Salamon, Simon; Gray, Alfred (2006). Modern Differential Geometry of Curves and Surfaces with Mathematica (3rd ed.). Chapman and Hall/CRC. ISBN   978-1584884484.
  2. Gray, A. Modern Differential Geometry of Curves and Surfaces with Mathematica, 2nd ed. Boca Raton, FL: CRC Press, 1997.
  3. Weisstein, Eric W. "Steinmetz Curve". Wolfram MathWorld. Retrieved October 28, 2018.