Steinmetz curve explained

a and b, whose axes intersect perpendicularly. In case of a = b the Steimetz curves are the edges of a Steinmetz solid. If the cylinder axes are the x- and y-axes and a\le b , then the Steinmetz curves are given by the parametric equations:\begin{align} x (t) & = a \cos t \\ y (t) & = \pm \sqrt{b ^{2} - a ^{2} \sin ^{2} t} \\ z (t) & = a \sin t \end{align}

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

• Cylinder

References

^{[1] [2] [3]}

Notes and References

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