## Viviani's Curve

The Space Curve giving the intersection of the Cylinder

 (1)

and the Sphere
 (2)

It is given by the parametric equations
 (3) (4) (5)

The Curvature and Torsion are given by
 (6) (7)

See also Cylinder, Sphere, Steinmetz Solid

References

Gray, A. Viviani's Curve.'' §7.6 in Modern Differential Geometry of Curves and Surfaces. Boca Raton, FL: CRC Press, pp. 140-142, 1993.

von Seggern, D. CRC Standard Curves and Surfaces. Boca Raton, FL: CRC Press, p. 270, 1993.

© 1996-9 Eric W. Weisstein
1999-05-26