The solid common to two (or three) right circular Cylinders of equal Radii intersecting at Right Angles is called the Steinmetz solid. (Two Cylinders intersecting at Right Angles are sometimes called a Bicylinder, and three intersecting Cylinders a Tricylinder.)

The Volume common to two intersecting right Cylinders of Radius is

(1) |

(2) |

The curves of intersection of two cylinders of Radii and , shown above, are given by the
parametric equations

(3) | |||

(4) | |||

(5) |

(Gray 1993).

The Volume common to two Elliptic Cylinders

(6) |

(7) |

For three Cylinders of Radii intersecting at Right Angles, the Volume of intersection is

(8) |

**References**

Bowman, F. *Introduction to Elliptic Functions, with Applications.* New York: Dover, 1961.

Gardner, M. *The Unexpected Hanging and Other Mathematical Diversions.* Chicago, IL: Chicago University Press,
pp. 183-185, 1991.

Gray, A. *Modern Differential Geometry of Curves and Surfaces.* Boca Raton, FL: CRC Press, pp. 149-150, 1993.

Wells, D. G. #555 in *The Penguin Book of Curious and Interesting Puzzles.* London: Penguin Books, 1992.

© 1996-9

1999-05-26