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Pappus's centroid theorem

Pappus's centroid theorem states that the area of a surface of revolution generated by rotating a plane curve C about an axis external to C and on the same plane is equal to the length of C times the distance traveled by its centroid.

For example, the surface area of the torus with minor radius r and major radius R is

A = (2\pi r)(2\pi R) = 4\pi^2 R r.\,

It is attributed to Pappus of Alexandria.

Last updated: 05-23-2005 06:42:16
Science Fair Project Encyclopedia Contents Page
10-26-2009 08:16:03
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