Harmonic Mean

The harmonic mean of points (where , ..., ) is

 (1)

The special case of is therefore
 (2)

or
 (3)

The Volume-to-Surface Area ratio for a cylindrical container with height and radius and the Mean Curvature of a general surface are related to the harmonic mean.

Hoehn and Niven (1985) show that

 (4)

for any Positive constant .

See also Arithmetic Mean, Arithmetic-Geometric Mean, Geometric Mean, Harmonic-Geometric Mean, Root-Mean-Square

References

Abramowitz, M. and Stegun, C. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, p. 10, 1972.

Hoehn, L. and Niven, I. Averages on the Move.'' Math. Mag. 58, 151-156, 1985.

© 1996-9 Eric W. Weisstein
1999-05-25