harmonic mean
If are positive numbers, we define their harmonic mean as the inverse number of the arithmetic mean
of their inverse numbers:
- •
It follows easily the estimation
- •
If you travel from city to city at miles per hour, and then you travel back at miles per hour. What was the average velocity for the whole trip?
The harmonic mean of and . That is, the average velocity is - •
If one draws through the intersecting point of the diagonals of a trapezoid
a line parallel
to the parallel sides of the trapezoid, then the segment of the line inside the trapezoid is equal to the harmonic mean of the parallel sides.
- •
In the harmonic series
every following it.
Title | harmonic mean |
Canonical name | HarmonicMean |
Date of creation | 2013-03-22 11:50:50 |
Last modified on | 2013-03-22 11:50:50 |
Owner | drini (3) |
Last modified by | drini (3) |
Numerical id | 15 |
Author | drini (3) |
Entry type | Definition |
Classification | msc 11-00 |
Related topic | ArithmeticMean |
Related topic | GeneralMeansInequality |
Related topic | WeightedPowerMean |
Related topic | PowerMean |
Related topic | ArithmeticGeometricMeansInequality |
Related topic | RootMeanSquare3 |
Related topic | ProofOfGeneralMeansInequality |
Related topic | ProofOfArithmeticGeometricHarmonicMeansInequality |
Related topic | HarmonicMeanInTrapezoid |
Related topic | ContraharmonicMean |
Related topic | Contr |