Consider the mean between two quantities:

The arithmetic mean is

The harmonic mean is

where

which equals the gamma factor of the Lorentz transformation.

The geometric mean is

Then the factor *γ*^{2} transforms a harmonic mean into an arithmetic mean:

The inverse *γ* factor transforms an arithmetic mean into a geometric mean:

so that

The inverse γ^{2} factor transforms an arithmetic mean into a harmonic mean.

Or consider the mean between these two:

The arithmetic mean is

The harmonic mean is

The geometric mean is

The factor *γ* transforms a geometric mean into an arithmetic mean. The factor *γ*^{2} transforms a harmonic mean into an arithmetic mean.

Or consider the mean between these two with *β* = *v*/*c*:

The arithmetic mean is

The harmonic mean is

The geometric mean is

The gamma factor relates the arithmetic mean and the harmonic mean, and the geometric mean combines them. An arithmetic mean and harmonic mean can be replaced by a geometric mean, in a sense.

*Revised 1/2024.*