Just like all
means, the Heronian mean is symmetric (it does not depend on the order in which its two arguments are given) and idempotent (the mean of any number with itself is the same number).
Therefore, it lies between these two means, and between the two given numbers.[1]
Application in solid geometry
The Heronian mean may be used in finding the
volume of a
frustum of a
pyramid or
cone. The volume is equal to the product of the height of the frustum and the Heronian mean of the areas of the opposing parallel faces.[2]