Heronian mean

In mathematics, the Heronian mean H of two non-negative real numbers A and B is given by the formula
It is named after Hero of Alexandria.

Properties

Just like all means, the Heronian mean is symmetric and idempotent.
The Heronian mean of the numbers A and B is a weighted mean of their arithmetic and geometric means:
Therefore, it lies between these two means, and between the two given numbers.

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.
A version of this formula, for square frusta, appears in the Moscow Mathematical Papyrus from Ancient Egyptian mathematics, whose content dates to roughly 1850 BC.