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.

[1] 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] 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.

A square frustum, with volume equal to the height times the Heronian mean of the square areas