Heronian mean

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The Heronian mean of two non-negative real numbers A and B is given by (A + \sqrt{A B} +B)/3.

The volume of a frustum of a pyramid (or cone) is found by multiplying the height of the frustum by the Heronian mean of the areas of the opposing parallel faces.

The Heronian mean can be generalised such that it can also be applied to more than two variables:

Her(x_1, x_2, .. , x_n) = \frac{2}{n(n+1)} \sum_{i=1}^n \sum_{j=i}^n \sqrt {x_i x_j}

See also: mean.

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