Hellenica World

he Heronian mean H of two non-negative real numbers A and B is given by the formula:

.

It is named after Hero of Alexandria, and 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.

The Heronian mean of the numbers A and B is a weighted mean of their arithmetic and geometric means:

.

Links

* Mean-Trapezoids Geometric comparison of some mathematical means

References

* Bullen, P.S. (2003), Handbook of Means and Their Inequalities (2nd ed.), Mathematics and Its Applications, Berlin, New York: Springer-Verlag, ISBN 978-1-4020-1522-9

* Eves, Howard Whitley (1980), Great Moments in Mathematics (Before 1650), Mathematical Association of America, ISBN 978-0-88385-310-8

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