In mathematics, the Heronian mean H of two non-negative real number

Real number

In mathematics, a real number is a value that represents a quantity along a continuum, such as -5 , 4/3 , 8.6 , √2 and π...

s A and B is given by the formula:


It is named after Hero of Alexandria

Hero of Alexandria

Hero of Alexandria was an ancient Greek mathematician and engineerEnc. Britannica 2007, "Heron of Alexandria" who was active in his native city of Alexandria, Roman Egypt...

, and used in finding the volume of a frustum

Frustum

In geometry, a frustum is the portion of a solid that lies between two parallel planes cutting it....

 of a pyramid

Pyramid

A pyramid is a structure whose outer surfaces are triangular and converge at a single point. The base of a pyramid can be trilateral, quadrilateral, or any polygon shape, meaning that a pyramid has at least three triangular surfaces...

 or cone

Cone (geometry)

A cone is an n-dimensional geometric shape that tapers smoothly from a base to a point called the apex or vertex. Formally, it is the solid figure formed by the locus of all straight line segments that join the apex to the base...

. 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

Weighted mean

The weighted mean is similar to an arithmetic mean , where instead of each of the data points contributing equally to the final average, some data points contribute more than others...

 of their arithmetic

Arithmetic mean

In mathematics and statistics, the arithmetic mean, often referred to as simply the mean or average when the context is clear, is a method to derive the central tendency of a sample space...

 and geometric mean

Geometric mean

The geometric mean, in mathematics, is a type of mean or average, which indicates the central tendency or typical value of a set of numbers. It is similar to the arithmetic mean, except that the numbers are multiplied and then the nth root of the resulting product is taken.For instance, the...

s:

External links

• Mean-Trapezoids Geometric comparison of some mathematical means