Definition:Heronian Mean

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Definition

The Heronian mean of two numbers $x$ and $y$ is defined as:

$H = \dfrac {x + \sqrt {x y} + y} 3$


It can also be defined as:

$H = \dfrac 2 3 \paren {\dfrac {x + y} 2} + \dfrac 1 3 \sqrt {x y}$


Thus it is seen to be a weighted mean of their arithmetic mean and geometric mean.


Source of Name

This entry was named for Heron of Alexandria.