Definition:Heronian Mean

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.