Definition:Heronian Mean

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


 * $\displaystyle H = \frac {x + \sqrt{xy} + y} 3$

It can also be defined as:


 * $\displaystyle H = \frac 2 3 \left({\frac {x + y} 2}\right) + \frac 1 3 \sqrt {x y}$

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