Definition:Heronian Mean

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


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

It can also be defined as:


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

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