\begin{definition}[Definition:Heronian Mean]
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.
{{NamedforDef|Heron of Alexandria|cat = Heron}}
Category:Definitions/Algebra
\end{definition}