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.
Sources
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): Heronian mean