Stochastic volatility: Difference between revisions

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In mathematics, the '''Heronian mean''' ''H'' of two non-negative [[real number]]s ''A'' and ''B'' is given by the formula:
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:<math>H = \frac{1}{3} \left(A + \sqrt{A B} +B \right).</math>
 
It is named after [[Hero of Alexandria]], and used in finding the volume of a [[frustum]] of a [[pyramid]] or [[cone (geometry)|cone]]. The volume is equal to the product of the height of the frustum and the Heronian mean of the areas of the opposing parallel faces.
 
The Heronian mean of the numbers ''A'' and ''B'' is a [[weighted mean]] of their [[arithmetic mean|arithmetic]] and [[geometric mean]]s:
:<math> H = \frac{2}{3}\cdot\frac{A+B}{2} + \frac{1}{3}\cdot\sqrt{A B}.</math>
 
== References ==
* {{Citation | last1=Bullen | first1=P.S. | title=Handbook of Means and Their Inequalities | publisher=[[Springer Science+Business Media]] | location=Berlin, New York | edition=2nd | series=Mathematics and Its Applications | isbn=978-1-4020-1522-9 | year=2003}}
* {{Citation | last1=Eves | first1=Howard Whitley | author1-link=Howard Eves | title=Great Moments in Mathematics (Before 1650) | publisher=[[Mathematical Association of America]] | isbn=978-0-88385-310-8 | year=1980}}
 
== External links ==
* [http://jwilson.coe.uga.edu/EMT668/EMAT6680.2000/Umberger/EMAT6690smu/Essay3smu/Essay3smu.html  Mean-Trapezoids] Geometric comparison of some mathematical means
 
{{DEFAULTSORT:Heronian Mean}}
[[Category:Means]]
 
 
{{elementary-geometry-stub}}

Revision as of 19:05, 13 February 2014

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