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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>
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| 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.
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| The Heronian mean of the numbers ''A'' and ''B'' is a [[weighted mean]] of their [[arithmetic mean|arithmetic]] and [[geometric mean]]s:
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| :<math> H = \frac{2}{3}\cdot\frac{A+B}{2} + \frac{1}{3}\cdot\sqrt{A B}.</math>
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| == References ==
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| * {{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}}
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| * {{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}}
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| == External links ==
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| * [http://jwilson.coe.uga.edu/EMT668/EMAT6680.2000/Umberger/EMAT6690smu/Essay3smu/Essay3smu.html Mean-Trapezoids] Geometric comparison of some mathematical means
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| {{DEFAULTSORT:Heronian Mean}}
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| [[Category:Means]]
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| {{elementary-geometry-stub}}
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Latest revision as of 12:18, 31 December 2014
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