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geometric mean (Definition)

Geometric Mean.
If $a_1,a_2,\ldots,a_n$ are real numbers, we define their geometric mean as $$G.M. =\sqrt[n]{a_1a_2\cdots a_n}$$


(We usually require the numbers to be non negative so the mean always exists.)




"geometric mean" is owned by drini. [ owner history (1) ]
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See Also: arithmetic mean, general means inequality, weighted power mean, power mean, arithmetic-geometric-harmonic means inequality, root-mean-square, proof of general means inequality, derivation of zeroth weighted power mean, proof of arithmetic-geometric-harmonic means inequality, derivation of geometric mean as the limit of the power mean, mean, a prime theorem of a convergent sequence


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compass and straightedge construction of geometric mean (Algorithm) by Wkbj79
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Cross-references: mean, negative, numbers, real numbers
There are 26 references to this entry.

This is version 2 of geometric mean, born on 2001-10-20, modified 2001-11-09.
Object id is 407, canonical name is GeometricMean.
Accessed 19479 times total.

Classification:
AMS MSC11-00 (Number theory :: General reference works )

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Additional References by smithpith on 2009-04-25 18:25:54
You may also be interested to read about averages, weighted averages, and means in the following book and article.

* Jane Grossman, Michael Grossman, Robert Katz. "Averages: A New Approach", ISBN 0977117049, 1983. (Available for reading at Google Book Search:
http://books.google.com/books?q=%22Non-Newtonian+Calculus%22&btnG=Search+Books&as_brr=0).

* Michael Grossman and Robert Katz. "A new approach to means of two positive numbers", International Journal of Mathematical Education in Science and Technology, Volume 17, Number 2, March 1986, pages 205 - 208.
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