<?xml version="1.0" encoding="UTF-8"?>

<record version="2" id="407">
 <title>geometric mean</title>
 <name>GeometricMean</name>
 <created>2001-10-20 00:45:17</created>
 <modified>2001-11-09 22:29:11</modified>
 <type>Definition</type>
 <creator id="3" name="drini"/>
 <author id="3" name="drini"/>
 <classification>
	<category scheme="msc" code="11-00"/>
 </classification>
 <related>
	<object name="ArithmeticMean"/>
	<object name="GeneralMeansInequality"/>
	<object name="WeightedPowerMean"/>
	<object name="PowerMean"/>
	<object name="ArithmeticGeometricMeansInequality"/>
	<object name="ProofOfArithmeticGeome"/>
	<object name="RootMeanSquare3"/>
	<object name="ProofOfGeneralMeansInequality"/>
	<object name="DerivationOfZerothWeightedPowerMean"/>
	<object name="ProofOfArithmeticGeometricHarmonicMeansInequality"/>
	<object name="DerivationOfHarmonicMeanAsTheLimitOfThePowerMean"/>
	<object name="Mean3"/>
	<object name="APrimeTheoremOfAConvergentSequence"/>
 </related>
 <preamble>\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{graphicx}
\usepackage{xypic}
</preamble>
 <content>\textbf{Geometric Mean.}\\
If  $a_1,a_2,\ldots,a_n$ are real numbers, we define their \emph{geometric mean} as
$$G.M. =\sqrt[n]{a_1a_2\cdots a_n}$$
\bigskip

{\footnotesize
(We usually require the numbers to be non negative so the mean always exists.)
}</content>
</record>
