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11-00-GeometricMean.tex
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\documentclass[12pt]{article}
\usepackage{pmmeta}
\pmcanonicalname{GeometricMean}
\pmcreated{2013-03-22 11:50:46}
\pmmodified{2013-03-22 11:50:46}
\pmowner{drini}{3}
\pmmodifier{drini}{3}
\pmtitle{geometric mean}
\pmrecord{7}{30407}
\pmprivacy{1}
\pmauthor{drini}{3}
\pmtype{Definition}
\pmcomment{trigger rebuild}
\pmclassification{msc}{11-00}
\pmclassification{msc}{44A20}
\pmclassification{msc}{33E20}
\pmclassification{msc}{30D15}
\pmrelated{ArithmeticMean}
\pmrelated{GeneralMeansInequality}
\pmrelated{WeightedPowerMean}
\pmrelated{PowerMean}
\pmrelated{ArithmeticGeometricMeansInequality}
\pmrelated{ProofOfArithmeticGeome}
\pmrelated{RootMeanSquare3}
\pmrelated{ProofOfGeneralMeansInequality}
\pmrelated{DerivationOfZerothWeightedPowerMean}
\pmrelated{ProofOfArithmeticGeometricHarmonicMeansI}
\endmetadata
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{graphicx}
%%%%\usepackage{xypic}
\begin{document}
\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.)
}
%%%%%
%%%%%
%%%%%
%%%%%
\end{document}