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When talking investment portfolios, the geometric mean is also sometimes referred to as compounded annual growth rate or time-weighted rate of return.
The simple definition of a mean is that of a numeric quantity which represents the center of a collection of numbers. Here the trick lies in defining the exact type of numeric collection, as beyond… ...
Eugene Salamin, Computation of $\pi$ Using Arithmetic-Geometric Mean, Mathematics of Computation, Vol. 30, No. 135 (Jul., 1976), pp. 565-570 ...