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 ...

It focuses students' minds on the substance of the problem for which a mean is required, thus discouraging any automatic procedure, and it does not require a preliminary list of the different mean ...