On Some Power Means and Their Geometric Construction

Ralph H¯ibak, Dag Lukkasse

Abstract

The main aim of this paper is to further develop the recently initiated research concerning geometric construction of some power means where the variables are appearing as line segments. It will be demonstrated that the arithmetic mean, the harmonic mean and the quadratic mean can be constructed for any number of variables and that all power means where the number of variables are n = 2 m, m  1 2 N for all powers k = 2 q and k = 2 q ; q 2 N can be geometrically constructed.