Pythagorean Means

The Pythagorean means are the three "classic" means  (the arithmetic mean),  (the geometric mean), and  (the harmonic mean) are sometimes known as the Pythagorean means. The figure above shows how these means on two elements  and  could be constructed geometrically, and also demonstrates that .

REFERENCES:

Eves, H. "Means Appearing in Geometric Figures." Math. Mag. 76, 292-294, 2003.

Havil, J. Gamma: Exploring Euler's Constant. Princeton, NJ: Princeton University Press, p. 120, 2003.