# Harmonic-mean definitions

The reciprocal of the arithmetic mean of the reciprocals of a specified set of numbers.

noun

A number associated with a set of numbers, that is equal to the number of numbers divided by the sum of the reciprocals of the numbers (h = n ÷ (

^{1}_{a}+^{1}_{b}+^{1}_{c}+ …)) (Ex.: for^{1}_{2},^{1}_{3}, and^{1}_{4}, h = 3 ÷ (2 + 3 + 4) =^{1}_{3}; for^{1}_{2}and^{1}_{3}, h = 2 ÷ (2 + 3) =^{2}_{5})noun

The reciprocal of the arithmetic mean of the reciprocals of a specified set of numbers.

(mathematics) A type of measure of central tendency calculated as the reciprocal of the mean of the reciprocals, ie,

If an and bn denote the perimeters of inscribed and circumscribed regular n-gons, respectively, along some circle then the harmonic mean and geometric mean of those two perimeters yield the perimeters of the inscribed and circumscribed regular 2n-gons, respectively, along that same circle. (This is Archimedes' Recurrence Formula.)

noun