Harmonic-mean definitions

The reciprocal of the arithmetic mean of the reciprocals of a specified set of numbers.
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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 ÷ (1a +1b +1c + …)) (Ex.: for12,13, and14, h = 3 ÷ (2 + 3 + 4) =13 ; for12 and13, h = 2 ÷ (2 + 3) =25)
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The reciprocal of the arithmetic mean of the reciprocals of a specified set of numbers.
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(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.)

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