# harmonic mean

## English

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### Noun

harmonic mean (plural harmonic means)

1. (mathematics) A type of measure of central tendency calculated as the reciprocal of the mean of the reciprocals, ie, ${\displaystyle H={n \over {1 \over x_{1}}+{1 \over x_{2}}+\cdots {1 \over x_{n}}}}$
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.)