Geometric, Arithmetic, and Harmonic

Asked May 15 '15 at 20:27

Active May 15 '15 at 23:02

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I'm curious as to the origin of the words "geometric", "arithmetic", and "harmonic" means. What's so "geometric" about the geometric mean? How is the arithmetic mean more "arithmetic" than the other means? What "harmony" does the harmonic mean suggest?

I realize that the GM, AM, and HM are related to the geometric, arithmetic, and harmonic progressions (series), so if someone wants to answer in terms of those, that'd also be fine. I'm not sure which came first: the mean or the progression, but giving the typical answer that it's called a "geometric mean" because it's related to the "geometric series" and it's called a "geometric series" because it's related to the "geometric mean" is not very helpful.

Thanks in advance for your answers.

edited May 15 '15 at 23:02

asked May 15 '15 at 20:27

user240887

For the geometric mean see http://moodle.tbaisd.org/pluginfile.php/68848/mod_book/chapter/50864/AltGeomMean.jpg. For the harmonic mean see http://en.wikipedia.org/wiki/Harmonic_series_%28mathematics%29. – Qiaochu Yuan May 15 '15 at 20:55
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A similar question appeared yesterday. In a comment there, user Blue gave a link to "Earliest Known Uses of Some of the Words of Mathematics" that is worth a look. – Barry Cipra May 15 '15 at 23:20

Geometric, Arithmetic, and Harmonic

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