My favorite bit of trivia is related to the following game:

Start with 2 numbers, a and b and calculate HM and GM Now you have 2 numbers again, so you can play the game again with the new values Every step brings the results together, one from above, the other from below, sandwiching the value in the limit. That value is called Geometric-Harmonic Mean

This works for all 3 pairs of means (HM-GM, GM-AM, HM-AM). The fun fact I was talking about is about the last combination: playing the game with two "extremal" means, the AM and HM, the value they converge to is GM !!

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cperciva 2 days ago | parent [-]

Also fun: The Arithmetic-Geometric Mean can be used to calculate Pi! (Most usefully, the AGM of 1 and sqrt(1/2).)

	▲	NkVczPkybiXICG a day ago \| parent [-]
		I was confused by this because pi is not between 1 and sqrt(1/2). But I found https://www.cs.miami.edu/home/burt/manuscripts/gaussagm/agma... and it clarifies that this AGM is used in the course of approximating pi not that it’s sufficient on its own to do so.