If arithmetic and geometric means are so good, why not the harmonic mean? https://en.wikipedia.org/wiki/Pythagorean_means. What would a “harmonic rationality” look like?
Also here is a nice family that parametrizes these different kinds of average (https://m.youtube.com/watch?v=3r1t9Pf1Ffk)
Actually maybe this family is more relevant:https://en.wikipedia.org/wiki/Generalized_mean, where the geometric mean is the limit as we approach zero.
The “harmonic integral” would be the inverse of integral of the inverse of a function—https://math.stackexchange.com/questions/2408012/harmonic-integral
If arithmetic and geometric means are so good, why not the harmonic mean? https://en.wikipedia.org/wiki/Pythagorean_means. What would a “harmonic rationality” look like?
Also here is a nice family that parametrizes these different kinds of average (https://m.youtube.com/watch?v=3r1t9Pf1Ffk)
Actually maybe this family is more relevant:
https://en.wikipedia.org/wiki/Generalized_mean, where the geometric mean is the limit as we approach zero.
The “harmonic integral” would be the inverse of integral of the inverse of a function—https://math.stackexchange.com/questions/2408012/harmonic-integral