The Generalized mean[1] linked to in the blog comments was similarly insightful.
It unifies the inequalities:
max > root mean square > arithmetic mean > geometric mean > harmonic mean > min
that I remember from highschool math competitions.[2]
[1] http://en.wikipedia.org/wiki/Power_mean#Special_cases
[2] https://artofproblemsolving.com/wiki/index.php?title=Root-Me...