The Generalized mean[1] linked to in the blog comments was similarly insightful. It unifies the inequalities: max > root mean square > arithmetic mean > geome

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 http://en.wikipedia.org/wiki/Power_mean#Special_cases [2] https://artofproblemsolving.com/wiki/index.php?title=Root-Mean_Square-Arithmetic_Mean-Geometric_Mean-Harmonic_mean_Inequality https://artofproblemsolving.com/wiki/index.php?title=Root-Me...