A mechanically-based proof of the arithmetic mean harmonic mean inequality

ABSTRACT

Many proofs of the arithmetic mean harmonic mean inequality have been proposed based on the rich connections between mathematics and physics. Sometimes the Arithmetic Mean Harmonic Mean inequality is proved by using electric networks. In this note, we use a simple set of two springs, instead of four springs which would be the equivalent set to those using electric networks.

KEYWORDS:

• Arithmetic mean
• harmonic mean
• inequality

CLASSIFICATIONS:

• MSC: 97H30
• 97M50

Disclosure statement

No potential conflict of interest was reported by the authors.