Picard's Weighty Proof of Chebyshev's Sum Inequality

摘要

In his analysis course notes of 1882, Hermite included an algebraic inequality known today as Chebyshev's sum inequality. He presented a physical demonstration due to Picard which was based on the intuitive concept of the center of gravity.We first recall Picard's reasoning with some historical background and then, motivated by his idea, we provide a mechanical interpretation of the usual proof of Chebyshev's inequality carried out via the rearrangement inequality.