Abstract

This article provides a formalisation of the Weighted Arithmetic–Geometric Mean Inequality. As a corollary, the regular arithmetic–geometric mean inequality follows. I follow Pólya’s elegant proof, which uses the inequality exp(x) ≥ 1 + x as a starting point. Pólya claims that this proof came to him in a dream, and that it was “the best mathematics he had ever dreamt.”

BibTeX

@article{Weighted_Arithmetic_Geometric_Mean-AFP,
  author  = {Manuel Eberl},
  title   = {Pólya’s Proof of the Weighted Arithmetic–Geometric Mean Inequality},
  journal = {Archive of Formal Proofs},
  month   = {July},
  year    = {2022},
  note    = {\url{https://isa-afp.org/entries/Weighted_Arithmetic_Geometric_Mean.html},
            Formal proof development},
  ISSN    = {2150-914x},
}