Abstract

This entry provides a formalisation of Niven’s famously short one-page proof that pi is irrational. The proof uses only elementary algebra and analysis.

The intrinsic de Bruijn factor, i.e. the file size ratio between the gzipped Isabelle sources and a gzipped LaTeX version of the original paper’s content, is roughly 4 despite the original paper’s terse presentation.

BibTeX

@article{Pi_Irrational-AFP,
  author  = {Manuel Eberl},
  title   = {A simple proof that $\pi$ is irrational},
  journal = {Archive of Formal Proofs},
  month   = {September},
  year    = {2024},
  note    = {\url{https://isa-afp.org/entries/Pi_Irrational.html},
             Formal proof development},
  ISSN    = {2150-914x},
}