A simple proof that π is irrational

Manuel Eberl 📧

September 13, 2024

This is a development version of this entry. It might change over time and is not stable. Please refer to release versions for citations.

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.

License

BSD License

Topics

Session Pi_Irrational

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Cite

× 
@article{Pi_Irrational-AFP,
  author  = {Manuel Eberl},
  title   = {A simple proof that π 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},
}
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