Napoleon's Theorem

Arthur Freitas Ramos 📧, David Barros Hulak 📧 and Ruy Jose Guerra Barretto de Queiroz 📧

August 24, 2026

Abstract

Napoleon's theorem states that, for a non-degenerate triangle, the centres of the equilateral triangles constructed externally on its three sides form an equilateral triangle. We formalize this construction and conclusion using complex coordinates, including the exterior-side condition and both orientations of the 60-degree rotation.

License

BSD License

Note

AI assistance was used for proof engineering.

Topics

Session Napoleon

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Cite

× 
@article{Napoleon-AFP,
  author  = {Arthur Freitas Ramos and David Barros Hulak and Ruy Jose Guerra Barretto de Queiroz},
  title   = {Napoleon's Theorem},
  journal = {Archive of Formal Proofs},
  month   = {August},
  year    = {2026},
  note    = {\url{https://isa-afp.org/entries/Napoleon.html},
             Formal proof development},
  ISSN    = {2150-914x},
}
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