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A Symmetric 3D Proof of Heron’s Formula

  • Mathematical Gems and Curiosities
  • Sergei Tabachnikov, Editor
  • Published:
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Figure 1

References

  1. J. Scott Carter and D. A. Mullen. Heron’s formula from a 4-dimensional perspective. Published online at https://www.semanticscholar.org/paper/Heron-%E2%80%99-s-Formula-from-a-4-Dimensional-Perspective-Carter-Mullens/95d66d1d068c11480e023815a42b2b36db597e67.

  2. D. R. Conant and W. A. Beyer. Generalized Pythagorean Theorem. American Mathematical Monthly 81:3 (1974), 262–265.

  3. J. Conway and P. Doyle. Correspondence. Published online at https://math.dartmouth.edu/~doyle/docs/heron/heron.txt.

  4. M. Edwards. A proof of Heron’s theorem. American Mathematical Monthly 114:10 (December 2007), 937.

  5. T. L. Heath. A History of Greek Mathematics, vol. II. Oxford University Press, 1921.

  6. F. A. Kafker and J. Loveland. La vie agitée de l’abbé De Gua de Malves. Recherches sur Diderot et l’Encyclopédie 47 (2012), 187–205.

  7. D. A. Klain. An intuitive derivation of Heron’s formula. American Mathematical Monthly 111:8 (2004), 709–712.

  8. J.-M. Lévy-Leblond. The Pythagorean theorem extended—and deflated. Mathematical Intelligencer 27 (2004), 5–6.

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Acknowledgments

It is a pleasure to thank for their comments Jean-Pierre Boudine, Chandler Davis, Jean-Baptiste Hiriart-Urruty, and Serge Tabachnikov.

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Authors and Affiliations

  1. Université de Nice, Nice, France

    Jean-Marc Lévy-Leblond

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  1. Jean-Marc Lévy-Leblond
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Correspondence to Jean-Marc Lévy-Leblond.

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Lévy-Leblond, JM. A Symmetric 3D Proof of Heron’s Formula. Math Intelligencer 43, 37–39 (2021). https://doi.org/10.1007/s00283-020-09996-8

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  • DOI: https://doi.org/10.1007/s00283-020-09996-8

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