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Theorems of Euclidean Geometry Through Calculus

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References

  1. J. al-Kashi. Miftah al-hisab, 1427.

  2. Apollonius of Perga. De Locis Planis, c. 200 BCE.

  3. M. Buysse. Finite mixing angles in the standard model. https://arxiv.org/pdf/hep-ph/0205213.pdf, (2002).

  4. J.-P. de Gua de Malves. Propositions neuves, et non moins utiles que curieuses, sur le tétraèdre; ou Essai de Tétraédrométrie. Mémoires de l’Académie royale des sciences – ann. 1783 (1786), 363–402.

  5. R. Descartes. Opuscules. Cogitationes privatæ, 1619.

  6. Euclid of Alexandria. Elements, c. 300 BCE.

  7. M. Hardy. Pythagoras made difficult. Mathematical Intelligencer 10:3 (1988), 31.

    Google Scholar 

  8. T. Heath. History of Greek Mathematics. Oxford University Press, 1921.

  9. Heron of Alexandria. Metrica, c. 70 CE.

  10. G. Leibniz. Nova methodus pro maximis et minimis. Acta Eruditorum X (1684), 467–473.

  11. I. Newton. De Methodis Serierum et Fluxionum (1671). Henry Woodfall, 1736.

  12. M. Staring. The Pythagorean proposition: a proof by means of calculus. Mathematics Magazine 69 (1996), 45–46.

    Article  MathSciNet  Google Scholar 

  13. S. Stewart. Some General Theorems of Considerable Use in the Higher Parts of Mathematics. Edinburgh: printed by W. Sands, A. Murray, and J. Cochran. Sold by said W. Sands in the Parliament-Close, and by J. and P. Knapton, at the Crown in Ludgate street, London, 1746.

  14. S. Strogatz. Infinite Powers: How Calculus Reveals the Secrets of the Universe. Mariner Books, 2020.

  15. O. Terquem. Considérations sur le triangle rectiligne d’après Euler. Nouv. Ann. Math. (1) 1 (1842), 70–87.

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Acknowledgments

I thank Raphaël Lefevere for a critical reading of the manuscript and a fruitful collaboration. The initial idea came from previous work in particle physics looking for natural relations between mixing angles and the fermion mass ratios [3], supervised by Jean-Marc Gérard, whom I also thank.

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  1. Louvain Research Institute for Landscape, Architecture, Built Environment – LAB, UCLouvain, Ottignies-Louvain-la-Neuve , Belgium

    Martin Buysse

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Correspondence to Martin Buysse.

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Buysse, M. Theorems of Euclidean Geometry Through Calculus. Math Intelligencer 45, 338–345 (2023). https://doi.org/10.1007/s00283-022-10249-z

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