Theorems of Euclidean Geometry Through Calculus

Buysse, Martin
(2023) The Mathematical Intelligencer — (2023)

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We re-derive Thales, Pythagoras, Apollonius, Stewart, Heron, al Kashi, Terquem and de Gua's theorems by assuming the existence of an unknown relation between the geometric quantities at stake, observing how the relation behaves under small deviations of those quantities, and naturally establishing differential equations that we integrate out. Applying the general solution to some specific situation gives a particular solution corresponding to the expected theorem.
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Buysse, M. (2023). Theorems of Euclidean Geometry Through Calculus. The Mathematical Intelligencer. Accepted/in-press. https://doi.org/10.1007/s00283-022-10249-z (Original work published 2023)