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17 mai 2025
- ISIDORE Id: 10670/1.65bde7...
- hal: hal-05071812
http://creativecommons.org/licenses/by/ , info:eu-repo/semantics/OpenAccess
Mots-clés
Apollonius Descartes Elizabeth circle theorem Clifford algebras spinors multidimensional flowers. Math.GMAMS 01A45Sujets proches
Knowledge--Philosophy Correspondence, reminiscences, etc Letters Correspondence, reminiscences, etc Letters Standard of value Conviction Hours (Time) Pneuma Social theory Natural science Sciences Science of science Mental philosophy Math Correspondence Correspondence Writing of letters Letter writing, English English letter writing Article Donations Presents Blooms (Flowers) Flowering plants Blossoms Tastes Proof Human emotions Passions Feelings Geometric algebras Čechy (Czech Republic) Bohemia (Czechoslovakia) Böhmen (Czech Republic) Bohemia Czechy (Czech Republic) vérité (concept)Citer ce document
Daniel Parrochia, « Descartes' Circle Theorem, Elizabeth, and Spinors », HAL SHS (Sciences de l’Homme et de la Société), ID : 10670/1.65bde7...
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In this article, on Descartes' famous "circle theorem," we first attempt to explain how the philosopher could have arrived at the equation that he presents without demonstration in a letter to Princess Palatine Elizabeth of Bohemia in November 1643. Then we report some stages of the subsequent generalization of this theorem, whose Cliffordian flavor, via the equivalence of a quadratic form and the square of a linear form, still mobilizes mathematicians today. This statement, which, over time, has undergone different extensions, Euclidean and non-Euclidean, has found, {\it in fine}, a spinor formalization. We see there the proof of what we may call, in a Bachelardian style, an "inductive value" of the truth, which extends by successive generalizations. We conclude, more briefly, with the contacts between Elizabeth and Descartes, and the perhaps symbolic meaning of these considerations on "kissing circles," as they are called in Anglo-Saxon countries, in the context of their correspondence on the soul and the body, and the question of passions.
