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ECOLE DOCTORALE: numéro 400: SAVOIRS SCIENTIFIQUES: EPISTEMOLOGIE, HISTOIRE DES SCIENCES, DIDACTIQUE DES DISCIPLINES DOCTORAT
, 2011
"... TITRE: The works of KŐNIG Dénes (1884–1944) in the domain of mathematical recreations and his treatment of recreational problems in his works of graph theory. TITRE EN FRANÇAIS: Les oeuvres de KŐNIG Dénes (1884–1944) dans le domaine des récréations mathématiques et son traitement de problèmes récréa ..."
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récréatifs dans ses travaux de théorie des graphes. Thèse dirigée par Karine CHEMLA Soutenue le 3 décembre 2010
National Taiwan Normal University ECOLE DOCTORALE: Savoirs scientifiques DOCTORAT
, 2013
"... ii To Léonard 明 韶 who spent the first year of his life having milk and ancient Chinese algebra in my office. tel00770493, version 1 7 Jan 2013 iii Acknowledgments The little story This project started in 2007, when Karine Chemla suggested that I use my knowledge of Sanskrit and Chinese for mathe ..."
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ii To Léonard 明 韶 who spent the first year of his life having milk and ancient Chinese algebra in my office. tel00770493, version 1 7 Jan 2013 iii Acknowledgments The little story This project started in 2007, when Karine Chemla suggested that I use my knowledge of Sanskrit and Chinese
DOCUMENTING A PROCESS OF ABSTRACTION
"... Many pieces of evidence converge towards the conclusion that generality was the main theoretical value prized by the practitioners of mathematics in ancient China and that it was valued more than abstraction (Chemla 2003). More precisely, these scholars regularly aimed at the greatest generality pos ..."
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Many pieces of evidence converge towards the conclusion that generality was the main theoretical value prized by the practitioners of mathematics in ancient China and that it was valued more than abstraction (Chemla 2003). More precisely, these scholars regularly aimed at the greatest generality
DIFFERENT CONCEPTS OF EQUATIONS IN THE NINE CHAPTERS ON MATHEMATICAL PROCEDURES AND IN THE COMMENTARY ON IT BY LIU HUI (3RD CENTURY)
, 2013
"... operations which can be identified as equations 1: chapter VIII is devoted to the solution of systems of simultaneous linear equations, and problem 20 in chapter IX is solved by means of a quadratic equation 2. Are these operations, which we regard as being of the same kind conceived of as connected ..."
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operations which can be identified as equations 1: chapter VIII is devoted to the solution of systems of simultaneous linear equations, and problem 20 in chapter IX is solved by means of a quadratic equation 2. Are these operations, which we regard as being of the same kind conceived of as connected with one another in the Han classic and in its commentary by Liu Hui? This is the question I would like to raise in the present paper. I shall show that, even though these two kinds of equation have features in common, they present essential differences. Moreover, a brief comparison with equations as dealt with in alKhwarizmi's Concise Book on the Computation of algebra and almuqabala will show affinities between these and equations as treated in the eighth of The Nine Chapters rather than with the quadratic equations of chapter IX. In order to prove my point, I shall first examine the content of chapter VIII from this point of view, after which I shall compare the concept of the equation elaborated there with that of the quadratic equation which emerges from chapter IX. Finally, I shall compare both kinds to equations as conceived by alKhwarizmi. (*) REHSEISCNRS.
A formal system for Euclid’s elements
 THE REVIEW OF SYMBOLIC LOGIC
, 2009
"... We present a formal system, E, which provides a faithful model of the proofs in Euclid’s Elements, including the use of diagrammatic reasoning. ..."
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We present a formal system, E, which provides a faithful model of the proofs in Euclid’s Elements, including the use of diagrammatic reasoning.
A Chinese Mathematician in Plato’s Cave. Virtual/Real Dimensions of Internet Epistemology
"... The internet is a digital universe governed by algorithms, where numbers and the discrete operate to give the illusion of a continuum. Who can say where the internet is, even though it connects all of us to a seemingly bondless expanse of information? When considering the topic of this VIIth Congre ..."
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The internet is a digital universe governed by algorithms, where numbers and the discrete operate to give the illusion of a continuum. Who can say where the internet is, even though it connects all of us to a seemingly bondless expanse of information? When considering the topic of this VIIth Congress on Ontology, I began to think about what existence means in this digitalized world. Prior to 1987, my own research focused primarily on three figures: Georg Cantor, who systematically developed set theory and o created an accompanying theory of transfinite numbers; Charles S. Peirce, the founder of Pragmatism, who among many o other accomplishments developed a nonrigorous treatment of infinitesimals; and Abraham Robinson, who introduced a rigorous theory of o infinitesimals in the context of model theory and mathematical logic. ISSN:15762270 www.ontologia.net/studies
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