Titlebook: Geometry in History; S. G. Dani,Athanase Papadopoulos Book 2019 Springer Nature Switzerland AG 2019 58-02, 58-03, 14-02, 53-02, 77-02, 30D

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FLASK

Topology and Biology: From Aristotle to Thom,hat some assertions made by philosophers from Greek antiquity have a definite topological content, even if they were stated more than two and a half millennia before the field of topology was born. He adhered completely to Aristotle’s theory of form which the latter developed especially in his biolo

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,Time and Periodicity from Ptolemy to Schr?dinger: Paradigm Shifts vs Continuity in History of Matheontinuity of mathematical thought was undeservedly neglected in the historical studies. To this end, I focus on the history of mathematical theory of time and periodicity, from Ptolemy’s epicycles to Schr?dinger’s quantum amplitudes interference and contemporary cosmological models.

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On the Concept of Curve: Geometry and Algebra, from Mathematical Modernity to Mathematical Modernishe article argues, by the movement from the primacy of geometrical to the primacy of algebraic thinking. The article also explores the ontological and epistemological aspects of this transition and the connections between modernist mathematics and modernist physics, especially quantum theory, in thi

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From Euclid to Riemann and Beyond: How to Describe the Shape of the Universe,shape of the universe.” More specifically, our aim is to consider, without a claim to completeness, the origin of Riemannian geometry, which is indispensable to the description of the space of the universe as a “generalized curved space.”

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A Path in History, from Curvature to Convexity,g through the works of Huygens, Euler, and Monge and his students, and ending in the twentieth century at the works of Bonnesen, Fenchel, Busemann, Feller and Alexandrov. Our goal is not to review the whole history of curvature, but to show how the approaches to curves, surfaces and curvature evolve

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,René Thom and an Anticipated ,-Principle,ey sound counterintuitive: . Around a decade later, M. Gromov transformed Smale’s idea in what is now known as the .-.. Here, the . stands for ...Shortly after the astonishing discovery by Smale, Thom gave a lecture in Lille (1959) announcing a theorem which would deserve to be named .. The aim of o

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Flat Affine, Projective and Conformal Structures on Manifolds: A Historical Perspective,dean geometry, we describe some highlights of this subject and threads of its evolution. In particular, we discuss the relationship to the subject of discrete subgroups of Lie groups. We emphasize the classification of geometric structures from the point of view of fiber spaces and the later work of