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A Path in History, from Curvature to Convexity

In: Geometry in History

Author

Listed:
  • Annette A’Campo-Neuen

    (Universität Basel, Departement Mathematik und Informatik)

  • Athanase Papadopoulos

    (Université de Strasbourg and CNRS)

Abstract

We describe a path in the history of curvature, starting from Greek antiquity, in the works of Euclid, Apollonius, Archimedes and a few others, passing 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 evolved from the synthetic point of view of the Greeks to the methods of analytic geometry founded by Fermat, Descartes, Newton and Leibniz, and eventually, in the twentieth century, experienced a return to the synthetic methods of the Greeks.

Suggested Citation

  • Annette A’Campo-Neuen & Athanase Papadopoulos, 2019. "A Path in History, from Curvature to Convexity," Springer Books, in: S. G. Dani & Athanase Papadopoulos (ed.), Geometry in History, chapter 0, pages 305-353, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-13609-3_7
    DOI: 10.1007/978-3-030-13609-3_7
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