Revisiting floating bodies

  1. Ciaurri, Ó. 1
  2. Fernández, E. 1
  3. Roncal, L. 1
  1. 1 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

Revista:
Expositiones Mathematicae

ISSN: 0723-0869

Año de publicación: 2016

Volumen: 34

Número: 4

Páginas: 396-422

Tipo: Artículo

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DOI: 10.1016/J.EXMATH.2016.06.001 SCOPUS: 2-s2.0-84998799663 WoS: WOS:000390501700003 GOOGLE SCHOLAR

Otras publicaciones en: Expositiones Mathematicae

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Resumen

The conic sections, as well as the solids obtained by revolving these curves, and many of their surprising properties, were already studied by Greek mathematicians since at least the fourth century B.C. Some of these properties come to the light, or are rediscovered, from time to time. In this paper we characterize the conic sections as the plane curves whose tangent lines cut off from a certain similar curve segments of constant area. We also characterize some quadrics as the surfaces whose tangent planes cut off from a certain similar surface compact sets of constant volume. Our work is developed in the most general multidimensional case. © 2016 Elsevier GmbH