Revisiting floating bodies
| Autor: | Luz Roncal, Emilio Fernández, Óscar Ciaurri |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Surface (mathematics)
Archimedes Plane curve General Mathematics 010102 general mathematics Tangent Multidimensional conoids Metric Geometry (math.MG) Geometry 01 natural sciences Compact space Mathematics - Metric Geometry Conic section Tangent lines to circles FOS: Mathematics Clairaut equations 0101 mathematics Constant (mathematics) Floating bodies Mathematics |
| Zdroj: | RIUR. Repositorio Institucional de la Universidad de La Rioja instname |
| ISSN: | 0723-0869 |
| DOI: | 10.1016/j.exmath.2016.06.001 |
| Popis: | 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. Comment: 23 pages, 9 figures. To appear in Expositiones Mathematicae |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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