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Periodica Mathematica Hungarica

, Volume 49, Issue 2, pp 9–23 | Cite as

Carousels, Zindler curves and the floating body problem

  • J. Bracho
  • L. Montejano
  • D. Oliveros
Article

Abstract

A carousel is a dynamical system that describes the movement of an equilateral linkage in which the midpoint of each rod travels parallel to it. They are closely related to the floating body problem. We prove, using the work of Auerbach, that any figure that floats in equilibrium in every position is drawn by a carousel. Of special interest are such figures with rational perimetral density of the floating chords, which are then drawn by carousels. In particular, we prove that for some perimetral densities the only such figure is the circle, as the problem suggests.

density carousel floating in equilibrium Zindler curves 

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References

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Copyright information

© Akadémiai Kiadó, Budapest 2004

Authors and Affiliations

  • J. Bracho
    • 1
  • L. Montejano
    • 1
  • D. Oliveros
    • 2
  1. 1.Instituto de MatemáticasUniversidad Nacional Autónoma de México Circuíto ExteriorMéxico D.F.México
  2. 2.Department of Mathematics and StatisticsUniversity of CalgaryAlbertaCanada

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