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Towards a Completion of Archimedes' Treatise on Floating Bodies

Authors
  • Girstmair, Kurt
  • Kirchner, Gerhard
Type
Preprint
Publication Date
Jun 01, 2007
Submission Date
Jun 01, 2007
Identifiers
arXiv ID: 0706.0119
Source
arXiv
License
Unknown
External links

Abstract

In his treatise on floating bodies Archimedes determines the equilibrium positions of a floating paraboloid segment, but only in the case when the basis of the segment is either completely outside of the fluid or completely submerged. Here we give a mathematical model for the remaining case, i.e., two simple conditions which describe the equilibria in closed form. We provide tools for finding all equilibria in a reliable way and for the classification of these equilibria. This paper can be considered as a continuation of a recent article of Rorres.

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