Towards a completion of Archimedes' treatise on floating bodies

  • Girstmair K
  • Kirchner G
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Abstract

In the said treatise 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 Rorres's article [C. Rorres, Completing book II of Archimedes's on floating bodies, Math. Intell. 26(3) (2004) 32-42]. © 2007 Elsevier GmbH. All rights reserved.

Author-supplied keywords

  • Archimedes
  • Equilibria of floating bodies
  • Greek mathematics

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Authors

  • Kurt Girstmair

  • Gerhard Kirchner

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