# Completing Book II of Archimedes’s On Floating Bodies

@article{Rorres2004CompletingBI, title={Completing Book II of Archimedes’s On Floating Bodies}, author={Chris Rorres}, journal={The Mathematical Intelligencer}, year={2004}, volume={26}, pages={32-42} }

ConclusionOne need only glance at Archimedes’s Proposition 8 above to see thatOn Floating Bodies is several orders of magnitude more sophisticated than anything else found in ancient mathematics. It ranks with Newton’sPrincipia Mathematica as a work in which basic physical laws are both formulated and accompanied by superb applications.

## 26 Citations

Archimedes' floating bodies on a spherical Earth

- Physics
- 2016

Archimedes was the first to systematically find the centers of gravity of various solid bodies and to apply this concept in determining stable configurations of floating bodies. In this paper, we…

Archimedes: Bathtub academicpar excellence

- Physics
- 2006

Stability and control of floating bodies is a major aspect of navigation from ancient to modern times. It is indeed remarkable that Archimedean concepts continue to guide watercraft designers even…

Archimedes the Mathematician

- Art
- 2017

Although Archimedes’ fame among the general populace in antiquity was based on his military machines, inventions, and legends, he earned his true immortality through his mathematical works. Here I…

Mechanics of floating bodies

- MathematicsProceedings of the Royal Society A
- 2021

We introduce and study the mechanical system which describes the dynamics and statics of rigid bodies of constant density floating in a calm incompressible fluid. Since much of the standard…

Floating body problems in two dimensions 1

- Physics
- 2011

Stanislav Ulam asked if the sphere is the only object floating in neutral equilibrium in every orientation and negative answer was provided recently. Here, several related problems are discussed. The…

Floating Body Problems in Two Dimensions

- Physics
- 2009

Stanislav Ulam asked if the sphere is the only object floating in neutral equilibrium in every orientation and a negative answer was provided recently. Here, several related problems are discussed.…

Mathematics of Floating 3D Printed Objects

- Computer Science
- 2022

This work explores the stability of ﬂoating objects through mathematical modeling and experimentation, based on standard ideas of center of gravity, center of buoyancy, and Archimedes’ Principle, and identifies a potential energy landscape that helps identify stable and unstable orientations.

Floating Bodies in the Absence of Gravity

- Geology
- 2011

The study of infinitely long cylinders of constant cross-section floating in an infinite fluid bath in zero-gravity environments has primarily been focused on bodies whose crosssections are strictly…

Using surface integrals for checking Archimedes' law of buoyancy

- Physics
- 2011

A mathematical derivation of the force exerted by an inhomogeneous (i.e. compressible) fluid on the surface of an arbitrarily shaped body immersed in it is not found in the literature, which may be…

## References

SHOWING 1-10 OF 18 REFERENCES

The Impact of Archimedes on Medieval Science

- PhysicsIsis
- 1959

THE importance of the role played by Archimedes in the history of science can scarcely be exaggerated. He was emulated and admired in his own day and at successive periods in later times. His name…

Floating equilibrium of symmetrical objects and the breaking of symmetry. Part 1: Prisms

- Physics
- 1992

The equilibrium configurations of solid prisms of square and equilateral triangular cross section floating in a liquid are examined. It is found that these bodies float in different symmetrical or…

A history of Greek mathematics

- Mathematics
- 1921

A text which looks at the history of Greek mathematics - a subject on which the author established a special authority by his succession of works on Diophantus, Apolonius of Perga, Archimedes, Euclid…

How things float

- Mathematics
- 1991

S. M. Ulam once asked if spheres are the only homogeneous bodies that can float in every orientation. Here an affirmative answer is given for a special class of bodies of revolution that seemed lik...

Floating equilibrium of symmetrical objects and the breaking of symmetry. Part 2: The cube, the octahedron, and the tetrahedron

- Geology
- 1992

The analysis of the equilibrium configurations of floating bodies (see part 1) is extended to the cube, for which a complete discussion is given. The symmetric floating configurations of the…

An Introduction to Dynamical Systems

- Mathematics
- 1990

Preface 1. Diffeomorphisms and flows 2. Local properties of flow and diffeomorphims 3. Structural stability, hyperbolicity and homoclinic points 4. Local bifurcations I: planar vector fields and…

Dynamics and Bifurcations

- Mathematics
- 1991

This study presents ideas and examples about the geometry of dynamics and bifurcations of ordinary differential equations. The subject of differential and difference equations is an old and…

The Floating Plank

- Mathematics
- 1987

The stable floating configuration of a long plank of rectangular cross section depends on the relative density of the plank to the fluid and on the ratio of the sides. The complete solution of this…

Solution of the Cattle Problem of Archimedes

- Mathematics
- 1965

1. Introduction. In 1773 G. E. Lessing published a Greek epigram [1], attributed in substance, to Archimedes, which states a problem now commonly referred to as the "cattle problem". The verse, when…

The use of Catastrophe Theory to Analyse the Stability and Toppling of Icebergs

- PhysicsAnnals of Glaciology
- 1980

As an iceberg melts, the resulting change of shape can cause it to list gradually or to become unstable and topple over suddenly. Similarly, when an iceberg breaks up some of the individual pieces…