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Shapes of worn stones

Part of: General convexity

Published online by Cambridge University Press:  26 February 2010

William J. Firey
William J. Firey
Affiliation:
Oregon State University, Corvallis, Oregon 97331
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Extract

Often stones on beaches pounded by waves wear into quite smooth, regular shapes, sometimes apparently ellipsoidal and even spherical [8]. This paper begins with an idealization of this wearing process for materials isotropic with respect to wear, then develops an equation governing the idealized process, and goes on to show that a stone which is initially convex and centrally symmetric tends to assume a spherical shape as a consequence of the governing equation. This conclusion is predicated on the assumption that the mathematical conditions describing the wearing process are those of a well-posed problem.

MSC classification

Secondary: 52A15: Convex sets in $3$ dimensions (including convex surfaces)
Type
Research Article
Information
Mathematika , Volume 21 , Issue 1 , June 1974 , pp. 1 - 11
Copyright
Copyright © University College London 1974

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References

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