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Shapes of worn stones

  • William J. Firey (a1)

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.

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8.Reynolds, G.. “Two weeks on the west coast”, Pacific Yachting, 6, No. 3 (Mar. 1973), 2630.
9.Santaló, L. A.. “Un invariante afln para los cuerpos convexos del espacio de n dimensionas”, Portugaliae Math., 8 (1949), 155161.
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  • ISSN: 0025-5793
  • EISSN: 2041-7942
  • URL: /core/journals/mathematika
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