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Notes and references

  1. The earliest solution of the inverse-square orbit problem was evidently constructed by John Keill and published in the 1708 volume of thePhilosophical Transactions. The latest published solution, so far as I am aware, can be found in Robert Weinstock, “Inverse-square orbits: Three little-known solutions and a novel integration technique,”Am. J. Phys. 60 (1992) 615–619.

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  2. If, instead of erecting the perpendicular toOp at its midpoint in Fig. 1 (as does J/G2), we constructed the perpendicular toOp at, say, 0.75 of its length from O, and considered the pointP′ at which this perpendicular intersectsCp, then, as θ increases from 0 to 2π, the intersection P′ would still trace a closed smooth curve. However, you will find the tangent to this curve at each P′ is not (except for θ = 0 and θ= π perpendicular to the segmentOp. Only the choice of the halfway pointP works.

  3. J. Clerk Maxwell,Matter and Motion, D. Van Nostrand, New York (1878), Chap. VIII; reprinted from Van Nostrand’s Magazine.

  4. T.L. Hankins,Sir William Rowan Hamilton, Johns Hopkins University Press, Baltimore (1980), pp. 326–333.

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  2. John Searle,Minds, Brains and Science (Cambridge, Massachusetts: Harvard University Press, 1984).

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  3. John Searle,The Rediscovery of the Mind (Cambridge, Massachusetts: MIT Press, 1992).

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  4. Alan Turing, “Computing Machinery and Intelligence,” inThe Mind’s I, edited by Douglas Hofstader and Daniel Dennett (New York: Basic Books, 1981).

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  5. Ludwig Wittgenstein,Philosophical Investigations, translated by G. E. M. Anscombe (New York: Macmillan Publishing, 1958).

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  6. Ludwig Wittgenstein,Wittgenstein’s Lectures on the Foundations of Mathematics, edited by Cora Diamond (Chicago: University of Chicago Press, 1976).

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Author information

Authors and Affiliations

  1. Department of Mathematics, Drexel University, 19104, Philadelphia, PA, USA

    Jet Wimp

  2. Department of Physics, Oberlin College, 44074, Oberlin, OH, USA

    Robert Weinstock

  3. Department of Mathematics, Washington University, 63130-4899, St. Louis, MO, USA

    Steven G. Krantz

  4. School of Information Resources and Department of Philosophy, University of Arizona, 85719, Tucson, AZ, USA

    Don Fallis & Kay Mathiesen

Authors
  1. Jet Wimp
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  2. Robert Weinstock
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  3. Steven G. Krantz
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  4. Don Fallis
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  5. Kay Mathiesen
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Wimp, J., Weinstock, R., Krantz, S.G. et al. Reviews. The Mathematical Intelligencer 21, 71–79 (1999). https://doi.org/10.1007/BF03025419

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