The Mathematical Intelligencer

, Volume 21, Issue 3, pp 71–79 | Cite as


  • Jet Wimp
  • Robert Weinstock
  • Steven G. Krantz
  • Don Fallis
  • Kay Mathiesen


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Notes and references

  1. 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.CrossRefzbMATHMathSciNetGoogle Scholar
  2. 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.Google Scholar
  3. 3.
    J. Clerk Maxwell,Matter and Motion, D. Van Nostrand, New York (1878), Chap. VIII; reprinted from Van Nostrand’s Magazine.Google Scholar
  4. 4.
    T.L. Hankins,Sir William Rowan Hamilton, Johns Hopkins University Press, Baltimore (1980), pp. 326–333.zbMATHGoogle Scholar


  1. [1]
    H. M. Collins,Artificial Experts (Cambridge, Massachusetts: MIT Press, 1990).Google Scholar
  2. [2]
    John Searle,Minds, Brains and Science (Cambridge, Massachusetts: Harvard University Press, 1984).Google Scholar
  3. [3]
    John Searle,The Rediscovery of the Mind (Cambridge, Massachusetts: MIT Press, 1992).Google Scholar
  4. [4]
    Alan Turing, “Computing Machinery and Intelligence,” inThe Mind’s I, edited by Douglas Hofstader and Daniel Dennett (New York: Basic Books, 1981).Google Scholar
  5. [5]
    Ludwig Wittgenstein,Philosophical Investigations, translated by G. E. M. Anscombe (New York: Macmillan Publishing, 1958).Google Scholar
  6. [6]
    Ludwig Wittgenstein,Wittgenstein’s Lectures on the Foundations of Mathematics, edited by Cora Diamond (Chicago: University of Chicago Press, 1976).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 1999

Authors and Affiliations

  • Jet Wimp
    • 1
  • Robert Weinstock
    • 2
  • Steven G. Krantz
    • 3
  • Don Fallis
    • 4
  • Kay Mathiesen
    • 4
  1. 1.Department of MathematicsDrexel UniversityPhiladelphiaUSA
  2. 2.Department of PhysicsOberlin CollegeOberlinUSA
  3. 3.Department of MathematicsWashington UniversitySt. LouisUSA
  4. 4.School of Information Resources and Department of PhilosophyUniversity of ArizonaTucsonUSA

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