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Introduction

  • Arthur Jones
  • Kenneth R. Pearson
  • Sidney A. Morris
Chapter
  • 478 Downloads
Part of the Universitext book series (UTX)

Abstract

In this book we discuss three of the oldest problems in mathematics. Each of them is over 2,000 years old. The three problems are known as:
  1. [I]

    doubling the cube (or duplicating the cube, or the Delian problem);

     
  2. [II]

    trisecting an arbitrary angle;

     
  3. [III]

    squaring the circle (or quadrature of the circle).

     

Keywords

Regular Polygon Arbitrary Angle Delian Problem Greek Mathematic Perpetual Motion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Additional Reading for the Introduction

  1. [EB1]
    E.T. Bell, Men of Mathematics, Simon and Shuster, New York, 1937.zbMATHGoogle Scholar
  2. [EB2]
    E.T. Bell, The Development of Mathematics, McGraw-Hill, New York, 1945.zbMATHGoogle Scholar
  3. [CB]
    C.B. Boyer, A History of Mathematics, Wiley, New York, 1968.zbMATHGoogle Scholar
  4. [RC]
    R. Courant and H. Robbins, What is Mathematics?, Oxford University Press, New York, 1941.Google Scholar
  5. [AD]
    A. De Morgan, A Budget of Paradoxes, Dover, New York, 1954.zbMATHGoogle Scholar
  6. [UD]
    U. Dudley, A Budget of Trisections, Springer-Verlag, New York, 1987.CrossRefzbMATHGoogle Scholar
  7. [JG]
    J. Gow, A Short History of Greek Mathematics, Chelsea, New York, 1968.Google Scholar
  8. [CH]
    C.R. Hadlock, Field Theory and its Classical Problems, Carus Mathematical Monographs, No. 19, Mathematical Association of America, 1978.Google Scholar
  9. [TH]
    T.L. Heath, A History of Greek Mathematics Vol.I & II, Clarendon Press, Oxford, 1921.Google Scholar
  10. [EH]
    E.W. Hobson, Squaring the Circle, Cambridge University Press, 1913; reprinted in Squaring the Circle, and Other Monographs, Chelsea, 1953.Google Scholar
  11. [HH]
    H.P. Hudson, Ruler and Compass, Longmans Green, 1916; reprinted in Squaring the Circle, and Other Monographs, Chelsea, 1953.Google Scholar
  12. [FK]
    F. Klein, Famous Problems, and other monographs, Chelsea, New York, 1962.Google Scholar
  13. [MK]
    M. Kline, Mathematical Thought from Ancient to Modern Times, Oxford University Press, 1972.Google Scholar
  14. [FLa]
    F. Lasserre, The Birth of Mathematics in the Age of Plato, Hutchinson, London, 1964.zbMATHGoogle Scholar
  15. [FL]
    F.L. Lindemann, “Über die Zahl π”, Mathematische Annalen, 20 (1882), 213–225.MathSciNetCrossRefzbMATHGoogle Scholar
  16. [DS]
    D.J. Struik, A Concise History of Mathematics, Dover, New York, 1967.zbMATHGoogle Scholar
  17. [VS]
    V. Sanford, A Short History of Mathematics, Harrap, London, 1958.Google Scholar
  18. [HT]
    H.W. Turnbull, The Great Mathematicians, Methuen, London 1933.Google Scholar
  19. [MW]
    M.L. Wantzel, “Recherches sur les moyens de reconnaître si un Problème de Géométrie peut se résoudre avec la règle et le compas”, Journal de Mathématiques Pures et Appliquées, 2 (1837), 366–372.Google Scholar

Copyright information

© Springer Science+Business Media New York 1991

Authors and Affiliations

  • Arthur Jones
    • 1
  • Kenneth R. Pearson
    • 1
  • Sidney A. Morris
    • 2
  1. 1.Department of MathematicsLa Trobe UniversityBundooraAustralia
  2. 2.Faculty of InformaticsUniversity of WollongongWollongongAustralia

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