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Straightedge and Compass Constructions

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

Abstract

In the previous chapters we developed the algebraic machinery for proving that the three famous geometric constructions are impossible. In this chapter we introduce some geometry and start to show the connection between algebra and the geometry of constructions.

Keywords

Line Segment Geometrical Construction Construction Problem Compass Point Original Angle 
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 Chapter 5

  1. [LD]
    L. Dubins, M.W. Hirsch and J. Karush, “Scissor Congruence”, Israel Journal of Mathematics, 1 (1963), 239–247.MathSciNetCrossRefGoogle Scholar
  2. [HE]
    H. Eves, A Survey of Geometry, Allyn and Bacon, Boston, Massachusetts, 1972.zbMATHGoogle Scholar
  3. [JF]
    J.B. Fraleigh, A First Course in Abstract Algebra, 3rd edition, Addison-Wesley, Reading, Massachusetts, 1982.Google Scholar
  4. [RF]R.M.
    French, “The Banach-Tarski Theorem”, The Mathematical Intelligencer, 10 (1988), 21–28.MathSciNetCrossRefzbMATHGoogle Scholar
  5. [MG]
    M. Gardner, Mathematical Circus, Penguin Books, Middlesex, England, 1981.Google Scholar
  6. [EH]
    E.W. Hobson, Squaring the Circle, Cambridge University Press, 1913; reprinted in Squaring the Circle, and Other Monographs, Chelsea, 1953.Google Scholar
  7. [HH]
    H.P. Hudson, Ruler and Compass, Longmans Green, 1916; reprinted in Squaring the Circle, and Other Monographs, Chelsea, 1953.Google Scholar
  8. [HJ]
    U.R. Jacobs, Geometry, Freeman, San Francisco, California, 1974.Google Scholar
  9. [AK]
    A.N. Kostovskii, Geometrical Constructions Using Compasses Only, Blaisdell, New York, 1961.Google Scholar
  10. [RR]
    R. Ruthen, “Squaring the Circle”, Scientific American, 261 (1989), 11–12.Google Scholar
  11. [JS]
    J. Steiner, “Geometrical Constructions with a Ruler Given a Fixed Circle with its Center”, Scripta Mathematica, 14 (1948), 187–264.Google Scholar
  12. [SW]
    S. Wagon, “Circle-Squaring in the Twentieth Century”, The Mathematical Intelligencer, 3 (1981), 176–181.MathSciNetCrossRefzbMATHGoogle 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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