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Straightedge and Compass Constructions

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Abstract Algebra and Famous Impossibilities

Part of the book series: Universitext ((UTX))

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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.

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Additional Reading for Chapter 5

  1. L. Dubins, M.W. Hirsch and J. Karush, “Scissor Congruence”, Israel Journal of Mathematics, 1 (1963), 239–247.

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  2. H. Eves, A Survey of Geometry, Allyn and Bacon, Boston, Massachusetts, 1972.

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  3. J.B. Fraleigh, A First Course in Abstract Algebra, 3rd edition, Addison-Wesley, Reading, Massachusetts, 1982.

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  4. French, “The Banach-Tarski Theorem”, The Mathematical Intelligencer, 10 (1988), 21–28.

    Article  MathSciNet  MATH  Google Scholar 

  5. M. Gardner, Mathematical Circus, Penguin Books, Middlesex, England, 1981.

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  6. E.W. Hobson, Squaring the Circle, Cambridge University Press, 1913; reprinted in Squaring the Circle, and Other Monographs, Chelsea, 1953.

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  7. H.P. Hudson, Ruler and Compass, Longmans Green, 1916; reprinted in Squaring the Circle, and Other Monographs, Chelsea, 1953.

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  8. U.R. Jacobs, Geometry, Freeman, San Francisco, California, 1974.

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  9. A.N. Kostovskii, Geometrical Constructions Using Compasses Only, Blaisdell, New York, 1961.

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  10. R. Ruthen, “Squaring the Circle”, Scientific American, 261 (1989), 11–12.

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  11. J. Steiner, “Geometrical Constructions with a Ruler Given a Fixed Circle with its Center”, Scripta Mathematica, 14 (1948), 187–264.

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  12. S. Wagon, “Circle-Squaring in the Twentieth Century”, The Mathematical Intelligencer, 3 (1981), 176–181.

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, La Trobe University, Bundoora, 3083, Australia

    Arthur Jones & Kenneth R. Pearson

  2. Faculty of Informatics, University of Wollongong, Wollongong, 2500, Australia

    Sidney A. Morris

Authors
  1. Arthur Jones
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  2. Kenneth R. Pearson
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  3. Sidney A. Morris
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© 1991 Springer Science+Business Media New York

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Jones, A., Pearson, K.R., Morris, S.A. (1991). Straightedge and Compass Constructions. In: Abstract Algebra and Famous Impossibilities. Universitext. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-8552-1_6

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  • DOI: https://doi.org/10.1007/978-1-4419-8552-1_6

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-97661-7

  • Online ISBN: 978-1-4419-8552-1

  • eBook Packages: Springer Book Archive

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