Straightedge and Compass Constructions
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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.
KeywordsLine Segment Geometrical Construction Construction Problem Compass Point Original Angle
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Additional Reading for Chapter 5
- [JF]J.B. Fraleigh, A First Course in Abstract Algebra, 3rd edition, Addison-Wesley, Reading, Massachusetts, 1982.Google Scholar
- [MG]M. Gardner, Mathematical Circus, Penguin Books, Middlesex, England, 1981.Google Scholar
- [EH]E.W. Hobson, Squaring the Circle, Cambridge University Press, 1913; reprinted in Squaring the Circle, and Other Monographs, Chelsea, 1953.Google Scholar
- [HH]H.P. Hudson, Ruler and Compass, Longmans Green, 1916; reprinted in Squaring the Circle, and Other Monographs, Chelsea, 1953.Google Scholar
- [HJ]U.R. Jacobs, Geometry, Freeman, San Francisco, California, 1974.Google Scholar
- [AK]A.N. Kostovskii, Geometrical Constructions Using Compasses Only, Blaisdell, New York, 1961.Google Scholar
- [RR]R. Ruthen, “Squaring the Circle”, Scientific American, 261 (1989), 11–12.Google Scholar
- [JS]J. Steiner, “Geometrical Constructions with a Ruler Given a Fixed Circle with its Center”, Scripta Mathematica, 14 (1948), 187–264.Google Scholar