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Symmetry

  • David R. Finston
  • Patrick J. Morandi
Chapter
Part of the Springer Undergraduate Texts in Mathematics and Technology book series (SUMAT)

Abstract

In this chapter we explore another connection between algebra and geometry. One of the main issues studied in plane geometry is congruence; roughly, two geometric figures are said to be congruent if one can be moved to coincide exactly with the other. We will be more precise below in our description of congruence, and investigating this notion will lead us to new examples of groups. The culmination of this discussion is the mathematical classification of frieze patterns and wallpaper patterns based on the structure of the groups that arise.

References

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    Mackiw G (1985) Applications of abstract algebra. Wiley, HobokenzbMATHGoogle Scholar
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    Schwartzenberger R (1974) The 17 plane symmetry groups. Math Gazette 58:123–131MathSciNetCrossRefGoogle Scholar
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    Schattschneider D (1978) Tiling the plane with congruent pentagons. Math Mag 51:29–44MathSciNetCrossRefGoogle Scholar
  4. 4.
    Schattschneider D (1978), The plane symmetry groups: their recognition and notation. Am Math Monthly 85(6):439–450MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • David R. Finston
    • 1
    • 2
  • Patrick J. Morandi
    • 3
  1. 1.Department of MathematicsBrooklyn College of the City University of New YorkBrooklynUSA
  2. 2.CUNY Graduate CenterNew YorkUSA
  3. 3.Department of Mathematical SciencesNew Mexico State UniversityLas CrucesUSA

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