Abstract
In Part 1 of this article1, we had introduced the idea of symmetry as a mapping that maps a given object onto itself, and we studied an important class of mappings, theisometries — the maps that leave distances unchanged. We showed that every isometry is either the identity, a rotation, a reflection, a translation or a glide reflection. In this part, we consider some further properties of isometries and make some remarks on the Erlangen programme of Felix Klein; then we classify the so-called frieze groups.
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Suggested reading
HS M Coxeter,Introduction to Geometry, Wiley, 1961.
Michael Artin,Algebra, Eastern Economy Edition.
E George Martin,Transformation Geometry: An Introduction to Symmetry, Springer Verlag, 1982.
L Tarasov,This Amazingly Symmetrical World, Mir Publishers, 1986.
Elmer Rees,Notes on Geometry, Springer Verlag, 1985.
Hermann Weyl,Symmetry, Princeton University Press, 1952.
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Shirali, S.A. Symmetry in the world of man and nature. Reson 6, 53–59 (2001). https://doi.org/10.1007/BF02907365
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DOI: https://doi.org/10.1007/BF02907365