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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Mackiw G (1985) Applications of abstract algebra. Wiley, Hoboken
Schwartzenberger R (1974) The 17 plane symmetry groups. Math Gazette 58:123–131
Schattschneider D (1978) Tiling the plane with congruent pentagons. Math Mag 51:29–44
Schattschneider D (1978), The plane symmetry groups: their recognition and notation. Am Math Monthly 85(6):439–450
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Finston, D.R., Morandi, P.J. (2014). Symmetry. In: Abstract Algebra. Springer Undergraduate Texts in Mathematics and Technology. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-04498-9_10
Download citation
DOI: https://doi.org/10.1007/978-3-319-04498-9_10
Published:
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-04497-2
Online ISBN: 978-3-319-04498-9
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)