Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-13T06:45:58.279Z Has data issue: false hasContentIssue false
  • English
  • Français

Frieze Patterns in the Hyperbolic Plane

Published online by Cambridge University Press:  20 November 2018

C. W. L. Garner
C. W. L. Garner*
Affiliation:
Castleton Univ., Ottawa
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

It is well known that in the Euclidean plane there are seven distinct frieze patterns, i.e. seven ways to generate an infinite design bounded by two parallel lines. In the hyperbolic plane, this can be generalized to two types of frieze patterns, those bounded by concentric horocycles and those bounded by concentric equidistant curves. There are nine such frieze patterns; as in the Euclidean case, their symmetry groups are and

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 17 , Issue 1 , 01 March 1974 , pp. 45 - 50
Copyright
Copyright © Canadian Mathematical Society 1974

References

1. Bachmann, F., Aufbau der Géométrie aus dem Spiegelungsbegriff (Berlin, 1959).Google Scholar
2. M, H. S.. Coxeter, Non-Euclidean Geometry (5th ed., Toronto, 1965).Google Scholar
3. M, H. S., Introduction to Geometry (2nd éd., New York, 1969).Google Scholar
4. Fejes Töth, L., Regular Figures (New York, 1964).Google Scholar
5. Guggenheimer, H. W., Plane Geometry and its Groups (San Francisco, 1967).Google Scholar
6. Speiser, A., Théorie der Gruppen von endlicher Ordnung (3rd ed., New York, 1945).Google Scholar