Skip to main content
SpringerLink
Log in

On a Model of the Modular Group

  • Chapter
Applications of Fibonacci Numbers

  • 270 Accesses

Abstract

An important group of 2 x 2 matrices with integer elements is the modular group. Its elements have determinant unity; and the group operation is ordinary matrix multiplication.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Coxeter, H.S.M. and Moser, W.O.J. Generators and Relations for Discrete Groups (3rd edn.). Springer-Verlag (1972).

    MATH  Google Scholar 

  2. Schroeder, M. Fractals, Chaos and Power Laws. W.H. Freeman, New York (1991).

    MATH  Google Scholar 

  3. Trott, S. “A pair of generators for the unimodular group”. Canad. Math. Bull., Vol. 3 (1962): pp. 245–252.

    Article  MathSciNet  Google Scholar 

  4. Turner, J.C. and Schaake, A.G. “The Elements of Enteger Geometry”. Applications of Fibonacci Numbers, Vol. 5. Edited by G.E. Bergum, A.N. Philippou and A.F. Horadam. Kluwer Academic Publishers (1993): pp. 569–583.

    Chapter  Google Scholar 

  5. Turner, J.C. and Schaake, A.G. “Number Trees for Pythagoras, Plato, Euler, and the Modular Group”. Research Report No. 200, Dept. Math. & Stats., University of Waikato, N.Z., 1990.

    Google Scholar 

  6. Turner, J.C. and Schaake, A.G. “Number Trees, Diagrams, and Tables for the Modular Group Number Tree”. Dept Math, &., University of Waikato, N.Z., 1994.

    Google Scholar 

  7. Turner, J.C., Garcia, H. and Schaake, A.G. “Totient Functions on the Euler Number Tree”. Applications of Fibonacci Numbers, Vol. 5. Edited by G.E. Bergum, A.N. Philippou and A.F. Horadam. Kluwer Academic Publishers (1993): pp. 585–600.

    Chapter  Google Scholar 

Download references

Authors
  1. J. C. Turner
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. G. Schaake
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Computer Science Department, South Dakota State University, Box 2201, 57007-1596, Brookings, South Dakota, USA

    Gerald E. Bergum

  2. 26 Atlantis Street, Aglangia, Nicosia, Cyprus

    Andreas N. Philippou

  3. Department of Mathematics, Statistics and Computer Science, The University of New England, Armidale, New South Wales, 2351, Australia

    Alwyn F. Horadam

Rights and permissions

Reprints and permissions

Copyright information

© 1996 Kluwer Academic Publishers

About this chapter

Cite this chapter

Turner, J.C., Schaake, A.G. (1996). On a Model of the Modular Group. In: Bergum, G.E., Philippou, A.N., Horadam, A.F. (eds) Applications of Fibonacci Numbers. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-0223-7_40

Download citation

  • DOI: https://doi.org/10.1007/978-94-009-0223-7_40

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-6583-2

  • Online ISBN: 978-94-009-0223-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation