Skip to main content
SpringerLink
Log in

Phase Portraits of Hyperbolic Geometry

  • Article
  • Published:
The Mathematical Intelligencer Aims and scope Submit manuscript

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7
Figure 8
Figure 9
Figure 10
Figure 11
Figure 12
Figure 13
Figure 14
Figure 15
Figure 16
Figure 17
Figure 18
Figure 19
Figure 20
Figure 21
Figure 22

References

  1. D. N. Arnold and J. Rogness. Möbius transformations revealed. Notices of the AMS 55 (2008).

  2. D. N. Arnold and J. Rogness. Moebius Transformations Revealed [Video file]. Retrieved from https://www.youtube.com/watch?v=JX3VmDgiFnY, June 3, 2007.

  3. J. M. Borwein. The Life of Modern Homo Habilis Mathematicus: Experimental Computation and Visual Theorems. In Tools and Mathematics, pp. 23–90, Mathematics Education Library 347. Springer, 2016.

  4. J. M. Borwein and A. Straub. Moment function of a 4-step planar random walk. Complex Beauties 2016 (2016 Calendar). Available at http://www.mathe.tu-freiberg.de/files/information/calendar2016eng.pdf.

  5. J. E. Littlewood. A Mathematician’s Miscellany. London: Methuen, 1953. Republished in Béla Bollobás, ed., Littlewood’s Miscellany, Cambridge University Press, 1986.

  6. T. Needham. Visual Complex Analysis. Oxford University Press, 1997.

  7. E. Wegert. Visual Complex Functions: An Introduction with Phase Portraits. Springer, 2012.

  8. E. Wegert and G. Semmler. Phase Plots of Complex Functions: A Journey in Illustration. Notices of the American Mathematical Society 58(6) (2011), 768–780.

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. CARMA, University of Newcastle, Newcastle, NSW, Australia

    Scott B. Lindstrom

  2. University of Toronto Mississauga, Mississauga, ON, L5L 1C6, Canada

    Paul Vrbik

Authors
  1. Scott B. Lindstrom
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Paul Vrbik
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Scott B. Lindstrom.

Ethics declarations

Software

The Maple code used to generate all of the phase portraits in this paper is available at https://ogma.newcastle.edu.au/vital/access/manager/Repository/uon:29853.

Dedication

This project is dedicated to the memory of Jonathan M. Borwein, our adviser, mentor, and friend.

Additional information

This project is dedicated to the memory of Jonathan M. Borwein, our adviser, mentor, and friend.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lindstrom, S.B., Vrbik, P. Phase Portraits of Hyperbolic Geometry. Math Intelligencer 41, 1–9 (2019). https://doi.org/10.1007/s00283-019-09882-y

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00283-019-09882-y

Search

Navigation