Hostname: page-component-8448b6f56d-t5pn6 Total loading time: 0 Render date: 2024-04-20T03:04:51.809Z Has data issue: false hasContentIssue false
  • English
  • Français

Geometric “Floral” Configurations

Published online by Cambridge University Press:  20 November 2018

Leah Wrenn Berman ,
Jürgen Bokowski ,
Branko Grünbaum  and
Tomaž Pisanski
Leah Wrenn Berman
Affiliation:
Ursinus College, Collegeville, Pennylvania, U.S.A. e-mail: lberman@ursinus.edu
Jürgen Bokowski
Affiliation:
Technical University Darmstadt, Darmstadt, Germany e-mail: juergen.bokowski@googlemail.com
Branko Grünbaum
Affiliation:
University of Washington, Seattle, Washington, U.S.A. e-mail: grunbaum@math.washington.edu
Tomaž Pisanski
Affiliation:
University of Ljubljana, Ljubljana, Slovenia e-mail: Tomaz.Pisanski@fmf.uni-lj.si
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.

With an increase in size, configurations of points and lines in the plane usually become complicated and hard to analyze. The “floral” configurations we are introducing here represent a new type that makes accessible and visually intelligible even configurations of considerable size. This is achieved by combining a large degree of symmetry with a hierarchical construction. Depending on the details of the interdependence of these aspects, there are several subtypes that are described and investigated.

Keywords

52C3052C99
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 52 , Issue 3 , 01 September 2009 , pp. 327 - 341
Copyright
Copyright © Canadian Mathematical Society 2009

References

[1] Berman, L. W., Movable (n 4) configurations. Electron. J. Combin. 13(2006) Research paper 104.Google Scholar
[2] Berman, L. W., A characterization of astral (n 4) configurations. Discrete Comput. Geom. 26(2001), no. 4, 603–612.Google Scholar
[3] Boben, M. and Pisanski, T., Polycyclic configurations. European J. Combin. 24(2003), No. 4, 431–457.Google Scholar
[4] Grünbaum, B., Astral(nk configurations. Geombinatorics 3(1993), no. 3, 32–37.Google Scholar
[5] Grünbaum, B., Astra (n4) configurations. Geombinatorics 9(2000), no. 2, 127–134.Google Scholar
[6] Grünbaum, B., Configurations of points and lines. In: The Coxeter Legacy: Reflections and Projections. American Mathematical Society, Providence, RI, 2006, pp. 179–225.Google Scholar
[7] Grünbaum, B., Configurations of points and lines. To be published in the Graduate Studies inMathematics Series, American Mathematical Society, Providence, RI.Google Scholar
[8] Grünbaum, B. and Rigby, J. F., The real configuration (214). J. London Math. Soc 41(1990), no. 5, 336–346.Google Scholar