Math Awareness Week 1995
April 23-29, 1995

Mathematics and Symmetry

About Math Awareness Week:

What is Math Awareness Week?
Activities from last year's Math Awareness Week
The Theme for Math Awareness Week 1995
Math Awareness Week Home Page

Information related to Symmetry:

• Groups and Symmetry
  This article looks at group theory as the abstract study of symmetry. In order to study group structure, consider the symmetries of the group's action on a set. The article contains an example of this procedure. It is based on an interview with University of Minnesota professor Peter Webb.

• Quasicrystals
  In 1984, crystallographers found a metal alloy with no lattice structure or other short range symmetries. The X-ray diffraction patterns of such quasicrystals resemble Penrose tilings. This article discusses the relationship between X-ray diffraction patterns and crystalline structure. It also shows how Penrose tilings arise from projections of higher dimensional lattices. It is based on an interview with Smith College professor Marjorie Senechal.

• Quasitiler
  This article describes software with which to specify and create Penrose tilings. The process is based on de Bruijn's work showing that all planar Penrose tilings are projection of portions of five-dimensional lattices.

• Science Museum Math Exhibit
  There is a polyhedron corresponding to each regular tiling of the sphere. Understanding the relationship between the two makes it easier to understand the Platonic and Archimedian solids. This article describes a science museum exhibit and how it demonstrates the concepts of tilings of the sphere and corresponding polyhedra.

• Further Geometry Forum Articles
  Further mathematical articles.

The following pictures were contributed by Mike Field and Marty Golubitsky. Click on the name to see the figure.

• I Camera
  The 1995 Mathematics Awareness Week poster image I camera is a symmetric icon with 11-fold symmetry group Z_11. The image for the poster was computed using one billion iterations of the polynomial map

  

  The image was computed at 4,500 lines of resolution (that is, for a ``screen'' of 20,250,000 pixels). After coloring, a tiff file was produced of the resulting image and this was then processed by Houston PhotoLab to obtain the 4 by 5-inch transparency used to produce the poster.

• Blue Chaos
  Blue Chaos is a symmetric icon with symmetry group D_4 and was computed using the polynomial map

  

• Gothic Reflections
  The smaller image on the Mathematics Awareness Week poster is called Gothic reflections and was computed using a torus map with hexagonal symmetry according to the recipe described in the book Symmetry in Chaos by Michael Field and Martin Golubitsky, Oxford University Press, 1992. (Following the notation in Appendix D of Symmetry in Chaos, the parameters are given by m=p=0, lambda = 0.05, alpha = 0.25, beta = -0.45, gamma = 0.06.)

• Swirling Flowers
  Swirling Flowers is a chaotic quilt computed using a torus map with Z_6 symmetry (as opposed to the map used for computing Gothic Reflections, which had D_6 symmetry). Following the notation in Appendix D of Symmetry in Chaos, parameters are given by m = 2, p = 0, lambda = 0.155 + 0.2, alpha = 0.031 beta = -0.03, gamma = -0.071.

Quasitiler on WWW (An interactive Web Application)

Scheduled Talk at The Geometry Center:

Thomas Banchoff:

A motivational lecture for high school students studying math analysis/calculus.

Saturday, April 29, 9:00am-1:00pm
Geometry Center, Conference room 142
Anticipated participants 75 - 100
Participation by invitation only -- contact: olson@math.umn.edu

Proposed Agenda

9:00am - 10:00am Lecture
10:00am - 10:15am Break
10:15am - 11:15am Lecture continues
11:15am - to close Q & A (small group discussion)

Comments to: webmaster@www.geom.uiuc.edu
Created: January 20 1995 --- Last modified: Tue Apr 4 09:04:24 1995