The Geometry Center, formerly housed at the University of Minnesota, is one of five main areas in the Science U web site (others include a library and an observatory). It contains a variety of appealing material, both textual and visual, including interactive exhibits, online simulations, graphics software and a library of reference materials pertaining to geometric tilings and polyhedra. The three main sub topics are "Triangle Tilings and Polyhedra", "Symmetry and Tiling" and "Tetrahedral Puzzles", with "Symmetry and Tiling" receiving the most emphasis.
A mixture of lecture/presentation material along with animations and simulations. The most interesting are the interactive portions but all the illustrations are clear and effective. The section on Symmetry and Tiling could be used as a comprehensive tutorial.
Much of the material here could be used just for fun. Various subsites would be good supplements to courses in geometry, linear algebra, and group theory.
All aspects of the site are accessible with a java-enabled browser.
Identify Major Learning Goals:
This is mainly exploratory material for student motivation or classroom enrichment in the area of geometry.
Target Student Population:
This visual explorations on this site are primarily suited for students with limited mathematical background, although some explanations are suitable for college level math.
Prerequisite Knowledge or Skills:
Most of the visual material requires no math background to enjoy. Some of the explanations of particular sub-topics not only use algebra but make mention of groups and linear algebra
Evaluation and Observation
The "Triangle Tilings and Polyhedra" section contains three sub-articles on different possible patterns, the shape of the starting triangle, and the effect of 3-dimensional bending. There is an interactive module called "triangle tiler". The "Symmetry and Tilings" section contains seven sub-articles ranging from tilings in every day life and symmetry definitions through Penrose tiles. There are two interactive modules called "Kali" and "QuasiTiler" that produce tilings and Penrose tilings, respectively. (Please see separate listings and reviews for each of these pages.) The "Tetrahedral Puzzles" section contains three sub-articles on 3-dimensional dissection problems, history of dissection and current research. There is an activity module on creating your own paper models.In addition, there is a link to "Interactive" material where users may generate their own fractal images and another link to "Articles" where an extensive presentation is given on isometries. This is an excellent collection of visual geometry material that is attractive and easy to use for the beginner but it also contains explanations, references to further material, and one section commenting on current research.
Potential Effectiveness as a Teaching Tool
This site should be particularly effective as a motivational tool to encourage students to explore geometrical ideas beyond the standard curriculum. For anyone interested in mathematical tilings, this is an excellent collection of materials; the interactive graphics software adds a rich and interesting dimension to the subject matter. For those who want to pursue explanations, the text articles are generally easy to understand and contain occasional references to more advanced material.
There are some links to commercial sites such as book vendors - but they are not intrusive. The ability to obtain posters or T-shirts from the patterns created has been temporarily discontinued and may ultimately depend on overall user demand.
Ease of Use for Both Students and Faculty
The site features a nice mixture of material. The still diagrams are attractive and clear. There are real time animations and also interactive modules that redraw when parameters are changed. There is also a section of the site entitled "Studio" where users may save their interactive work for future use (but see note below). The general architecture of the site includes buttons for Interactive, Activities, Articles, Classroom, Facts and Figures, and a fairly sophisticated search engine.
The redraw feature is awkward on some pages such as QuasiTiler. The Kali wallpaper tiler does not include instructions - although they are available at the corresponding UMN page (http://www.geom.umn.edu/java/Kali/). Unfortunately, the Studio seemed unable to save users' work due to internal server errors; it would be nice for students to be able to show their creations in a post facto classroom setting.