The Kali pattern generator is a part of the Geometry Center at the Science U web site. (See separate review of Geometry Center.) It can also be found at http://www.geom.umn.edu/java . It provides an interactive exploration of the seventeen wallpaper tiling patterns as well as seven frieze groups and twelve rosette groups.
This is mainly visual material (although related explanations are available on a separate page). The material is real-time interactive using the mouse to change the diagram.
This site could be used just for fun, or as a supplement to a linear algebra or geometry course.
The only requirement is 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:
The visual explorations on this site are primarily suited for students with limited mathematical background. The related explanations are suitable for college level math students
Prerequisite Knowledge or Skills:
The visual material itself requires no math background to enjoy. Some of the background explanations of particular sub-topics not only use algebra but make mention of groups and linear algebra.
Evaluation and Observation
This interactive module allows exploration of the seventeen wallpaper patterns. The pattern and the color can be selected. A selection of line segments can be drawn and the program replicates the chosen pattern. Frieze group and Rosette patterns are also available. Related explanations are contained on a separate page at http://www.ScienceU.com/geometry/articles/tiling/wallpaper.html
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 those who want to pursue explanations, there are related text explanations elsewhere on the site. While this page is fairly simple in concept it is likely to attract students and encourage them to explore further on the rich selection of related pages on the Geometry Center.
Ease of Use for Both Students and Faculty
Once the basic steps for creating patterns is understood, it is easy to produce a wide variety of colorful and attractive patterns. The dynamic movement of the patterns in response to mouse movement is particularly effective.
The Kali tiler does not include instructions on the effects of different mouse clicks and movements which makes learning how to use the program a bit obscure. With a bit of trial and error, though, it does become apparent what is required. The instructions for use are available at the corresponding UMN page (www.geom.umn.edu/java/Kali) . The UMN page also features a wider variety of options including unix and source code and download versions.