Technology in the Geometry Classroom Course Materials

The following table of contents links directly to all course materials. The materials are divided into four self-contained parts: Internet Skills, Classical Geometry, Dynamical Systems, and Symmetries and Patterns. Within these parts, the materials build on each other. For example, Introductory Questions for Geometer's Sketchpad assumes less knowledge than Monge's Theorem, which in turn assumes less sophistication than Peaucellier's Linkage.

Table of Contents

Internet Skills

1. Introduction to the World-Wide Web
   An introduction to the the World-Wide Web designed specifically for high school mathematics teachers. It contains instructions for using Netscape on the Macintosh, gives lists of interesting Web locations for secondary math teachers, and explains how to design Web pages for use in the high school mathematics classroom.

   It is important to know about Copyright, and to be aware of the fact that anything you find on the World-Wide Web probably is copyrighted. In particular, you should know that when you publish a copied picture, for example, on the Web, even if your intent is to use it for only one class, it is publicly available, which means that you need permission to use copyrighted work. You can find more information in Notes on Copyright & Related Issues, or read Education and "Fair Use" and Copyright and Electronic Publishing as a quick, but incomplete, summary.

2. Technical Information
   A compilation of pages giving the technical details of internet communication on the Macintosh. Topics include using email and how to prepare documents for the Web on a Unix Web server.

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   Classical Geometry

3. Introductory Questions for Geometer's Sketchpad
   A set of geometry problems using Sketchpad. Although not difficult, the problems are not just a set of instructions leading you to the answer.

4. Monge's Theorem
   This lab uses Sketchpad to explore the geometry of circles, culminating in the discovery of a famous result of the nineteenth century called Monge's Theorem. It then proceeds to outline a proof of the theorem using dilations.

5. Peaucellier's Linkage
   Peaucellier's Linkage is a simple toy that could be constructed using straight rods attached together. The lab gives instructions for constructing and studying the linkage in Sketchpad. It then uses Sketchpad to explore the geometric properties of inversion, allowing the reader to discover how the linkage works.

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   Dynamical Systems

6. One-Dimensional Dynamical Systems
   The derivation and study of the Logistic growth model gives a new interpretation to the investigation of functions defined on the real line. The concept of iteration is visualized using three Java applets that let you explore the model at home. This Lab also uses the software package Mathematica, or Chaos and Dynamics (for Macintosh computers).

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   Symmetry and Patterns

7. Introduction to Symmetries
   This section introduces the concept of symmetry, focusing on rotation, reflection, and translation.

8. Wallpaper Patterns
   In this chapter, we use a computer program called Kali to generate wallpaper patterns and explore their symmetries.

9. Orbifolds
   We define the word and compute the orbifolds of wallpaper patterns and finite objects in 3-space. After compiling a list of all the features that can appear in an orbifold, we providing all the tools needed to discover all the symmetry groups of the sphere and of the plane.

10. Unfolding an Orbifold
    We study how a pattern can be reconstructed from an orbifold, using both hands-on exploration and the computer program TesselMania!. These activities are a good introduction to the movie Shape of Space.

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    Appendices

11. Materials used in class.

12. Videotapes shown in the course
    • Geometry Rules
    • Mad About Mirrors
    • Not Knot
    • Outside In
    • The Platonic Solids
    • The Shape of Space
    • The Stella Octangula

13. Software

14. Bibliography
    • Richard Courant and Herbert Robbins, What is Mathematics, Oxford University Press, 1941.
    • Grunbaum and Shephard, Tilings and Patterns, W. H. Freeman and Company, 1987.
    • Jim King, Getting Acquainted with The Geometer's Sketchpad.
    • Pat Murphy and William Neill, By Nature's Design, Chronicle Books, 1993.
    • Doris Schattschneider, "The Plane Symmetry Groups", American Mathematical Monthly, June-July 1978.
    • Doris Schattschneider, M. C. Escher: Visions of Symmetry, W. H. Freeman and Company, 1990.
    • Dorothy K. Washburn and Donald W. Crowe, Symmetries of Culture, University of Washington Press, 1988.
    • David Wells, Penguin Dictionary of Curious and Interesting Geometry.

15. Final Projects
    • Description
    • Previous Student Projects

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Created: Jun 06 1996 --- Last modified: Mon Apr 13 16:07:45 1998
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