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Technology in the Geometry Classroom Course Materials
These materials were developed at the Geometry Center
and are used for teaching pre- and in-service teachers of high-school
geometry who are interested in using technology in their classrooms.
See this quarter's syllabus for more details.
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
- 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
Notes on Copyright & Related Issues, or read
Education and "Fair Use" and
Copyright and Electronic Publishing as a quick, but incomplete,
- 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.
- 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
- 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.
- 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.
- 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
Chaos and Dynamics (for Macintosh computers).
Symmetry and Patterns
- Introduction to Symmetries
This section introduces the concept of symmetry, focusing on rotation,
reflection, and translation.
- Wallpaper Patterns
In this chapter, we use a computer program called Kali to generate
wallpaper patterns and explore their symmetries.
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
- 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.
- Materials used in class.
- Videotapes shown in the course
- 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
- Final Projects
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Created: Jun 06 1996 ---
Last modified: Mon Apr 13 16:07:45 1998
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The Geometry Center
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