Grant Number: DUE: 9550977
The goal of our project is to integrate computer visualization of geometric ideas into the geometry course of our department. To achieve this goal eight Silicon Graphics Indy workstations were purchased along with software packages including Mathematica and Geometer's Sketchpad. Two additional freely available software packages, GeomView and NonEuclid, were also used during this project. Stephen Hilding, a co-principal investigator and member of our department, taught the enhanced geometry course during the fall of 1995 and Hvidsten is currently teaching the course.
Hilding and Hvidsten developed a series of Mathematica notebooks to assist students in visualizing geometric constructions, polyhedra, and transformations. On the center panel of the poster are the five Platonic solids rendered by Mathematica as well as excerpts from a notebook on affine transformations. A major goal of the project was to give students real-time interactivity with geometric objects. To facilitate this goal Hvidsten wrote a Mathematica program to translate Mathematica's native 3-D format (3-Script) into the OpenInventor format and then display this in an OpenInventor viewer, thus giving students real-time interactivity with Mathematica objects.
On the left panel under the heading Non-Euclidean Geometry, the program NonEuclid is used to enhance student's intuitive understanding of how hyperbolic geometry differs from and is similar to Euclidean geometry. In the lab experience students are asked to explore whether certain standard theorems in Euclidean geometry still hold in non- Euclidean geometry. They gather data by creating representative examples and exploring their geometric properties.
On the right panel there are two sections. First, the program Geomview is used to expand students understanding of geometric objects by having students explore the tesseract demo and general properties of the hypercube. Ideas such as cross-sections and level sets are used along with the idea of reasoning by analogy with lower dimensional objects to gain insight into geometric objects that we cannot easily visualize. Finally in the second part of the right panel there is a discussion of how writing projects are integrated into the course and how we are integrating worldwide web activities into our course.
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