## Integrating Lab Activities into Geometry

at Gustavus Adolphus College

### Michael Hvidsten

Department of Mathematics and Computer Science

Gustavus Adolphus College

St. Peter, MN 56082
hvidsten@gac.edu

*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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