Geometry on the Surface of the Sphere
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Authors
Wofsy, Eva
Issue Date
1984
Type
Thesis
Language
en_US
Keywords
Alternative Title
Abstract
This paper was originally intended to serve as one
section of a larger project designed to assist Dr. Juliet
Vogel in her study of mathematically gifted children. Under
the notion that mathematically gifted students may approach
geometry problems from a non-Euclidean standpoint, I began
to study several non-Euclidean geometries and the existing
research on the approaches most students take in solving
geometry problems.
I started my study of non-Euclidean geometries with
Euclid's Fifth Postulate (about parallelism), which led to a
study of the hyperbolic, elliptic, and double-elliptic axioms
of parallelism. The hyperbolic axiom led me to study asymptotic
triangles, Saccheri Quadrilaterals, and the Poincare plane,
while the double-elliptic axiom led me to study the information
contained in this paper.
Having found no evidence of the validity of my original
hypothesis, my attention on the existing research on students'
approaches to geometry problems shifted to a model of the
development of geometric thought. Since my work on non-Euclidean
geometries didn't fit into the new framework of my study, I
have treated it in this paper (separately) and have narrowed
it to include only double-elliptic (spherical) geometry.
Description
iii, 12 p.
Citation
Publisher
Kalamazoo College
License
U.S. copyright laws protect this material. Commercial use or distribution of this material is not permitted without prior written permission of the copyright holder.