An Introductory Study of Hyperbolic Geometry
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Authors
Foreman, Jack
Issue Date
1965
Type
Thesis
Language
en_US
Keywords
Alternative Title
Abstract
The object of this paper is to develop Hyperbolic
geometry using, as tools, only the postulates
and propositions of Euclid (excluding the ones dealing
with parallel lines) and the tools of logic. To the
best of my knowledge and throughout my research I
have found no one work which contains a total picture
of Hyperbolic geometry. There are bits and pieces
scattered through a multitude of manuscripts. In the
University of Michigan's Math Library there is a set of
the complete works of Lobachevsky, which unfortunately
has not been translated from the original Russian. In
recent years there has been an increased interest in
Hyperbolic geometry because it is felt that 1t is a better description of physical space than is Euclidean
geometry. If it can be shown, logically, rather than by measurement, wh1ch even at best contain an error; that
the theorems of Hyperbolic geometry follow from our
set of axioms and postulates, then the error measurement and the error due to something appearing to
be "right" is avoided.
Description
iii, 79 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.