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Topics in Non-Euclidean geometry
Carter, Martin
Carter, Martin
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t1959_Carter.pdf
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1959-08
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Thesis
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Abstract
It is difficult for a high school student to fully
appreciate the study of Euclidean geometry without some
notion of its relation to other geometries and to the
space in which we live. Too often, he regards the geometry
of Euclid with near reverence, as one of the few things
that is completely definite. For this reason, an attempt
will be made to point out the development and basic char- .
acteristics of the Non-Euclidean geometries of Lobachevsky
and Riemann, which Klein designated as Hyperbolic and
Elliptic geometry, respectively.
Due to the limitations of the author and to the fact
that this may, at some time, be presented at the high
school level, no rigorous development will be attempted.
Instead, a logical sequence of the elementary principles
underlying Non-Euclidean geometry will be presented in
the hope that a reader may gain some concept, at least,
of the Non-Euclidean geometries.
Table of Contents
Origin of the mathematical method -- Euclid's elements -- The parallel postulate -- Hyperbolic geometry -- Elliptic geometry -- Consistency and significance of non-euclidean geometry
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Thesis (M.A.)-- University of Wichita, College of Liberal Arts and Sciences, Dept. of Mathematics
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Wichita State University
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Wichita State University