Geometry An Introduction
ISBN-13:
9784871877183
ISBN-10:
4871877183
Edition:
Illustrated
Author:
Marvin Jay Greenberg, Günther Ewald
Publication date:
2013
Publisher:
Ishi Press
Format:
Paperback
414 pages
Category:
Geometry & Topology
,
History
,
Mathematics
FREE US shipping
Book details
ISBN-13:
9784871877183
ISBN-10:
4871877183
Edition:
Illustrated
Author:
Marvin Jay Greenberg, Günther Ewald
Publication date:
2013
Publisher:
Ishi Press
Format:
Paperback
414 pages
Category:
Geometry & Topology
,
History
,
Mathematics
Summary
Geometry An Introduction (ISBN-13: 9784871877183 and ISBN-10: 4871877183), written by authors
Marvin Jay Greenberg, Günther Ewald, was published by Ishi Press in 2013.
With an overall rating of 4.2 stars, it's a notable title among other
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Description
One of the insights that arose not long after Hilbert's Foundations of Geometry was that it is possible to build geometry without notions of order or continuity. An essential tool in this direction was the calculus of reflections, an idea that owes much to Hjelmslev. Bachmann later deepened the study of reflection geometry in a systematic way and coined the concept of a metric plane, a structure that captures the core of the orthogonality properties common to the Euclidean and the classical non-Euclidean planes. All Hilbert planes, i. e. all models of the plane axioms of Hilbert's axiom system, without the parallel axiom and the continuity axioms, turn out to be metric planes. Metric planes can be embedded in projective-metric planes, and thus can also be described analytically, i. e. in terms of coordinates. Reflection geometry emphasizes the interplay between geometry and group theory. This "Introduction" by Ewald occupies a singular place in the English language literature. Ewald's book treats a central topic of geometry, the theory of metric planes in Bachmann's sense. It makes this theory accessible to readers of English, in a systematic manner, through an axiomatic-deductive approach. Hyperbolic and elliptic geometries are also treated as substructures of a circle geometry, the Mobius geometry. This geometry is also introduced axiomatically by using an axiom system of van der Waerden.
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