Undergraduate Texts in Mathematics Ser.: Theory of Join Spaces : A Contemporary

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Características del artículo

Estado
En muy buen estado: Libro que se ha leído y que no tiene un aspecto nuevo, pero que está en un ...
Features
Ex-Library
ISBN
9780387903408
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Product Identifiers

Publisher
Springer
ISBN-10
0387903402
ISBN-13
9780387903408
eBay Product ID (ePID)
4861078

Product Key Features

Number of Pages
534 Pages
Publication Name
Theory of Join Spaces : a Contemporary Approach to Convex Sets and Linear Geometry
Language
English
Subject
Geometry / Analytic, Geometry / General
Publication Year
1979
Type
Textbook
Subject Area
Mathematics
Author
J. Jantosciak, W. Prenowitz
Series
Undergraduate Texts in Mathematics Ser.
Format
Hardcover

Dimensions

Item Weight
33.3 Oz

Additional Product Features

Intended Audience
Scholarly & Professional
TitleLeading
The
Number of Volumes
1 vol.
Illustrated
Yes
Synopsis
The main object of this book is to reorient and revitalize classical geometry in a way that will bring it closer to the mainstream of contemporary mathematics. The postulational basis of the subject will be radically revised in order to construct a broad-scale and conceptually unified treatment. The familiar figures of classical geometry-points, segments, lines, planes, triangles, circles, and so on-stem from problems in the physical world and seem to be conceptually unrelated. However, a natural setting for their study is provided by the concept of convex set, which is compara tively new in the history of geometrical ideas. The familiarfigures can then appear as convex sets, boundaries of convex sets, or finite unions of convex sets. Moreover, two basic types of figure in linear geometry are special cases of convex set: linear space (point, line, and plane) and halfspace (ray, halfplane, and halfspace). Therefore we choose convex set to be the central type of figure in our treatment of geometry. How can the wealth of geometric knowledge be organized around this idea? By defini tion, a set is convex if it contains the segment joining each pair of its points; that is, if it is closed under the operation of joining two points to form a segment. But this is precisely the basic operation in Euclid.", The main object of this book is to reorient and revitalize classical geometry in a way that will bring it closer to the mainstream of contemporary mathematics. The postulational basis of the subject will be radically revised in order to construct a broad-scale and conceptually unified treatment. The familiar figures of classical geometry-points, segments, lines, planes, triangles, circles, and so on-stem from problems in the physical world and seem to be conceptually unrelated. However, a natural setting for their study is provided by the concept of convex set, which is compara­ tively new in the history of geometrical ideas. The familiarfigures can then appear as convex sets, boundaries of convex sets, or finite unions of convex sets. Moreover, two basic types of figure in linear geometry are special cases of convex set: linear space (point, line, and plane) and halfspace (ray, halfplane, and halfspace). Therefore we choose convex set to be the central type of figure in our treatment of geometry. How can the wealth of geometric knowledge be organized around this idea? By defini­ tion, a set is convex if it contains the segment joining each pair of its points; that is, if it is closed under the operation of joining two points to form a segment. But this is precisely the basic operation in Euclid.
LC Classification Number
QA639.5-640.7QA640.

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