# Join Geometries

## A Theory of Convex Sets and Linear Geometry

Authors: Prenowitz, W., Jantosciak, J.

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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 Join and Extension Operations in Euclidean Geometry

Pages 1-45

Prenowitz, Walter (et al.)

• The Abstract Theory of Join Operations

Pages 46-123

Prenowitz, Walter (et al.)

• The Generation of Convex Sets—Convex Hulls

Pages 124-155

Prenowitz, Walter (et al.)

• The Operation of Extension

Pages 156-207

Prenowitz, Walter (et al.)

• Join Geometries

Pages 208-244

Prenowitz, Walter (et al.)

eBook $64.99 price for USA in USD • ISBN 978-1-4613-9438-9 • Digitally watermarked, DRM-free • Included format: PDF • ebooks can be used on all reading devices • Immediate eBook download after purchase Softcover$84.99
price for USA in USD
• ISBN 978-1-4613-9440-2
• Free shipping for individuals worldwide
• Institutional customers should get in touch with their account manager
• Covid-19 shipping restrictions
• Usually ready to be dispatched within 3 to 5 business days, if in stock

## Bibliographic Information

Bibliographic Information
Book Title
Join Geometries
Book Subtitle
A Theory of Convex Sets and Linear Geometry
Authors
Series Title
1979
Publisher
Springer-Verlag New York
Springer-Verlag New York Inc.
eBook ISBN
978-1-4613-9438-9
DOI
10.1007/978-1-4613-9438-9
Softcover ISBN
978-1-4613-9440-2
Series ISSN
0172-6056
Edition Number
1
Number of Pages
534
Topics