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Projective geometry and projective metrics

Author: Herbert Busemann; Paul J Kelly
Publisher: New York : Academic Press, 1953.
Series: Pure and applied mathematics (Academic Press), 3.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
The present book differs widely in content, methods, and point of view from traditional presentations of the subject. Herein more space is devoted to the discussion of the basic concepts of distance, motion, area and perpendicularity. In fact, the non-Euclidean geometries are reached via general metric spaces and the Hilbert problem of finding those geometries in which straight lines are the shortest connections. Of  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Busemann, Herbert, 1905-
Projective geometry and projective metrics.
New York : Academic Press, 1953
(DLC) 52013363
(OCoLC)525581
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Herbert Busemann; Paul J Kelly
ISBN: 9780080873114 0080873111
OCLC Number: 316566904
Description: 1 online resource (viii, 332 pages) : illustrations.
Contents: The projective plane --
Polarities and conic sections --
Affine geometry --
Projective metrics --
Non-Euclidean geometry --
Spatial geometry.
Series Title: Pure and applied mathematics (Academic Press), 3.
Responsibility: by Herbert Busemann and Paul J. Kelly.

Abstract:

The present book differs widely in content, methods, and point of view from traditional presentations of the subject. Herein more space is devoted to the discussion of the basic concepts of distance, motion, area and perpendicularity. In fact, the non-Euclidean geometries are reached via general metric spaces and the Hilbert problem of finding those geometries in which straight lines are the shortest connections. Of course, the general problem is only formulated here; but this leads naturally to the consideration of geometries other than the Euclidean and two non-Euclidean ones, and thus to the modern view in which the three classical geometries are very special, and closely related, cases of general geometric structures. The overall aim is to counteract the impression of geometry as an isolated and static subject, and to present its methods and essential content as part of modern mathematics.

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