Overview

This work serves as an introduction to the theory of projective geometry. Techniques and concepts of modern algebra are presented for their role in the study of projective geometry. Topics covered include: affine and projective planes; homogeneous co-ordinates; and Desargues' theorem.

Full Product Details

Author:   Lars Kadison ,  Matthias T. Kromann
Publisher:   Birkhauser Boston Inc
Imprint:   Birkhauser Boston Inc
Edition:   1995 ed.
Dimensions:   Width: 15.50cm , Height: 1.40cm , Length: 23.50cm
Weight:   1.100kg
ISBN:  

9780817639006

ISBN 10:   0817639004
Pages:   208
Publication Date:   26 January 1996
Audience:   College/higher education ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

Historical foreword. Affine geometry: affine planes; transformations of the affine plane. Projective planes: completion of the affine plane; homogeneous coordinates for the real projective plane. Desargues' theorem and the principle of duality: the axiom P5 of Desargues; Moulton's example; axioms for projective space; principle of duality. A brief introduction to groups: elements of group theory; automorphisms of the projective plane of 7 points. Elementary synthetic projective geometry: Fano's axiom P6; harmonic points; perpectivities and projectivities. The fundamental theorem for projectivities on a line: the fundamental theorem: axiom P7; geometry of complex numbers; Pappu's theorem. A brief introduction to division rings: division rings; the quaternions H; a noncommutative division ring with characteristics p. Projective planes over division rings: P2(R); the automorphism group of P2 (R); the algebraic meaning of axioms P6 and P7; independence of axioms. Introduction of coordinates in a projective plane: the major and minor Desargues' axioms; division ring number lines; introducing coordinates in A. Mobius transformations and cross ratio: assessment; Mobius transformations of the extended field; cross ratio: a projective invariant. Projective collineations: projective collineations; elations and homologies; the fundamental theorem of projective collineation; Ceva's theorem. (Part contents).

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