Mathematik H.S.M. Coxeter Projective Geometry

ISBN 13: 9780387406237

Projective Geometry

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9780387406237: Projective Geometry

In Euclidean geometry, constructions are made with ruler and compass. Projective geometry is simpler: its constructions require only a ruler. In projective geometry one never measures anything, instead, one relates one set of points to another by a projectivity. The first two chapters of this book introduce the important concepts of the subject and provide the logical foundations. The third and fourth chapters introduce the famous theorems of Desargues and Pappus. Chapters 5 and 6 make use of projectivities on a line and plane, respectively. The next three chapters develop a self-contained account of von Staudt's approach to the theory of conics. The modern approach used in that development is exploited in Chapter 10, which deals with the simplest finite geometry that is rich enough to illustrate all the theorems nontrivially. The concluding chapters show the connections among projective, Euclidean, and analytic geometry.

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From the Back Cover:

In Euclidean geometry, constructions are made with a ruler and compass. Projective geometry is simpler: its constructions require only a ruler. In projective geometry one never measures anything, instead, one relates one set of points to another by a projectivity.

This classic book introduces the important concepts of the subject and provides the logical foundations, including the famous theorems of Desargues and Pappus and a self-contained account of von Staudt's approach to the theory of conics. The modern approach used in this account is then utilized to deal with the simplest finite geometry that is rich enough to illustrate all the theorems nontrivially. The book concludes by demonstrating the connections among projective, Euclidean, and analytic geometry.

From the reviews of Projective Geometry:

...The book is written with all the grace and lucidity that characterize the author's other writings. ... 

-T. G. Room, Mathematical Reviews

This is an elementary introduction to projective geometry based on the intuitive notions of perspectivity and projectivity and, formally, on axioms essentially the same as the classical ones of Vebber and Young...This book is an excellent introduction.

- T. G. Ostrom, Zentralblatt

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Coxeter, Harold S. M.
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Descrizione libro Condizione libro: New. Publisher/Verlag: Springer, Berlin | 1 Introduction.- 1.1 What is projective geometry?.- 1.2 Historical remarks.- 1.3 Definitions.- 1.4 The simplest geometric objects.- 1.5 Projectivities.- 1.6 Perspectivities.- 2 Triangles and Quadrangles.- 2.1 Axioms.- 2.2 Simple consequences of the axioms.- 2.3 Perspective triangles.- 2.4 Quadrangular sets.- 2.5 Harmonic sets.- 3 The Principle of Duality.- 3.1 The axiomatic basis of the principle of duality.- 3.2 The Desargues configuration.- 3.3 The invariance of the harmonic relation.- 3.4 Trilinear polarity.- 3.5 Harmonic nets.- 4 The Fundamental Theorem and Pappus's Theorem.- 4.1 How three pairs determine a projectivity.- 4.2 Some special projectivities.- 4.3 The axis of a projectivity.- 4.4 Pappus and Desargues.- 5 One-dimensional Projectivities.- 5.1 Superposed ranges.- 5.2 Parabolic projectivities.- 5.3 Involutions.- 5.4 Hyperbolic involutions.- 6 Two-dimensional Projectivities.- 6.1 Projective collineations.- 6.2 Perspective collineations.- 6.3 Involutory collineations.- 6.4 Projective correlations.- 7 Polarities.- 7.1 Conjugate points and conjugate lines.- 7.2 The use of a self-polar triangle.- 7.3 Polar triangles.- 7.4 A construction for the polar of a point.- 7.5 The use of a self-polar pentagon.- 7.6 A self-conjugate quadrilateral.- 7.7 The product of two polarities.- 7.8 The self-polarity of the Desargues configuration.- 8 The Conic.- 8.1 How a hyperbolic polarity determines a conic.- 8.2 The polarity induced by a conic.- 8.3 Projectively related pencils.- 8.4 Conics touching two lines at given points.- 8.5 Steiner's definition for a conic.- 9 The Conic, Continued.- 9.1 The conic touching five given lines.- 9.2 The conic through five given points.- 9.3 Conics through four given points.- 9.4 Two self-polar triangles.- 9.5 Degenerate conies.- 10 A Finite Projective Plane.- 10.1 The idea of a finite geometry.- 10.2 A combinatorial scheme for PG(2, 5).- 10.3 Verifying the axioms.- 10.4 Involutions.- 10.5 Collineations and correlations.- 10.6 Conies.- 11 Parallelism.- 11.1 Is the circle a conic?.- 11.2 Affine space.- 11.3 How two coplanar lines determine a flat pencil and a bundle.- 11.4 How two planes determine an axial pencil.- 11.5 The language of pencils and bundles.- 11.6 The plane at infinity.- 11.7 Euclidean space.- 12 Coordinates.- 12.1 The idea of analytic geometry.- 12.2 Definitions.- 12.3 Verifying the axioms for the projective plane.- 12.4 Projective collineations.- 12.5 Polarities.- 12.6 Conics.- 12.7 The analytic geometry of PG(2, 5).- 12.8 Cartesian coordinates.- 12.9 Planes of characteristic two.- Answers to Exercises.- References. | Format: Paperback | Language/Sprache: english | 305 gr | 234x158x11 mm | 162 pp. Codice libro della libreria K9780387406237

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Descrizione libro Springer New York, New York, NY. paperback. Condizione libro: New. Codice libro della libreria 9780387406237

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Descrizione libro Springer-Verlag New York Inc., United States, 2003. Paperback. Condizione libro: New. 2nd ed. 1974. 2nd printing 2003. Language: English . Brand New Book. In Euclidean geometry, constructions are made with ruler and compass. Projective geometry is simpler: its constructions require only a ruler. In projective geometry one never measures anything, instead, one relates one set of points to another by a projectivity. The first two chapters of this book introduce the important concepts of the subject and provide the logical foundations. The third and fourth chapters introduce the famous theorems of Desargues and Pappus. Chapters 5 and 6 make use of projectivities on a line and plane, respectively. The next three chapters develop a self-contained account of von Staudt s approach to the theory of conics. The modern approach used in that development is exploited in Chapter 10, which deals with the simplest finite geometry that is rich enough to illustrate all the theorems nontrivially. The concluding chapters show the connections among projective, Euclidean, and analytic geometry. Codice libro della libreria LIB9780387406237

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ISBN 10: 0387406239 ISBN 13: 9780387406237
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Descrizione libro Springer-Verlag New York Inc., United States, 2003. Paperback. Condizione libro: New. 2nd ed. 1974. 2nd printing 2003. Language: English . Brand New Book. In Euclidean geometry, constructions are made with ruler and compass. Projective geometry is simpler: its constructions require only a ruler. In projective geometry one never measures anything, instead, one relates one set of points to another by a projectivity. The first two chapters of this book introduce the important concepts of the subject and provide the logical foundations. The third and fourth chapters introduce the famous theorems of Desargues and Pappus. Chapters 5 and 6 make use of projectivities on a line and plane, respectively. The next three chapters develop a self-contained account of von Staudt s approach to the theory of conics. The modern approach used in that development is exploited in Chapter 10, which deals with the simplest finite geometry that is rich enough to illustrate all the theorems nontrivially. The concluding chapters show the connections among projective, Euclidean, and analytic geometry. Codice libro della libreria LIB9780387406237

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Descrizione libro Springer-Verlag New York Inc., 2003. PAP. Condizione libro: New. New Book. Shipped from US within 10 to 14 business days. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Codice libro della libreria IQ-9780387406237

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Descrizione libro Springer, 2003. Paperback. Condizione libro: New. book. Codice libro della libreria M0387406239

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Descrizione libro Springer, 2016. Paperback. Condizione libro: New. PRINT ON DEMAND Book; New; Publication Year 2016; Not Signed; Fast Shipping from the UK. No. book. Codice libro della libreria ria9780387406237_lsuk

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Descrizione libro Springer-Verlag New York Inc., 2003. PAP. Condizione libro: New. New Book. Delivered from our UK warehouse in 3 to 5 business days. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Codice libro della libreria LQ-9780387406237

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Descrizione libro Springer 10/9/2003, 2003. Paperback or Softback. Condizione libro: New. Projective Geometry. Book. Codice libro della libreria BBS-9780387406237

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Descrizione libro Springer. Condizione libro: Brand New. FREE domestic ground shipping. Fast priority express available. Tracking service included. Ships from USA (United States of America). Codice libro della libreria 0387406239

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