Modern Projective Geometry

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Modern Projective Geometry

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Author : Robert J. Bumcrot
language : en
Publisher:
Release Date : 1969

Modern Projective Geometry written by Robert J. Bumcrot and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1969 with Mathematics categories.

Modern Projective Geometry

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Author : Claude-Alain Faure
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-18

Modern Projective Geometry written by Claude-Alain Faure and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-18 with Mathematics categories.

Projective geometry is a very classical part of mathematics and one might think that the subject is completely explored and that there is nothing new to be added. But it seems that there exists no book on projective geometry which provides a systematic treatment of morphisms. We intend to fill this gap. It is in this sense that the present monograph can be called modern. The reason why morphisms have not been studied much earlier is probably the fact that they are in general partial maps between the point sets G and G, noted ' 9 : G -- ~ G', i.e. maps 9 : D -4 G' whose domain Dom 9 := D is a subset of G. We give two simple examples of partial maps which ought to be morphisms. The first example is purely geometric. Let E, F be complementary subspaces of a projective geometry G. If x E G \ E, then g(x) := (E V x) n F (where E V x is the subspace generated by E U {x}) is a unique point of F, i.e. one obtains a map 9 : G \ E -4 F. As special case, if E = {z} is a singleton and F a hyperplane with z tf. F, then g: G \ {z} -4 F is the projection with center z of G onto F.

Modern Projective Geometry

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Author : Claude-Alain Faure
language : en
Publisher:
Release Date : 2014-01-15

Modern Projective Geometry written by Claude-Alain Faure and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.

Desargues And The Development Of Modern Projective Geometry

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Author : Charles Lincoln Maxey
language : en
Publisher:
Release Date : 1924

Desargues And The Development Of Modern Projective Geometry written by Charles Lincoln Maxey and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1924 with categories.

Projective Geometry

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Author : Linnaeus Wayland Dowling
language : en
Publisher:
Release Date : 1917

Projective Geometry written by Linnaeus Wayland Dowling and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1917 with Geometry, Projective categories.

Projective Geometry And Modern Algebra

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Author : Lars Kadison
language : en
Publisher: Birkhäuser Boston
Release Date : 1996-01-26

Projective Geometry And Modern Algebra written by Lars Kadison and has been published by Birkhäuser Boston this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-01-26 with Mathematics categories.

The techniques and concepts of modern algebra are introduced for their natural role in the study of projectile geometry; groups appear as automorphism groups of configurations, division rings appear in the study of Desargues' theorem and the study of the independence of the seven axioms given for projectile geometry.

A Course In Modern Geometries

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Author : Judith N. Cederberg
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09

A Course In Modern Geometries written by Judith N. Cederberg and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.

A Course in Modern Geometries is designed for a junior-senior level course for mathematics majors, including those who plan to teach in secondary school. Chapter 1 presents several finite geometries in an axiomatic framework. Chapter 2 introduces Euclid's geometry and the basic ideas of non-Euclidean geometry. The synthetic approach of Chapters 1 - 2 is followed by the analytic treatment of transformations of the Euclidean plane in Chapter 3. Chapter 4 presents plane projective geometry both synthetically and analytically. The extensive use of matrix representations of groups of transformations in Chapters 3 - 4 reinforces ideas from linear algebra and serves as excellent preparation for a course in abstract algebra. Each chapter includes a list of suggested sources for applications and/or related topics.

Projective Geometry

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Author : Elisabetta Fortuna
language : en
Publisher: Springer
Release Date : 2016-12-17

Projective Geometry written by Elisabetta Fortuna and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-12-17 with Mathematics categories.

This book starts with a concise but rigorous overview of the basic notions of projective geometry, using straightforward and modern language. The goal is not only to establish the notation and terminology used, but also to offer the reader a quick survey of the subject matter. In the second part, the book presents more than 200 solved problems, for many of which several alternative solutions are provided. The level of difficulty of the exercises varies considerably: they range from computations to harder problems of a more theoretical nature, up to some actual complements of the theory. The structure of the text allows the reader to use the solutions of the exercises both to master the basic notions and techniques and to further their knowledge of the subject, thus learning some classical results not covered in the first part of the book. The book addresses the needs of undergraduate and graduate students in the theoretical and applied sciences, and will especially benefit those readers with a solid grasp of elementary Linear Algebra.

Modern Geometries

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Author : Michael Henle
language : en
Publisher: Pearson
Release Date : 2001

Modern Geometries written by Michael Henle and has been published by Pearson this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.

Engaging, accessible, and extensively illustrated, this brief, but solid introduction to modern geometry describes geometry as it is understood and used by contemporary mathematicians and theoretical scientists. Basically non-Euclidean in approach, it relates geometry to familiar ideas from analytic geometry, staying firmly in the Cartesian plane. It uses the principle geometric concept of congruence or geometric transformation--introducing and using the Erlanger Program explicitly throughout. It features significant modern applications of geometry--e.g., the geometry of relativity, symmetry, art and crystallography, finite geometry and computation. Covers a full range of topics from plane geometry, projective geometry, solid geometry, discrete geometry, and axiom systems. For anyone interested in an introduction to geometry used by contemporary mathematicians and theoretical scientists.

Modern Geometry With Applications

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Author : George A. Jennings
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Modern Geometry With Applications written by George A. Jennings and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

This book is an introduction to the theory and applications of "modern geometry" ~ roughly speaking, geometry that was developed after Euclid. It covers three major areas of non-Euclidean geometry and their applica tions: spherical geometry (used in navigation and astronomy), projective geometry (used in art), and spacetime geometry (used in the Special The ory of Relativity). In addition it treats some of the more useful topics from Euclidean geometry, focusing on the use of Euclidean motions, and includes a chapter on conics and the orbits of planets. My aim in writing this book was to balance theory with applications. It seems to me that students of geometry, especially prospective mathe matics teachers, need to be aware of how geometry is used as well as how it is derived. Every topic in the book is motivated by an application and many additional applications are given in the exercises. This emphasis on applications is responsible for a somewhat nontraditional choice of top ics: I left out hyperbolic geometry, a traditional topic with practically no applications that are intelligible to undergraduates, and replaced it with the spacetime geometry of Special Relativity, a thoroughly non-Euclidean geometry with striking implications for our own physical universe. The book contains enough material for a one semester course in geometry at the sophomore-to-senior level, as well as many exercises, mostly of a non routine nature (the instructor may want to supplement them with routine exercises of his/her own).