Modern Projective Geometry
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Projective Geometry
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Author : H.S.M. Coxeter
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-10-09
Projective Geometry written by H.S.M. Coxeter 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 2003-10-09 with Mathematics categories.
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.
Projective Geometry
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Author : Olive Whicher
language : en
Publisher: Rudolf Steiner Press
Release Date : 2013
Projective Geometry written by Olive Whicher and has been published by Rudolf Steiner Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Mathematics categories.
Whicher explores the concepts of polarity and movement in modern projective geometry as a discipline of thought that transcends the limited and rigid space and forms of Euclid, and the corresponding material forces conceived in classical mechanics. Rudolf Steiner underlined the importance of projective geometry as, "a method of training the imaginative faculties of thinking, so that they become an instrument of cognition no less conscious and exact than mathematical reasoning." This seminal approach allows for precise scientific understanding of the concept of creative fields of formative (etheric) forces at work in nature--in plants, animals and in the human being. Olive Whicher's groundbreaking book presents an accessible--non-mathematician's--approach to projective geometry. Profusely illustrated, and written with fire and intuitive genius, this work will be of interest to anyone wishing to cultivate the power of inner visualization in a realm of structural beauty.
Perspectives On Projective Geometry
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Author : Jürgen Richter-Gebert
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-02-04
Perspectives On Projective Geometry written by Jürgen Richter-Gebert 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 2011-02-04 with Mathematics categories.
Projective geometry is one of the most fundamental and at the same time most beautiful branches of geometry. It can be considered the common foundation of many other geometric disciplines like Euclidean geometry, hyperbolic and elliptic geometry or even relativistic space-time geometry. This book offers a comprehensive introduction to this fascinating field and its applications. In particular, it explains how metric concepts may be best understood in projective terms. One of the major themes that appears throughout this book is the beauty of the interplay between geometry, algebra and combinatorics. This book can especially be used as a guide that explains how geometric objects and operations may be most elegantly expressed in algebraic terms, making it a valuable resource for mathematicians, as well as for computer scientists and physicists. The book is based on the author’s experience in implementing geometric software and includes hundreds of high-quality illustrations.
On The Geometry Of Some Special Projective Varieties
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Author : Francesco Russo
language : en
Publisher: Springer
Release Date : 2016-02-01
On The Geometry Of Some Special Projective Varieties written by Francesco Russo and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-02-01 with Mathematics categories.
Providing an introduction to both classical and modern techniques in projective algebraic geometry, this monograph treats the geometrical properties of varieties embedded in projective spaces, their secant and tangent lines, the behavior of tangent linear spaces, the algebro-geometric and topological obstructions to their embedding into smaller projective spaces, and the classification of extremal cases. It also provides a solution of Hartshorne’s Conjecture on Complete Intersections for the class of quadratic manifolds and new short proofs of previously known results, using the modern tools of Mori Theory and of rationally connected manifolds. The new approach to some of the problems considered can be resumed in the principle that, instead of studying a special embedded manifold uniruled by lines, one passes to analyze the original geometrical property on the manifold of lines passing through a general point and contained in the manifold. Once this embedded manifold, usually of lower codimension, is classified, one tries to reconstruct the original manifold, following a principle appearing also in other areas of geometry such as projective differential geometry or complex geometry.
Projective Geometry
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Author : Rey Casse
language : en
Publisher: Oxford University Press, USA
Release Date : 2006-08-03
Projective Geometry written by Rey Casse and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-08-03 with Mathematics categories.
This lucid, accessible text provides an introductory guide to projective geometry, an area of mathematics concerned with the properties and invariants of geometric figures under projection. Including numerous examples and exercises, this text is ideal for year 3 and 4 mathematics undergraduates.
A Modern View Of Geometry
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Author : Leonard M. Blumenthal
language : en
Publisher: Courier Dover Publications
Release Date : 2017-04-19
A Modern View Of Geometry written by Leonard M. Blumenthal and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-04-19 with Mathematics categories.
Elegant exposition of postulation geometry of planes offers rigorous, lucid treatment of coordination of affine and projective planes, set theory, propositional calculus, affine planes with Desargues and Pappus properties, more. 1961 edition.
Modern Geometry With Applications
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Author : George A. Jennings
language : en
Publisher: Springer Science & Business Media
Release Date : 1997-06-12
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 1997-06-12 with Mathematics categories.
This introduction to modern geometry differs from other books in the field due to its emphasis on applications and its discussion of special relativity as a major example of a non-Euclidean geometry. Additionally, it covers the two important areas of non-Euclidean geometry, spherical geometry and projective geometry, as well as emphasising transformations, and conics and planetary orbits. Much emphasis is placed on applications throughout the book, which motivate the topics, and many additional applications are given in the exercises. It makes an excellent introduction for those who need to know how geometry is used in addition to its formal theory.
Symmetry And Pattern In Projective Geometry
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Author : Eric Lord
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-14
Symmetry And Pattern In Projective Geometry written by Eric Lord 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 2012-12-14 with Mathematics categories.
Symmetry and Pattern in Projective Geometry is a self-contained study of projective geometry which compares and contrasts the analytic and axiomatic methods. The analytic approach is based on homogeneous coordinates, and brief introductions to Plücker coordinates and Grassmann coordinates are presented. This book looks carefully at linear, quadratic, cubic and quartic figures in two, three and higher dimensions. It deals at length with the extensions and consequences of basic theorems such as those of Pappus and Desargues. The emphasis throughout is on special configurations that have particularly interesting symmetry properties. The intricate and novel ideas of ‘Donald’ Coxeter, who is considered one of the great geometers of the twentieth century, are also discussed throughout the text. The book concludes with a useful analysis of finite geometries and a description of some of the remarkable configurations discovered by Coxeter. This book will be appreciated by mathematics students and those wishing to learn more about the subject of geometry. It makes accessible subjects and theorems which are often considered quite complicated and presents them in an easy-to-read and enjoyable manner.
Lectures On Analytic And Projective Geometry
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Author : Dirk J. Struik
language : en
Publisher: Courier Corporation
Release Date : 2011-10-24
Lectures On Analytic And Projective Geometry written by Dirk J. Struik and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-24 with Mathematics categories.
This undergraduate text develops the geometry of plane and space, leading up to conics and quadrics, within the context of metrical, affine, and projective transformations. 1953 edition.
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.