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.
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.
Introduction To Projective Geometry
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Author : C. R. Wylie
language : en
Publisher: Courier Corporation
Release Date : 2008-12-09
Introduction To Projective Geometry written by C. R. Wylie and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-12-09 with Mathematics categories.
This lucid introductory text offers both analytic and axiomatic approaches to plane projective geometry. Strong reinforcement for its teachings include detailed examples and numerous theorems, proofs, and exercises, plus answers to all odd-numbered problems. In addition to its value to students, this volume provides an excellent reference for professionals. 1970 edition.
Projective Geometry
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Author : Albrecht Beutelspacher
language : en
Publisher: Cambridge University Press
Release Date : 1998-01-29
Projective Geometry written by Albrecht Beutelspacher and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-01-29 with Mathematics categories.
Projective geometry is not only a jewel of mathematics, but has also many applications in modern information and communication science. This book presents the foundations of classical projective and affine geometry as well as its important applications in coding theory and cryptography. It also could serve as a first acquaintance with diagram geometry. Written in clear and contemporary language with an entertaining style and around 200 exercises, examples and hints, this book is ideally suited to be used as a textbook for study in the classroom or on its own.
Lectures On Curves Surfaces And Projective Varieties
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Author : Mauro Beltrametti
language : en
Publisher: European Mathematical Society
Release Date : 2009
Lectures On Curves Surfaces And Projective Varieties written by Mauro Beltrametti and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.
This book offers a wide-ranging introduction to algebraic geometry along classical lines. It consists of lectures on topics in classical algebraic geometry, including the basic properties of projective algebraic varieties, linear systems of hypersurfaces, algebraic curves (with special emphasis on rational curves), linear series on algebraic curves, Cremona transformations, rational surfaces, and notable examples of special varieties like the Segre, Grassmann, and Veronese varieties. An integral part and special feature of the presentation is the inclusion of many exercises, not easy to find in the literature and almost all with complete solutions. The text is aimed at students in the last two years of an undergraduate program in mathematics. It contains some rather advanced topics suitable for specialized courses at the advanced undergraduate or beginning graduate level, as well as interesting topics for a senior thesis. The prerequisites have been deliberately limited to basic elements of projective geometry and abstract algebra. Thus, for example, some knowledge of the geometry of subspaces and properties of fields is assumed. The book will be welcomed by teachers and students of algebraic geometry who are seeking a clear and panoramic path leading from the basic facts about linear subspaces, conics and quadrics to a systematic discussion of classical algebraic varieties and the tools needed to study them. The text provides a solid foundation for approaching more advanced and abstract literature.
Lectures In Projective Geometry
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Author : A. Seidenberg
language : en
Publisher: Courier Corporation
Release Date : 2012-06-14
Lectures In Projective Geometry written by A. Seidenberg and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-06-14 with Mathematics categories.
An ideal text for undergraduate courses, this volume takes an axiomatic approach that covers relations between the basic theorems, conics, coordinate systems and linear transformations, quadric surfaces, and the Jordan canonical form. 1962 edition.
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.
Oriented Projective Geometry
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Author : Jorge Stolfi
language : en
Publisher: Academic Press
Release Date : 2014-05-10
Oriented Projective Geometry written by Jorge Stolfi and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.
Oriented Projective Geometry: A Framework for Geometric Computations proposes that oriented projective geometry is a better framework for geometric computations than classical projective geometry. The aim of the book is to stress the value of oriented projective geometry for practical computing and develop it as a rich, consistent, and effective tool for computer programmers. The monograph is comprised of 20 chapters. Chapter 1 gives a quick overview of classical and oriented projective geometry on the plane, and discusses their advantages and disadvantages as computational models. Chapters 2 through 7 define the canonical oriented projective spaces of arbitrary dimension, the operations of join and meet, and the concept of relative orientation. Chapter 8 defines projective maps, the space transformations that preserve incidence and orientation; these maps are used in chapter 9 to define abstract oriented projective spaces. Chapter 10 introduces the notion of projective duality. Chapters 11, 12, and 13 deal with projective functions, projective frames, relative coordinates, and cross-ratio. Chapter 14 tells about convexity in oriented projective spaces. Chapters 15, 16, and 17 show how the affine, Euclidean, and linear vector spaces can be emulated with the oriented projective space. Finally, chapters 18 through 20 discuss the computer representation and manipulation of lines, planes, and other subspaces. Computer scientists and programmers will find this text invaluable.
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.
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.