C Projective Geometry

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C-Projective Geometry

David M Calderbank,Michael G. Eastwood,Vladimir S. Matveev,Katharina Neusser
C Projective Geometry Book PDF

Author : David M Calderbank,Michael G. Eastwood,Vladimir S. Matveev,Katharina Neusser
Publisher : American Mathematical Society
Page : 137 pages
File Size : 46,6 Mb
Release : 2021-02-10
Category : Mathematics
ISBN : 9781470443009

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C-Projective Geometry by David M Calderbank,Michael G. Eastwood,Vladimir S. Matveev,Katharina Neusser Pdf

The authors develop in detail the theory of (almost) c-projective geometry, a natural analogue of projective differential geometry adapted to (almost) complex manifolds. The authors realise it as a type of parabolic geometry and describe the associated Cartan or tractor connection. A Kähler manifold gives rise to a c-projective structure and this is one of the primary motivations for its study. The existence of two or more Kähler metrics underlying a given c-projective structure has many ramifications, which the authors explore in depth. As a consequence of this analysis, they prove the Yano–Obata Conjecture for complete Kähler manifolds: if such a manifold admits a one parameter group of c-projective transformations that are not affine, then it is complex projective space, equipped with a multiple of the Fubini-Study metric.

Complex Projective Geometry

G. Ellingsrud
Complex Projective Geometry Book PDF

Author : G. Ellingsrud
Publisher : Cambridge University Press
Page : 354 pages
File Size : 49,8 Mb
Release : 1992-07-30
Category : Mathematics
ISBN : 9780521433525

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Complex Projective Geometry by G. Ellingsrud Pdf

A volume of papers describing new methods in algebraic geometry.

Projective Geometry

Olive Whicher
Projective Geometry Book PDF

Author : Olive Whicher
Publisher : Rudolf Steiner Press
Page : 294 pages
File Size : 46,7 Mb
Release : 2013
Category : Mathematics
ISBN : 9781855843790

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Projective Geometry by Olive Whicher Pdf

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.

Projective Geometry

Albrecht Beutelspacher,Ute Rosenbaum
Projective Geometry Book PDF

Author : Albrecht Beutelspacher,Ute Rosenbaum
Publisher : Cambridge University Press
Page : 272 pages
File Size : 44,8 Mb
Release : 1998-01-29
Category : Mathematics
ISBN : 0521483646

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Projective Geometry by Albrecht Beutelspacher,Ute Rosenbaum Pdf

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 in Projective Geometry

A. Seidenberg
Lectures in Projective Geometry Book PDF

Author : A. Seidenberg
Publisher : Courier Corporation
Page : 244 pages
File Size : 52,5 Mb
Release : 2012-06-14
Category : Mathematics
ISBN : 9780486154732

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Lectures in Projective Geometry by A. Seidenberg Pdf

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.

Introduction to Projective Geometry

C. R. Wylie
Introduction to Projective Geometry Book PDF

Author : C. R. Wylie
Publisher : Courier Corporation
Page : 578 pages
File Size : 52,9 Mb
Release : 2011-09-12
Category : Mathematics
ISBN : 9780486141701

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Introduction to Projective Geometry by C. R. Wylie Pdf

This lucid introductory text offers both an analytic and an axiomatic approach to plane projective geometry. The analytic treatment builds and expands upon students' familiarity with elementary plane analytic geometry and provides a well-motivated approach to projective geometry. Subsequent chapters explore Euclidean and non-Euclidean geometry as specializations of the projective plane, revealing the existence of an infinite number of geometries, each Euclidean in nature but characterized by a different set of distance- and angle-measurement formulas. Outstanding pedagogical features include worked-through examples, introductions and summaries for each topic, and numerous theorems, proofs, and exercises that reinforce each chapter's precepts. Two helpful indexes conclude the text, along with answers to all odd-numbered exercises. In addition to its value to undergraduate students of mathematics, computer science, and secondary mathematics education, this volume provides an excellent reference for computer science professionals.

The Real Projective Plane

H.S.M. Coxeter
The Real Projective Plane Book PDF

Author : H.S.M. Coxeter
Publisher : Springer Science & Business Media
Page : 236 pages
File Size : 50,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461227342

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The Real Projective Plane by H.S.M. Coxeter Pdf

Along with many small improvements, this revised edition contains van Yzeren's new proof of Pascal's theorem (§1.7) and, in Chapter 2, an improved treatment of order and sense. The Sylvester-Gallai theorem, instead of being introduced as a curiosity, is now used as an essential step in the theory of harmonic separation (§3.34). This makes the logi cal development self-contained: the footnotes involving the References (pp. 214-216) are for comparison with earlier treatments, and to give credit where it is due, not to fill gaps in the argument. H.S.M.C. November 1992 v Preface to the Second Edition Why should one study the real plane? To this question, put by those who advocate the complex plane, or geometry over a general field, I would reply that the real plane is an easy first step. Most of the prop erties are closely analogous, and the real field has the advantage of intuitive accessibility. Moreover, real geometry is exactly what is needed for the projective approach to non· Euclidean geometry. Instead of introducing the affine and Euclidean metrics as in Chapters 8 and 9, we could just as well take the locus of 'points at infinity' to be a conic, or replace the absolute involution by an absolute polarity.

Modern Projective Geometry

Claude-Alain Faure,Alfred Frölicher
Modern Projective Geometry Book PDF

Author : Claude-Alain Faure,Alfred Frölicher
Publisher : Springer Science & Business Media
Page : 370 pages
File Size : 52,6 Mb
Release : 2013-04-18
Category : Mathematics
ISBN : 9789401595902

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Modern Projective Geometry by Claude-Alain Faure,Alfred Frölicher Pdf

This monograph develops projective geometries and provides a systematic treatment of morphisms. It introduces a new fundamental theorem and its applications describing morphisms of projective geometries in homogeneous coordinates by semilinear maps. Other topics treated include three equivalent definitions of projective geometries and their correspondence with certain lattices; quotients of projective geometries and isomorphism theorems; and recent results in dimension theory.

Oriented Projective Geometry

Jorge Stolfi
Oriented Projective Geometry Book PDF

Author : Jorge Stolfi
Publisher : Academic Press
Page : 246 pages
File Size : 47,5 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483265193

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Oriented Projective Geometry by Jorge Stolfi Pdf

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.

Multiple View Geometry in Computer Vision

Richard Hartley,Andrew Zisserman
Multiple View Geometry in Computer Vision Book PDF

Author : Richard Hartley,Andrew Zisserman
Publisher : Cambridge University Press
Page : 676 pages
File Size : 41,5 Mb
Release : 2004-03-25
Category : Computers
ISBN : 9781139449144

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Multiple View Geometry in Computer Vision by Richard Hartley,Andrew Zisserman Pdf

A basic problem in computer vision is to understand the structure of a real world scene given several images of it. Techniques for solving this problem are taken from projective geometry and photogrammetry. Here, the authors cover the geometric principles and their algebraic representation in terms of camera projection matrices, the fundamental matrix and the trifocal tensor. The theory and methods of computation of these entities are discussed with real examples, as is their use in the reconstruction of scenes from multiple images. The new edition features an extended introduction covering the key ideas in the book (which itself has been updated with additional examples and appendices) and significant new results which have appeared since the first edition. Comprehensive background material is provided, so readers familiar with linear algebra and basic numerical methods can understand the projective geometry and estimation algorithms presented, and implement the algorithms directly from the book.

Analytic Projective Geometry

Eduardo Casas-Alvero
Analytic Projective Geometry Book PDF

Author : Eduardo Casas-Alvero
Publisher : Susaeta
Page : 640 pages
File Size : 50,5 Mb
Release : 2014
Category : Geometry, Analytic
ISBN : 3037191384

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Analytic Projective Geometry by Eduardo Casas-Alvero Pdf

Projective geometry is concerned with the properties of figures that are invariant by projecting and taking sections. It is considered one of the most beautiful parts of geometry and plays a central role because its specializations cover the whole of the affine, Euclidean and non-Euclidean geometries. The natural extension of projective geometry is projective algebraic geometry, a rich and active field of research. The results and techniques of projective geometry are intensively used in computer vision. This book contains a comprehensive presentation of projective geometry, over the real and complex number fields, and its applications to affine and Euclidean geometries. It covers central topics such as linear varieties, cross ratio, duality, projective transformations, quadrics and their classifications--projective, affine and metric--as well as the more advanced and less usual spaces of quadrics, rational normal curves, line complexes and the classifications of collineations, pencils of quadrics and correlations. Two appendices are devoted to the projective foundations of perspective and to the projective models of plane non-Euclidean geometries. The book uses modern language, is based on linear algebra, and provides complete proofs. Exercises are proposed at the end of each chapter; many of them are beautiful classical results. The material in this book is suitable for courses on projective geometry for undergraduate students, with a working knowledge of a standard first course on linear algebra. The text is a valuable guide to graduate students and researchers working in areas using or related to projective geometry, such as algebraic geometry and computer vision, and to anyone looking for an advanced view of geometry as a whole.

Affine and Projective Geometry

M. K. Bennett
Affine and Projective Geometry Book PDF

Author : M. K. Bennett
Publisher : John Wiley & Sons
Page : 251 pages
File Size : 50,9 Mb
Release : 2011-02-14
Category : Mathematics
ISBN : 9781118030820

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Affine and Projective Geometry by M. K. Bennett Pdf

An important new perspective on AFFINE AND PROJECTIVEGEOMETRY This innovative book treats math majors and math education studentsto a fresh look at affine and projective geometry from algebraic,synthetic, and lattice theoretic points of view. Affine and Projective Geometry comes complete with ninetyillustrations, and numerous examples and exercises, coveringmaterial for two semesters of upper-level undergraduatemathematics. The first part of the book deals with the correlationbetween synthetic geometry and linear algebra. In the second part,geometry is used to introduce lattice theory, and the bookculminates with the fundamental theorem of projectivegeometry. While emphasizing affine geometry and its basis in Euclideanconcepts, the book: * Builds an appreciation of the geometric nature of linear algebra * Expands students' understanding of abstract algebra with itsnontraditional, geometry-driven approach * Demonstrates how one branch of mathematics can be used to provetheorems in another * Provides opportunities for further investigation of mathematicsby various means, including historical references at the ends ofchapters Throughout, the text explores geometry's correlation to algebra inways that are meant to foster inquiry and develop mathematicalinsights whether or not one has a background in algebra. Theinsight offered is particularly important for prospective secondaryteachers who must major in the subject they teach to fulfill thelicensing requirements of many states. Affine and ProjectiveGeometry's broad scope and its communicative tone make it an idealchoice for all students and professionals who would like to furthertheir understanding of things mathematical.

Projective Geometry and Projective Metrics

Herbert Busemann,Paul J. Kelly
Projective Geometry and Projective Metrics Book PDF

Author : Herbert Busemann,Paul J. Kelly
Publisher : Courier Corporation
Page : 350 pages
File Size : 47,5 Mb
Release : 2012-11-14
Category : Mathematics
ISBN : 9780486154695

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Projective Geometry and Projective Metrics by Herbert Busemann,Paul J. Kelly Pdf

This text examines the 3 classical geometries and their relationship to general geometric structures, with particular focus on affine geometry, projective metrics, non-Euclidean geometry, and spatial geometry. 1953 edition.

Projective Geometry and Projective Metrics

Anonim
Projective Geometry and Projective Metrics Book PDF

Author : Anonim
Publisher : Academic Press
Page : 341 pages
File Size : 47,5 Mb
Release : 2011-08-29
Category : Mathematics
ISBN : 9780080873114

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Projective Geometry and Projective Metrics by Anonim Pdf

Projective Geometry and Projective Metrics

Projective Geometry

H.S.M. Coxeter
Projective Geometry Book PDF

Author : H.S.M. Coxeter
Publisher : Springer Science & Business Media
Page : 180 pages
File Size : 40,6 Mb
Release : 2003-10-09
Category : Mathematics
ISBN : 0387406239

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Projective Geometry by H.S.M. Coxeter Pdf

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.