Perspectives On Projective Geometry

Author : Jürgen Richter-Gebert
Publisher : Springer Science & Business Media
Page : 571 pages
File Size : 49,8 Mb
Release : 2011-02-04
Category : Mathematics
ISBN : 9783642172861

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Perspectives on Projective Geometry by Jürgen Richter-Gebert Pdf

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.

Author : Annalisa Crannell,Marc Frantz,Fumiko Futamura
Publisher : Princeton University Press
Page : 290 pages
File Size : 50,9 Mb
Release : 2019-12-10
Category : Mathematics
ISBN : 9780691196565

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Perspective and Projective Geometry by Annalisa Crannell,Marc Frantz,Fumiko Futamura Pdf

Frontmatter -- Contents -- 0. Introduction and First Action -- 1. Window Taping -- 2. Drawing ART -- 3. What's the Image of a Line? -- 4. The Geometry of R2 and R3 -- 5. Extended Euclidean Space -- 6. Of Meshes and Maps -- 7. Desargues's Theorem -- 8. Collineations -- 9. Dynamic Cubes and Viewing Distance -- 10. Drawing Boxes and Cubes in Two-Point Perspective -- 11. Perspective by the Numbers -- 12. Coordinate Geometry -- 13. The Shape of Extended Space -- Appendix G. Introduction to GEOGEBRA -- Appendix R. Reference Manual -- Appendix W. Writing Mathematical Prose -- Acknowledgments -- Bibliography -- Index

Author : Rey Casse
Publisher : OUP Oxford
Page : 212 pages
File Size : 46,7 Mb
Release : 2006-08-03
Category : Mathematics
ISBN : 9780191538360

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Projective Geometry by Rey Casse Pdf

This lucid and 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 worked examples and exercises throughout, the book covers axiomatic geometry, field planes and PG(r, F), coordinatising a projective plane, non-Desarguesian planes, conics and quadrics in PG(3, F). Assuming familiarity with linear algebra, elementary group theory, partial differentiation and finite fields, as well as some elementary coordinate geometry, this text is ideal for 3rd and 4th year mathematics undergraduates.

Author : C. R. Wylie
Publisher : Courier Corporation
Page : 578 pages
File Size : 52,8 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.

Author : Marc Frantz,Annalisa Crannell
Publisher : Princeton University Press
Page : 248 pages
File Size : 48,6 Mb
Release : 2011-07-05
Category : Mathematics
ISBN : 140083905X

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Viewpoints by Marc Frantz,Annalisa Crannell Pdf

An undergraduate textbook devoted exclusively to relationships between mathematics and art, Viewpoints is ideally suited for math-for-liberal-arts courses and mathematics courses for fine arts majors. The textbook contains a wide variety of classroom-tested activities and problems, a series of essays by contemporary artists written especially for the book, and a plethora of pedagogical and learning opportunities for instructors and students. Viewpoints focuses on two mathematical areas: perspective related to drawing man-made forms and fractal geometry related to drawing natural forms. Investigating facets of the three-dimensional world in order to understand mathematical concepts behind the art, the textbook explores art topics including comic, anamorphic, and classical art, as well as photography, while presenting such mathematical ideas as proportion, ratio, self-similarity, exponents, and logarithms. Straightforward problems and rewarding solutions empower students to make accurate, sophisticated drawings. Personal essays and short biographies by contemporary artists are interspersed between chapters and are accompanied by images of their work. These fine artists--who include mathematicians and scientists--examine how mathematics influences their art. Accessible to students of all levels, Viewpoints encourages experimentation and collaboration, and captures the essence of artistic and mathematical creation and discovery. Classroom-tested activities and problem solving Accessible problems that move beyond regular art school curriculum Multiple solutions of varying difficulty and applicability Appropriate for students of all mathematics and art levels Original and exclusive essays by contemporary artists Forthcoming: Instructor's manual (available only to teachers)

Author : R. J. Mihalek
Publisher : Academic Press
Page : 232 pages
File Size : 48,8 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483265209

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Projective Geometry and Algebraic Structures by R. J. Mihalek Pdf

Projective Geometry and Algebraic Structures focuses on the relationship of geometry and algebra, including affine and projective planes, isomorphism, and system of real numbers. The book first elaborates on euclidean, projective, and affine planes, including axioms for a projective plane, algebraic incidence bases, and self-dual axioms. The text then ponders on affine and projective planes, theorems of Desargues and Pappus, and coordination. Topics include algebraic systems and incidence bases, coordinatization theorem, finite projective planes, coordinates, deletion subgeometries, imbedding theorem, and isomorphism. The publication examines projectivities, harmonic quadruples, real projective plane, and projective spaces. Discussions focus on subspaces and dimension, intervals and complements, dual spaces, axioms for a projective space, ordered fields, completeness and the real numbers, real projective plane, and harmonic quadruples. The manuscript is a dependable reference for students and researchers interested in projective planes, system of real numbers, isomorphism, and subspaces and dimensions.

Author : Jorge Stolfi
Publisher : Academic Press
Page : 246 pages
File Size : 46,5 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.

Author : John Stillwell
Publisher : Springer Science & Business Media
Page : 240 pages
File Size : 55,9 Mb
Release : 2005-08-09
Category : Mathematics
ISBN : 9780387255309

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The Four Pillars of Geometry by John Stillwell Pdf

This book is unique in that it looks at geometry from 4 different viewpoints - Euclid-style axioms, linear algebra, projective geometry, and groups and their invariants Approach makes the subject accessible to readers of all mathematical tastes, from the visual to the algebraic Abundantly supplemented with figures and exercises

Author : Lynn E. Garner
Publisher : North-Holland
Page : 248 pages
File Size : 50,9 Mb
Release : 1981
Category : Mathematics
ISBN : UOM:39015015621587

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An Outline of Projective Geometry by Lynn E. Garner Pdf

Author : Ilia Itenberg,Burglind Jöricke,Mikael Passare
Publisher : Springer Science & Business Media
Page : 483 pages
File Size : 44,9 Mb
Release : 2011-12-14
Category : Mathematics
ISBN : 9780817682774

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Perspectives in Analysis, Geometry, and Topology by Ilia Itenberg,Burglind Jöricke,Mikael Passare Pdf

The articles in this volume are invited papers from the Marcus Wallenberg symposium and focus on research topics that bridge the gap between analysis, geometry, and topology. The encounters between these three fields are widespread and often provide impetus for major breakthroughs in applications. Topics include new developments in low dimensional topology related to invariants of links and three and four manifolds; Perelman's spectacular proof of the Poincare conjecture; and the recent advances made in algebraic, complex, symplectic, and tropical geometry.

Author : H.S.M. Coxeter
Publisher : Springer Science & Business Media
Page : 480 pages
File Size : 46,8 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.

Author : Arnold Emch
Publisher : Unknown
Page : 300 pages
File Size : 54,9 Mb
Release : 1905
Category : Geometry, Analytic
ISBN : WISC:89043163096

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An Introduction to Projective Geometry and Its Applications by Arnold Emch Pdf

Author : Eduardo Casas-Alvero
Publisher : Susaeta
Page : 640 pages
File Size : 41,5 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.

Author : Eric Lord
Publisher : Springer Science & Business Media
Page : 184 pages
File Size : 55,5 Mb
Release : 2012-12-14
Category : Mathematics
ISBN : 9781447146315

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Symmetry and Pattern in Projective Geometry by Eric Lord Pdf

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.

Author : Richard Hartley,Andrew Zisserman
Publisher : Cambridge University Press
Page : 676 pages
File Size : 54,6 Mb
Release : 2003
Category : Computers
ISBN : 0521540518

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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.