Perspectives On Projective Geometry
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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.
Perspectives On Projective Geometry
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Author : J Rgen Richter-Gebert
language : en
Publisher: Springer
Release Date : 2016-05-01
Perspectives On Projective Geometry written by J Rgen Richter-Gebert and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-05-01 with categories.
This book provides a comprehensive introduction into the classical topic of projective geometry. It explains how metric concepts may be best understood in projective terms and explores the beauty of the interplay of geometry, algebra and combinatorics."
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.
Perspective And Projective Geometry
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Author : Annalisa Crannell
language : en
Publisher: Princeton University Press
Release Date : 2019-12-10
Perspective And Projective Geometry written by Annalisa Crannell and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-12-10 with Mathematics categories.
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
The Four Pillars Of Geometry
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Author : John Stillwell
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-08-09
The Four Pillars Of Geometry written by John Stillwell 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 2005-08-09 with Mathematics categories.
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
Viewpoints
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Author : Marc Frantz
language : en
Publisher: Princeton University Press
Release Date : 2011-07-05
Viewpoints written by Marc Frantz and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-07-05 with Mathematics categories.
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)
Multiple View Geometry In Computer Vision
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Author : Richard Hartley
language : en
Publisher: Cambridge University Press
Release Date : 2004-03-25
Multiple View Geometry In Computer Vision written by Richard Hartley 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 2004-03-25 with Computers categories.
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.
Foundations Of Projective Geometry
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Author : Robin Hartshorne
language : en
Publisher: Ishi Press
Release Date : 2009
Foundations Of Projective Geometry written by Robin Hartshorne and has been published by Ishi Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.
The first geometrical properties of a projective nature were discovered in the third century by Pappus of Alexandria. Filippo Brunelleschi (1404-1472) started investigating the geometry of perspective in 1425. Johannes Kepler (1571-1630) and Gerard Desargues (1591-1661) independently developed the pivotal concept of the "point at infinity." Desargues developed an alternative way of constructing perspective drawings by generalizing the use of vanishing points to include the case when these are infinitely far away. He made Euclidean geometry, where parallel lines are truly parallel, into a special case of an all-encompassing geometric system. Desargues's study on conic sections drew the attention of 16-years old Blaise Pascal and helped him formulate Pascal's theorem. The works of Gaspard Monge at the end of 18th and beginning of 19th century were important for the subsequent development of projective geometry. The work of Desargues was ignored until Michel Chasles chanced upon a handwritten copy in 1845. Meanwhile, Jean-Victor Poncelet had published the foundational treatise on projective geometry in 1822. Poncelet separated the projective properties of objects in individual class and establishing a relationship between metric and projective properties. The non-Euclidean geometries discovered shortly thereafter were eventually demonstrated to have models, such as the Klein model of hyperbolic space, relating to projective geometry.
Euclidean And Non Euclidean Geometry International Student Edition
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Author : Patrick J. Ryan
language : en
Publisher: Cambridge University Press
Release Date : 2009-09-04
Euclidean And Non Euclidean Geometry International Student Edition written by Patrick J. Ryan 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 2009-09-04 with Mathematics categories.
This book gives a rigorous treatment of the fundamentals of plane geometry: Euclidean, spherical, elliptical and hyperbolic.
Commutative Algebra
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Author : David Eisenbud
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Commutative Algebra written by David Eisenbud 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 2013-12-01 with Mathematics categories.
Commutative Algebra is best understood with knowledge of the geometric ideas that have played a great role in its formation, in short, with a view towards algebraic geometry. The author presents a comprehensive view of commutative algebra, from basics, such as localization and primary decomposition, through dimension theory, differentials, homological methods, free resolutions and duality, emphasizing the origins of the ideas and their connections with other parts of mathematics. Many exercises illustrate and sharpen the theory and extended exercises give the reader an active part in complementing the material presented in the text. One novel feature is a chapter devoted to a quick but thorough treatment of Grobner basis theory and the constructive methods in commutative algebra and algebraic geometry that flow from it. Applications of the theory and even suggestions for computer algebra projects are included. This book will appeal to readers from beginners to advanced students of commutative algebra or algebraic geometry. To help beginners, the essential ideals from algebraic geometry are treated from scratch. Appendices on homological algebra, multilinear algebra and several other useful topics help to make the book relatively self- contained. Novel results and presentations are scattered throughout the text.