Projective Geometry
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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.
Projective Geometry
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Author : Rey Casse
language : en
Publisher: OUP Oxford
Release Date : 2006-08-03
Projective Geometry written by Rey Casse and has been published by OUP Oxford 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 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.
Projective Geometry And Projective Metrics
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Author : Herbert Busemann
language : en
Publisher: Courier Corporation
Release Date : 2012-11-14
Projective Geometry And Projective Metrics written by Herbert Busemann and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-11-14 with Mathematics categories.
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
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Author : Fouad Sabry
language : en
Publisher: One Billion Knowledgeable
Release Date : 2024-04-30
Projective Geometry written by Fouad Sabry and has been published by One Billion Knowledgeable this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-30 with Computers categories.
What is Projective Geometry Projective geometry is a branch of mathematics that focuses on the study of geometric qualities that remain unchanged regardless of the transformations that are being applied to them. This indicates that, in contrast to simple Euclidean geometry, projective geometry is characterized by a distinct environment, a space that is the subject of the project, and a limited collection of fundamental geometric notions. For a given dimension, the fundamental intuitions are that projective space has a greater number of points than Euclidean space does, and that geometric transformations are allowed that change the extra points into Euclidean points, and vice versa. How you will benefit (I) Insights, and validations about the following topics: Chapter 1: Projective geometry Chapter 2: Projective plane Chapter 3: Projective space Chapter 4: Affine geometry Chapter 5: Desargues's theorem Chapter 6: Duality (projective geometry) Chapter 7: Complete quadrangle Chapter 8: Homography Chapter 9: Desargues configuration Chapter 10: Conic section (II) Answering the public top questions about projective geometry. (III) Real world examples for the usage of projective geometry in many fields. Who this book is for Professionals, undergraduate and graduate students, enthusiasts, hobbyists, and those who want to go beyond basic knowledge or information for any kind of Projective Geometry.
Projective Geometry
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Author : John Wesley Young
language : en
Publisher: American Mathematical Soc.
Release Date : 1930-12-31
Projective Geometry written by John Wesley Young and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1930-12-31 with Geometry, Projective categories.
John Wesley Young co-authored with Oswald Veblen the first monograph on projective geometry in English. That careful and thorough axiomatic treatment remains read today. This volume is Young's attempt to write an accessible and intuitive treatment for non-specialists. The first five chapters are a careful and elementary treatment of the subject culminating in the theorems of Pascal and Brianchon and the polar system of a conic. Later chapters pull metric consequences from projective results and consider the Kleinian classification of geometries by their groups of transformations. This book, nearly a century after its initial publication, remains a very approachable and understandable treatment of the subject.
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.
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.
Elements Of Projective Geometry
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Author : Luigi Cremona
language : en
Publisher:
Release Date : 1885
Elements Of Projective Geometry written by Luigi Cremona and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1885 with Geometry, Projective categories.
The Axioms Of Projective Geometry
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Author : Alfred North Whitehead
language : en
Publisher:
Release Date : 1906
The Axioms Of Projective Geometry written by Alfred North Whitehead and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1906 with Axiomas categories.
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.