Projective Geometry

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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.

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.

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.

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 : Pierre Samuel
language : en
Publisher: Springer
Release Date : 1988-09-12

Projective Geometry written by Pierre Samuel and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988-09-12 with Mathematics categories.

The purpose of this book is to revive some of the beautiful results obtained by various geometers of the 19th century, and to give its readers a taste of concrete algebraic geometry. A good deal of space is devoted to cross-ratios, conics, quadrics, and various interesting curves and surfaces. The fundamentals of projective geometry are efficiently dealt with by using a modest amount of linear algebra. An axiomatic characterization of projective planes is also given. While the topology of projective spaces over real and complex fields is described, and while the geometry of the complex projective libe is applied to the study of circles and Möbius transformations, the book is not restricted to these fields. Interesting properties of projective spaces, conics, and quadrics over finite fields are also given. This book is the first volume in the Readings in Mathematics sub-series of the UTM. From the reviews: "...The book of P. Samuel thus fills a gap in the literature. It is a little jewel. Starting from a minimal background in algebra, he succeeds in 160 pages in giving a coherent exposition of all of projective geometry. ... one reads this book like a novel. " D.Lazard in Gazette des Mathématiciens#1

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 : T. Ewan Faulkner
language : en
Publisher: Courier Corporation
Release Date : 2013-02-20

Projective Geometry written by T. Ewan Faulkner and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-02-20 with Mathematics categories.

Highlighted by numerous examples, this book explores methods of the projective geometry of the plane. Examines the conic, the general equation of the 2nd degree, and the relationship between Euclidean and projective geometry. 1960 edition.

Modern Projective Geometry

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Author : Robert J. Bumcrot
language : en
Publisher:
Release Date : 1969

Modern Projective Geometry written by Robert J. Bumcrot and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1969 with Mathematics categories.

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.

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.