Projective And Euclidean Geometry

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Perspectives on Projective Geometry

Author : Jürgen Richter-Gebert
Publisher : Springer Science & Business Media
ISBN 13 : 3642172865
Total Pages : 573 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Perspectives on Projective Geometry by : Jürgen Richter-Gebert

Download or read book Perspectives on Projective Geometry written by Jürgen Richter-Gebert and published by Springer Science & Business Media. This book was released on 2011-02-04 with total page 573 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Projective Geometry

Author : H.S.M. Coxeter
Publisher : Springer Science & Business Media
ISBN 13 : 9780387406237
Total Pages : 180 pages
Book Rating : 4.4/5 (62 download)

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Book Synopsis Projective Geometry by : H.S.M. Coxeter

Download or read book Projective Geometry written by H.S.M. Coxeter and published by Springer Science & Business Media. This book was released on 2003-10-09 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Introduction to Projective Geometry

Author : C. R. Wylie
Publisher : Courier Corporation
ISBN 13 : 0486141705
Total Pages : 578 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Introduction to Projective Geometry by : C. R. Wylie

Download or read book Introduction to Projective Geometry written by C. R. Wylie and published by Courier Corporation. This book was released on 2011-09-12 with total page 578 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Projective and Euclidean Geometry

Author : W. T. Fishback
Publisher : John Wiley & Sons
ISBN 13 :
Total Pages : 324 pages
Book Rating : 4.:/5 (319 download)

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Book Synopsis Projective and Euclidean Geometry by : W. T. Fishback

Download or read book Projective and Euclidean Geometry written by W. T. Fishback and published by John Wiley & Sons. This book was released on 1969-01-15 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Foundations of Geometry

Author : Karol Borsuk
Publisher : Courier Dover Publications
ISBN 13 : 0486828093
Total Pages : 465 pages
Book Rating : 4.4/5 (868 download)

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Book Synopsis Foundations of Geometry by : Karol Borsuk

Download or read book Foundations of Geometry written by Karol Borsuk and published by Courier Dover Publications. This book was released on 2018-11-14 with total page 465 pages. Available in PDF, EPUB and Kindle. Book excerpt: In Part One of this comprehensive and frequently cited treatment, the authors develop Euclidean and Bolyai-Lobachevskian geometry on the basis of an axiom system due, in principle, to the work of David Hilbert. Part Two develops projective geometry in much the same way. An Introduction provides background on topological space, analytic geometry, and other relevant topics, and rigorous proofs appear throughout the text. Topics covered by Part One include axioms of incidence and order, axioms of congruence, the axiom of continuity, models of absolute geometry, and Euclidean geometry, culminating in the treatment of Bolyai-Lobachevskian geometry. Part Two examines axioms of incidents and order and the axiom of continuity, concluding with an exploration of models of projective geometry.

Projective Geometry

Author : Rey Casse
Publisher : OUP Oxford
ISBN 13 : 0191538361
Total Pages : 212 pages
Book Rating : 4.1/5 (915 download)

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Book Synopsis Projective Geometry by : Rey Casse

Download or read book Projective Geometry written by Rey Casse and published by OUP Oxford. This book was released on 2006-08-03 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Elements of Projective Geometry

Author : Luigi Cremona
Publisher :
ISBN 13 :
Total Pages : 341 pages
Book Rating : 4.L/5 ( download)

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Book Synopsis Elements of Projective Geometry by : Luigi Cremona

Download or read book Elements of Projective Geometry written by Luigi Cremona and published by . This book was released on 1885 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Projective Geometry

Author : T. Ewan Faulkner
Publisher : Courier Corporation
ISBN 13 : 0486154890
Total Pages : 148 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Projective Geometry by : T. Ewan Faulkner

Download or read book Projective Geometry written by T. Ewan Faulkner and published by Courier Corporation. This book was released on 2013-02-20 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Geometries

Author : Michael Henle
Publisher : Pearson
ISBN 13 :
Total Pages : 404 pages
Book Rating : 4.3/5 (97 download)

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Book Synopsis Modern Geometries by : Michael Henle

Download or read book Modern Geometries written by Michael Henle and published by Pearson. This book was released on 2001 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: Engaging, accessible, and extensively illustrated, this brief, but solid introduction to modern geometry describes geometry as it is understood and used by contemporary mathematicians and theoretical scientists. Basically non-Euclidean in approach, it relates geometry to familiar ideas from analytic geometry, staying firmly in the Cartesian plane. It uses the principle geometric concept of congruence or geometric transformation--introducing and using the Erlanger Program explicitly throughout. It features significant modern applications of geometry--e.g., the geometry of relativity, symmetry, art and crystallography, finite geometry and computation. Covers a full range of topics from plane geometry, projective geometry, solid geometry, discrete geometry, and axiom systems. For anyone interested in an introduction to geometry used by contemporary mathematicians and theoretical scientists.

Projective and Euclidean Geometry

Author : William Thompson Fishback
Publisher :
ISBN 13 :
Total Pages : 244 pages
Book Rating : 4.:/5 (16 download)

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Book Synopsis Projective and Euclidean Geometry by : William Thompson Fishback

Download or read book Projective and Euclidean Geometry written by William Thompson Fishback and published by . This book was released on 1966 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Oriented Projective Geometry

Author : Jorge Stolfi
Publisher : Academic Press
ISBN 13 : 1483265196
Total Pages : 246 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Oriented Projective Geometry by : Jorge Stolfi

Download or read book Oriented Projective Geometry written by Jorge Stolfi and published by Academic Press. This book was released on 2014-05-10 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Albrecht Beutelspacher
Publisher : Cambridge University Press
ISBN 13 : 9780521483643
Total Pages : 272 pages
Book Rating : 4.4/5 (836 download)

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Book Synopsis Projective Geometry by : Albrecht Beutelspacher

Download or read book Projective Geometry written by Albrecht Beutelspacher and published by Cambridge University Press. This book was released on 1998-01-29 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

The Real Projective Plane

Author : H.S.M. Coxeter
Publisher : Springer Science & Business Media
ISBN 13 : 1461227348
Total Pages : 236 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis The Real Projective Plane by : H.S.M. Coxeter

Download or read book The Real Projective Plane written by H.S.M. Coxeter and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Projective Geometry and Algebraic Structures

Author : R. J. Mihalek
Publisher : Academic Press
ISBN 13 : 148326520X
Total Pages : 233 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Projective Geometry and Algebraic Structures by : R. J. Mihalek

Download or read book Projective Geometry and Algebraic Structures written by R. J. Mihalek and published by Academic Press. This book was released on 2014-05-10 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Classical Geometry

Author : I. E. Leonard
Publisher : John Wiley & Sons
ISBN 13 : 1118679148
Total Pages : 501 pages
Book Rating : 4.1/5 (186 download)

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Book Synopsis Classical Geometry by : I. E. Leonard

Download or read book Classical Geometry written by I. E. Leonard and published by John Wiley & Sons. This book was released on 2014-04-30 with total page 501 pages. Available in PDF, EPUB and Kindle. Book excerpt: Features the classical themes of geometry with plentiful applications in mathematics, education, engineering, and science Accessible and reader-friendly, Classical Geometry: Euclidean, Transformational, Inversive, and Projective introduces readers to a valuable discipline that is crucial to understanding bothspatial relationships and logical reasoning. Focusing on the development of geometric intuitionwhile avoiding the axiomatic method, a problem solving approach is encouraged throughout. The book is strategically divided into three sections: Part One focuses on Euclidean geometry, which provides the foundation for the rest of the material covered throughout; Part Two discusses Euclidean transformations of the plane, as well as groups and their use in studying transformations; and Part Three covers inversive and projective geometry as natural extensions of Euclidean geometry. In addition to featuring real-world applications throughout, Classical Geometry: Euclidean, Transformational, Inversive, and Projective includes: Multiple entertaining and elegant geometry problems at the end of each section for every level of study Fully worked examples with exercises to facilitate comprehension and retention Unique topical coverage, such as the theorems of Ceva and Menalaus and their applications An approach that prepares readers for the art of logical reasoning, modeling, and proofs The book is an excellent textbook for courses in introductory geometry, elementary geometry, modern geometry, and history of mathematics at the undergraduate level for mathematics majors, as well as for engineering and secondary education majors. The book is also ideal for anyone who would like to learn the various applications of elementary geometry.

Lectures on Analytic and Projective Geometry

Author : Dirk J. Struik
Publisher : Courier Corporation
ISBN 13 : 0486173526
Total Pages : 306 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Lectures on Analytic and Projective Geometry by : Dirk J. Struik

Download or read book Lectures on Analytic and Projective Geometry written by Dirk J. Struik and published by Courier Corporation. This book was released on 2014-03-05 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: This undergraduate text develops the geometry of plane and space, leading up to conics and quadrics, within the context of metrical, affine, and projective transformations. 1953 edition.

Projective Geometry and Projective Metrics

Author : Herbert Busemann
Publisher : Courier Corporation
ISBN 13 : 0486154696
Total Pages : 350 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Projective Geometry and Projective Metrics by : Herbert Busemann

Download or read book Projective Geometry and Projective Metrics written by Herbert Busemann and published by Courier Corporation. This book was released on 2012-11-14 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.