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The Real Projective Plane

The Real Projective Plane Author H.S.M. Coxeter
ISBN-10 9781461227342
Release 2012-12-06
Pages 227
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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

Projective Geometry and Algebraic Structures Author R. J. Mihalek
ISBN-10 9781483265209
Release 2014-05-10
Pages 232
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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.



Pencils of Cubics and Algebraic Curves in the Real Projective Plane

Pencils of Cubics and Algebraic Curves in the Real Projective Plane Author Sverine Fiedler Le Touz
ISBN-10 1138590517
Release 2018-08-03
Pages 256
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Pencils of Cubics and Algebraic Curves in the Real Projective Plane thoroughly examines the combinatorial configurations of n generic points in RP2. Especially how it is the data describing the mutual position of each point with respect to lines and conics passing through others. The first part of the book answers questions related to using rational cubics and pencils of cubics. The other two parts deal with configurations of eight points in convex position, and applications and results around Hilbert's sixteenth problem.



Perspectives on Projective Geometry

Perspectives on Projective Geometry Author Jürgen Richter-Gebert
ISBN-10 3642172865
Release 2011-02-04
Pages 571
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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

Oriented Projective Geometry Author Jorge Stolfi
ISBN-10 9781483265193
Release 2014-05-10
Pages 246
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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.



Linear Algebra and Projective Geometry

Linear Algebra and Projective Geometry Author Reinhold Baer
ISBN-10 9780486154664
Release 2012-06-11
Pages 336
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Geared toward upper-level undergraduates and graduate students, this text establishes that projective geometry and linear algebra are essentially identical. The supporting evidence consists of theorems offering an algebraic demonstration of certain geometric concepts. 1952 edition.



Mathematical Models

Mathematical Models Author Gerd Fischer
ISBN-10 9783658188658
Release 2017-09-04
Pages 216
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This book presents beautiful photos of mathematical models of geometric surfaces made from a variety of materials including plaster, metal, paper, wood, and string. The construction of these models at the time (of Felix Klein and others) was not an end in itself, but was accompanied by mathematical research especially in the field of algebraic geometry. The models were used to illustrate the mathematical objects defined by abstract formulas, either as equations or parameterizations. In the second part of the book, the models are explained by experts in the field of geometry. This book is a reprint thirty years after the original publication in 1986 with a new preface by Gert-Martin Greuel. The models have a timeless appeal and a historical value.



Projective and Euclidean geometry

Projective and Euclidean geometry Author William Thompson Fishback
ISBN-10 MINN:31951D00041985S
Release 1969
Pages 298
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Projective and Euclidean geometry has been writing in one form or another for most of life. You can find so many inspiration from Projective and Euclidean geometry also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Projective and Euclidean geometry book for free.



An Introduction to Finite Projective Planes

An Introduction to Finite Projective Planes Author Abraham Adrian Albert
ISBN-10 9780486789941
Release 2015-02-18
Pages 112
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Text for both beginning and advanced undergraduate and graduate students covers finite planes, field planes, coordinates in an arbitrary plane, central collineations and the little Desargues' property, the fundamental theorem, and non-Desarguesian planes. 1968 edition.



An outline of projective geometry

An outline of projective geometry Author Lynn E. Garner
ISBN-10 UOM:39015015621587
Release 1981
Pages 220
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An outline of projective geometry has been writing in one form or another for most of life. You can find so many inspiration from An outline of projective geometry also informative, and entertaining. Click DOWNLOAD or Read Online button to get full An outline of projective geometry book for free.



A Guide to the Classification Theorem for Compact Surfaces

A Guide to the Classification Theorem for Compact Surfaces Author Jean Gallier
ISBN-10 9783642343643
Release 2013-02-05
Pages 178
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This welcome boon for students of algebraic topology cuts a much-needed central path between other texts whose treatment of the classification theorem for compact surfaces is either too formalized and complex for those without detailed background knowledge, or too informal to afford students a comprehensive insight into the subject. Its dedicated, student-centred approach details a near-complete proof of this theorem, widely admired for its efficacy and formal beauty. The authors present the technical tools needed to deploy the method effectively as well as demonstrating their use in a clearly structured, worked example. Ideal for students whose mastery of algebraic topology may be a work-in-progress, the text introduces key notions such as fundamental groups, homology groups, and the Euler-Poincaré characteristic. These prerequisites are the subject of detailed appendices that enable focused, discrete learning where it is required, without interrupting the carefully planned structure of the core exposition. Gently guiding readers through the principles, theory, and applications of the classification theorem, the authors aim to foster genuine confidence in its use and in so doing encourage readers to move on to a deeper exploration of the versatile and valuable techniques available in algebraic topology.



A Modern View of Geometry

A Modern View of Geometry Author Leonard M. Blumenthal
ISBN-10 9780486639628
Release 1980
Pages 191
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Elegant exposition of the postulation geometry of planes, including coordination of affine and projective planes. Historical background, set theory, propositional calculus, affine planes with Desargues and Pappus properties, construction of metrical planes, much more. Rigorous, lucid treatment of important area in modern mathematics. Corrected republication of the 3rd (1961) edition. Includes 56 figures.



Projective Geometry

Projective Geometry Author Rey Casse
ISBN-10 9780199298853
Release 2006-08-03
Pages 198
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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), coordinating 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.



Introduction to Projective Geometry

Introduction to Projective Geometry Author C. R. Wylie
ISBN-10 9780486141701
Release 2011-09-12
Pages 576
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This introductory volume offers strong reinforcement for its teachings, with detailed examples and numerous theorems, proofs, and exercises, plus complete answers to all odd-numbered end-of-chapter problems. 1970 edition.



Foundations of Projective Geometry

Foundations of Projective Geometry Author Robin Hartshorne
ISBN-10 UCAL:B3813369
Release 1967
Pages 167
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Foundations of Projective Geometry has been writing in one form or another for most of life. You can find so many inspiration from Foundations of Projective Geometry also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Foundations of Projective Geometry book for free.



Projective Geometry

Projective Geometry Author Albrecht Beutelspacher
ISBN-10 0521483646
Release 1998-01-29
Pages 258
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A textbook on projective geometry that emphasises applications in modern information and communication science.



The Universe of Conics

The Universe of Conics Author Georg Glaeser
ISBN-10 9783662454503
Release 2016-03-22
Pages 488
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This text presents the classical theory of conics in a modern form. It includes many novel results that are not easily accessible elsewhere. The approach combines synthetic and analytic methods to derive projective, affine and metrical properties, covering both Euclidean and non-Euclidean geometries. With more than two thousand years of history, conic sections play a fundamental role in numerous fields of mathematics and physics, with applications to mechanical engineering, architecture, astronomy, design and computer graphics. This text will be invaluable to undergraduate mathematics students, those in adjacent fields of study, and anyone with an interest in classical geometry. Augmented with more than three hundred fifty figures and photographs, this innovative text will enhance your understanding of projective geometry, linear algebra, mechanics, and differential geometry, with careful exposition and many illustrative exercises.