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Projective And Cayley Klein Geometries
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Book Synopsis Projective and Cayley-Klein Geometries by : Arkadij L. Onishchik
Download or read book Projective and Cayley-Klein Geometries written by Arkadij L. Onishchik and published by Springer Science & Business Media. This book was released on 2006-11-22 with total page 445 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an introduction into projective geometry. The first part presents n-dimensional projective geometry over an arbitrary skew field; the real, the complex, and the quaternionic geometries are the central topics, finite geometries playing only a minor part. The second deals with classical linear and projective groups and the associated geometries. The final section summarizes selected results and problems from the geometry of transformation groups.
Author :Jürgen Richter-Gebert Publisher :Springer Science & Business Media ISBN 13 :3642172865 Total Pages :573 pages Book Rating :4.6/5 (421 download)
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.
Book Synopsis Lectures on Geometry by : Lucian Bădescu
Download or read book Lectures on Geometry written by Lucian Bădescu and published by Springer. This book was released on 2024-04-03 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an introductory textbook on geometry (affine, Euclidean and projective) suitable for any undergraduate or first-year graduate course in mathematics and physics. In particular, several parts of the first ten chapters can be used in a course of linear algebra, affine and Euclidean geometry by students of some branches of engineering and computer science. Chapter 11 may be useful as an elementary introduction to algebraic geometry for advanced undergraduate and graduate students of mathematics. Chapters 12 and 13 may be a part of a course on non-Euclidean geometry for mathematics students. Chapter 13 may be of some interest for students of theoretical physics (Galilean and Einstein’s general relativity). It provides full proofs and includes many examples and exercises. The covered topics include vector spaces and quadratic forms, affine and projective spaces over an arbitrary field; Euclidean spaces; some synthetic affine, Euclidean and projective geometry; affine and projective hyperquadrics with coefficients in an arbitrary field of characteristic different from 2; Bézout’s theorem for curves of P^2 (K), where K is a fixed algebraically closed field of arbitrary characteristic; and Cayley-Klein geometries.
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.
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.
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.
Book Synopsis An Introduction to Projective Geometry and Its Applications by : Arnold Emch
Download or read book An Introduction to Projective Geometry and Its Applications written by Arnold Emch and published by . This book was released on 1905 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Projective Geometry by : Peter Field
Download or read book Projective Geometry written by Peter Field and published by . This book was released on 1923 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Projective Geometry by : John Wesley Young
Download or read book Projective Geometry written by John Wesley Young and published by American Mathematical Soc.. This book was released on 1930-12-31 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis An Introduction to Projective Geometry by : Roy Martin Winger
Download or read book An Introduction to Projective Geometry written by Roy Martin Winger and published by . This book was released on 1923 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Projective Geometry by : Oswald Veblen
Download or read book Projective Geometry written by Oswald Veblen and published by . This book was released on 1910 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Two-dimensional EP Geometry in Terms of Cayley-Klein by : Miroljub Milojevic
Download or read book Two-dimensional EP Geometry in Terms of Cayley-Klein written by Miroljub Milojevic and published by LAP Lambert Academic Publishing. This book was released on 2015-04-09 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: According to classification of Cayley-Klein, EP Geometry is one of the nine two-dimensional geometries, i.e. geometry which is dual to the classical Euclidean (PE) geometry. The first chapter contains a system of axioms of this geometry, not the Hilbert's system and principle of duality. Fundamental objects (points and straight lines) and fundamental relations (of incidence, separateness of point couples and of line segment congruence) are defined by four groups of axioms (axioms of incidence, order, continuity and congruence). Based on the proposed system of axioms, some important consequences are proved, and some more important geometric figures and their features are defined. The second chapter is about central and axial symmetry of EP plane. The third one defines transformation of congruence and its basic characteristics. Also, the relation of figure congruence is defined. Theorems are proved about the provision according to which congruence of certain geometric figures (angle, triangle, monogon) is defined. The end of the book is dedicated to the proof of logical non-contradiction of a given axiom system, through a projective model.
Book Synopsis Lectures in Projective Geometry by : A. Seidenberg
Download or read book Lectures in Projective Geometry written by A. Seidenberg and published by Courier Corporation. This book was released on 2012-06-14 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: An ideal text for undergraduate courses, this volume takes an axiomatic approach that covers relations between the basic theorems, conics, coordinate systems and linear transformations, quadric surfaces, and the Jordan canonical form. 1962 edition.
Book Synopsis Projective Geometry by : Oswald Veblen
Download or read book Projective Geometry written by Oswald Veblen and published by . This book was released on 1918 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Projective Geometry for Use in Colleges and Schools by : William Proctor Milne
Download or read book Projective Geometry for Use in Colleges and Schools written by William Proctor Milne and published by . This book was released on 1911 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Elementary Projective Geometry by : Alfred Garside Pickford
Download or read book Elementary Projective Geometry written by Alfred Garside Pickford and published by . This book was released on 1909 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Geometries and Transformations by : Norman W. Johnson
Download or read book Geometries and Transformations written by Norman W. Johnson and published by Cambridge University Press. This book was released on 2018-06-07 with total page 455 pages. Available in PDF, EPUB and Kindle. Book excerpt: A readable exposition of how Euclidean and other geometries can be distinguished using linear algebra and transformation groups.
