Projective Geometry PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Projective Geometry PDF full book. Access full book title Projective Geometry by Albrecht Beutelspacher. Download full books in PDF and EPUB format.
Author: Albrecht Beutelspacher
Publisher: Cambridge University Press
ISBN: 9780521483643
Category : Mathematics
Languages : en
Pages : 272
Get Book Here
Book Description
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.
Author: Albrecht Beutelspacher
Publisher: Cambridge University Press
ISBN: 9780521483643
Category : Mathematics
Languages : en
Pages : 272
Get Book Here
Book Description
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.
Author: H.S.M. Coxeter
Publisher: Springer Science & Business Media
ISBN: 9780387406237
Category : Mathematics
Languages : en
Pages : 180
Get Book Here
Book Description
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.
Author: Jürgen Richter-Gebert
Publisher: Springer Science & Business Media
ISBN: 3642172865
Category : Mathematics
Languages : en
Pages : 573
Get Book Here
Book Description
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.
Author: Mauro Beltrametti
Publisher: European Mathematical Society
ISBN: 9783037190647
Category : Mathematics
Languages : en
Pages : 512
Get Book Here
Book Description
This book offers a wide-ranging introduction to algebraic geometry along classical lines. It consists of lectures on topics in classical algebraic geometry, including the basic properties of projective algebraic varieties, linear systems of hypersurfaces, algebraic curves (with special emphasis on rational curves), linear series on algebraic curves, Cremona transformations, rational surfaces, and notable examples of special varieties like the Segre, Grassmann, and Veronese varieties. An integral part and special feature of the presentation is the inclusion of many exercises, not easy to find in the literature and almost all with complete solutions. The text is aimed at students in the last two years of an undergraduate program in mathematics. It contains some rather advanced topics suitable for specialized courses at the advanced undergraduate or beginning graduate level, as well as interesting topics for a senior thesis. The prerequisites have been deliberately limited to basic elements of projective geometry and abstract algebra. Thus, for example, some knowledge of the geometry of subspaces and properties of fields is assumed. The book will be welcomed by teachers and students of algebraic geometry who are seeking a clear and panoramic path leading from the basic facts about linear subspaces, conics and quadrics to a systematic discussion of classical algebraic varieties and the tools needed to study them. The text provides a solid foundation for approaching more advanced and abstract literature.
Author: Elisabetta Fortuna
Publisher: Springer
ISBN: 3319428241
Category : Mathematics
Languages : en
Pages : 275
Get Book Here
Book Description
This book starts with a concise but rigorous overview of the basic notions of projective geometry, using straightforward and modern language. The goal is not only to establish the notation and terminology used, but also to offer the reader a quick survey of the subject matter. In the second part, the book presents more than 200 solved problems, for many of which several alternative solutions are provided. The level of difficulty of the exercises varies considerably: they range from computations to harder problems of a more theoretical nature, up to some actual complements of the theory. The structure of the text allows the reader to use the solutions of the exercises both to master the basic notions and techniques and to further their knowledge of the subject, thus learning some classical results not covered in the first part of the book. The book addresses the needs of undergraduate and graduate students in the theoretical and applied sciences, and will especially benefit those readers with a solid grasp of elementary Linear Algebra.
Author: Olive Whicher
Publisher: Rudolf Steiner Press
ISBN: 185584379X
Category : Mathematics
Languages : en
Pages : 294
Get Book Here
Book Description
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.
Author: John Stillwell
Publisher: Springer Science & Business Media
ISBN: 0387255303
Category : Mathematics
Languages : en
Pages : 240
Get Book Here
Book Description
This book is unique in that it looks at geometry from 4 different viewpoints - Euclid-style axioms, linear algebra, projective geometry, and groups and their invariants Approach makes the subject accessible to readers of all mathematical tastes, from the visual to the algebraic Abundantly supplemented with figures and exercises
Author: C. R. Wylie
Publisher: Courier Corporation
ISBN: 0486141705
Category : Mathematics
Languages : en
Pages : 578
Get Book Here
Book Description
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.
Author: Rey Casse
Publisher: OUP Oxford
ISBN: 0191538361
Category : Mathematics
Languages : en
Pages : 211
Get Book Here
Book Description
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.
Author: Reinhold Baer
Publisher: Courier Corporation
ISBN: 0486154661
Category : Mathematics
Languages : en
Pages : 338
Get Book Here
Book Description
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.
