Lectures in Projective Geometry

Author: A. Seidenberg
Publisher: Courier Corporation
ISBN: 9780486154732
Release Date: 2012-06-14
Genre: Mathematics

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.

Lectures on Analytic and Projective Geometry

Author: Dirk J. Struik
Publisher: Courier Corporation
ISBN: 9780486173528
Release Date: 2014-03-05
Genre: Mathematics

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.

Lectures on Curves Surfaces and Projective Varieties

Author: Mauro Beltrametti
Publisher: European Mathematical Society
ISBN: 3037190647
Release Date: 2009-01-01
Genre: Mathematics

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 of the last two years of an undergraduate program in mathematics. It contains some rather advanced topics suitable for specialized courses on 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.

Projective Geometry

Author: T. Ewan Faulkner
Publisher: Courier Corporation
ISBN: 9780486154893
Release Date: 2013-02-20
Genre: Mathematics

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.

The Use of Projective Geometry in Computer Graphics

Author: Ivan Herman
Publisher: Springer
ISBN: 366218799X
Release Date: 2014-10-09
Genre: Computers

The ultimate goal of all 3D graphics systems is to render 3D objects on a two-dimensional surface such as plotter output or a workstation screen. The approach adopted by most graphics systems is to perform a central or parallel projection of the objects onto the view surface. These systems have to make use of the mathematical results of projective geometry. This monograph has as its aim the derivation of a framework for analyzing the behavior of projective transformations in graphics systems. It is shown that a mathematically precise description of the projective geometrical nature of a graphics system leads not only to a deeper understanding of the system but also to new approaches which result in faster or more precise algorithms. A further aim of the book is to show the importance of advanced mathematics for computer science. Many problems become easier to describe or to solve when the appropriate mathematical tools are used. The author demonstrates that projective geometry has a major role to play in computer graphics.

Projective Geometry

Author: Olive Whicher
ISBN: 9781855843790
Release Date: 2013-07-01
Genre: Mathematics

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.

Dynamics Statistics and Projective Geometry of Galois Fields

Author: V. I. Arnold
Publisher: Cambridge University Press
ISBN: 9781139493444
Release Date: 2010-12-02
Genre: Mathematics

V. I. Arnold reveals some unexpected connections between such apparently unrelated theories as Galois fields, dynamical systems, ergodic theory, statistics, chaos and the geometry of projective structures on finite sets. The author blends experimental results with examples and geometrical explorations to make these findings accessible to a broad range of mathematicians, from undergraduate students to experienced researchers.

Elements of Projective Geometry

Author: Luigi Cremona
ISBN: STANFORD:36105046445461
Release Date: 1893
Genre: Geometry, Projective

One of the best, most complete treatments of projective geometry, this treatise features detailed proofs, plus complete solutions for more than 150 examples and problems and numerous diagrams. 1913 edition.

Introduction to Projective Geometry

Author: C. R. Wylie
Publisher: Courier Corporation
ISBN: 9780486141701
Release Date: 2011-09-12
Genre: Mathematics

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.