**Author**: Albrecht Beutelspacher

**Publisher:** Cambridge University Press

**ISBN:** 9780521483643

**Category : **Mathematics

**Languages : **en

**Pages : **258

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**Book Description**
A textbook on projective geometry that emphasises applications in modern information and communication science.

**Author**: John Wesley Young

**Publisher:** American Mathematical Soc.

**ISBN:** 1614440042

**Category : **Geometry, Projective

**Languages : **en

**Pages : **185

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**Book Description**
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.

**Author**: Claude-Alain Faure

**Publisher:** Springer Science & Business Media

**ISBN:** 9401595909

**Category : **Mathematics

**Languages : **en

**Pages : **363

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**Book Description**
This monograph develops projective geometries and provides a systematic treatment of morphisms. It introduces a new fundamental theorem and its applications describing morphisms of projective geometries in homogeneous coordinates by semilinear maps. Other topics treated include three equivalent definitions of projective geometries and their correspondence with certain lattices; quotients of projective geometries and isomorphism theorems; and recent results in dimension theory.

**Author**: T. Ewan Faulkner

**Publisher:** Courier Corporation

**ISBN:** 048645326X

**Category : **Mathematics

**Languages : **en

**Pages : **129

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**Book Description**
Highlighted by numerous examples, this book explores methods of the projective geometry of the plane. It derives the projective properties of the conic and discusses representation by the general equation of the 2nd degree, concluding with a study of the relationship between Euclidean and projective geometry. 1960 edition.

**Author**: Jorge Stolfi

**Publisher:** Academic Press

**ISBN:** 1483265196

**Category : **Mathematics

**Languages : **en

**Pages : **246

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**Book Description**
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.

**Author**: C. R. Wylie

**Publisher:** Courier Corporation

**ISBN:** 048646895X

**Category : **Mathematics

**Languages : **en

**Pages : **556

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**Book Description**
This lucid introductory text offers both analytic and axiomatic approaches to plane projective geometry. Strong reinforcement for its teachings include detailed examples and numerous theorems, proofs, and exercises, plus answers to all odd-numbered problems. In addition to its value to students, this volume provides an excellent reference for professionals. 1970 edition.

**Author**: John R. Faulkner

**Publisher:** American Mathematical Soc.

**ISBN:** 1470418495

**Category : **Mathematics

**Languages : **en

**Pages : **229

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**Book Description**
There is a particular fascination when two apparently disjoint areas of mathematics turn out to have a meaningful connection to each other. The main goal of this book is to provide a largely self-contained, in-depth account of the linkage between nonassociative algebra and projective planes, with particular emphasis on octonion planes. There are several new results and many, if not most, of the proofs are new. The development should be accessible to most graduate students and should give them introductions to two areas which are often referenced but not often taught. On the geometric side, the book introduces coordinates in projective planes and relates coordinate properties to transitivity properties of certain automorphisms and to configuration conditions. It also classifies higher-dimensional geometries and determines their automorphisms. The exceptional octonion plane is studied in detail in a geometric context that allows nondivision coordinates. An axiomatic version of that context is also provided. Finally, some connections of nonassociative algebra to other geometries, including buildings, are outlined. On the algebraic side, basic properties of alternative algebras are derived, including the classification of alternative division rings. As tools for the study of the geometries, an axiomatic development of dimension, the basics of quadratic forms, a treatment of homogeneous maps and their polarizations, and a study of norm forms on hermitian matrices over composition algebras are included.

**Author**: G. Ellingsrud

**Publisher:** Cambridge University Press

**ISBN:** 0521433525

**Category : **Mathematics

**Languages : **en

**Pages : **340

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**Book Description**
A volume of papers describing new methods in algebraic geometry.

**Author**: Sherif Ghali

**Publisher:** Springer Science & Business Media

**ISBN:** 1848001150

**Category : **Computers

**Languages : **en

**Pages : **340

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**Book Description**
Computing is quickly making much of geometry intriguing not only for philosophers and mathematicians, but also for scientists and engineers. What is the core set of topics that a practitioner needs to study before embarking on the design and implementation of a geometric system in a specialized discipline? This book attempts to find the answer. Every programmer tackling a geometric computing problem encounters design decisions that need to be solved. This book reviews the geometric theory then applies it in an attempt to find that elusive "right" design.

**Author**: Helmut Pottmann

**Publisher:** Springer Science & Business Media

**ISBN:** 9783540420583

**Category : **Mathematics

**Languages : **en

**Pages : **564

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**Book Description**
From the reviews: " A unique and fascinating blend, which is shown to be useful for a variety of applications, including robotics, geometrical optics, computer animation, and geometric design. The contents of the book are visualized by a wealth of carefully chosen illustrations, making the book a shear pleasure to read, or even to just browse in." Mathematical Reviews