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Introduction to Projective Geometry

2011-09-12 Mathematics
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Release : 2011-09-12
Genre : Mathematics
Kind : eBook
Book Rating : 705/5 ( reviews)

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Book Synopsis Introduction to Projective Geometry by : C. R. Wylie

Download or read book Introduction to Projective Geometry written by C. R. Wylie. This book was released on 2011-09-12. 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.

Projective Geometry

2006-08-03 Mathematics
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Release : 2006-08-03
Genre : Mathematics
Kind : eBook
Book Rating : 361/5 ( reviews)

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Book Synopsis Projective Geometry by : Rey Casse

Download or read book Projective Geometry written by Rey Casse. This book was released on 2006-08-03. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Projective Geometry

2003-10-09 Mathematics
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Release : 2003-10-09
Genre : Mathematics
Kind : eBook
Book Rating : 237/5 ( reviews)

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Book Synopsis Projective Geometry by : H.S.M. Coxeter

Download or read book Projective Geometry written by H.S.M. Coxeter. This book was released on 2003-10-09. 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.

The Four Pillars of Geometry

2005-08-09 Mathematics
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Release : 2005-08-09
Genre : Mathematics
Kind : eBook
Book Rating : 303/5 ( reviews)

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Book Synopsis The Four Pillars of Geometry by : John Stillwell

Download or read book The Four Pillars of Geometry written by John Stillwell. This book was released on 2005-08-09. Available in PDF, EPUB and Kindle. Book excerpt: 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

Perspectives on Projective Geometry

2011-02-04 Mathematics
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Release : 2011-02-04
Genre : Mathematics
Kind : eBook
Book Rating : 865/5 ( reviews)

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Book Synopsis Perspectives on Projective Geometry by : Jürgen Richter-Gebert

Download or read book Perspectives on Projective Geometry written by Jürgen Richter-Gebert. This book was released on 2011-02-04. 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.

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