Geometries and Transformations PDF Download
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Author: Norman W. Johnson
Publisher: Cambridge University Press
ISBN: 1107103401
Category : Mathematics
Languages : en
Pages : 455
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Book Description
A readable exposition of how Euclidean and other geometries can be distinguished using linear algebra and transformation groups.
Author: Norman W. Johnson
Publisher: Cambridge University Press
ISBN: 1107103401
Category : Mathematics
Languages : en
Pages : 455
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Book Description
A readable exposition of how Euclidean and other geometries can be distinguished using linear algebra and transformation groups.
Author: David Gans
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 424
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Book Description
Author: Reinhold Baer
Publisher: Courier Corporation
ISBN: 0486154661
Category : Mathematics
Languages : en
Pages : 338
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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.
Author: John Stillwell
Publisher: Springer Science & Business Media
ISBN: 0387255303
Category : Mathematics
Languages : en
Pages : 240
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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: Hans Schwerdtfeger
Publisher: Courier Corporation
ISBN: 0486135861
Category : Mathematics
Languages : en
Pages : 228
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Book Description
Illuminating, widely praised book on analytic geometry of circles, the Moebius transformation, and 2-dimensional non-Euclidean geometries.
Author: Dan Pedoe
Publisher: Courier Corporation
ISBN: 0486131734
Category : Mathematics
Languages : en
Pages : 466
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Book Description
Introduction to vector algebra in the plane; circles and coaxial systems; mappings of the Euclidean plane; similitudes, isometries, Moebius transformations, much more. Includes over 500 exercises.
Author: Isaak Moiseevich I︠A︡glom
Publisher:
ISBN:
Category : Transformations (Mathematics)
Languages : en
Pages : 206
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Book Description
Author: Vaughn Climenhaga
Publisher: American Mathematical Soc.
ISBN: 1470434792
Category : Mathematics
Languages : en
Pages : 442
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Book Description
Groups arise naturally as symmetries of geometric objects, and so groups can be used to understand geometry and topology. Conversely, one can study abstract groups by using geometric techniques and ultimately by treating groups themselves as geometric objects. This book explores these connections between group theory and geometry, introducing some of the main ideas of transformation groups, algebraic topology, and geometric group theory. The first half of the book introduces basic notions of group theory and studies symmetry groups in various geometries, including Euclidean, projective, and hyperbolic. The classification of Euclidean isometries leads to results on regular polyhedra and polytopes; the study of symmetry groups using matrices leads to Lie groups and Lie algebras. The second half of the book explores ideas from algebraic topology and geometric group theory. The fundamental group appears as yet another group associated to a geometric object and turns out to be a symmetry group using covering spaces and deck transformations. In the other direction, Cayley graphs, planar models, and fundamental domains appear as geometric objects associated to groups. The final chapter discusses groups themselves as geometric objects, including a gentle introduction to Gromov's theorem on polynomial growth and Grigorchuk's example of intermediate growth. The book is accessible to undergraduate students (and anyone else) with a background in calculus, linear algebra, and basic real analysis, including topological notions of convergence and connectedness. This book is a result of the MASS course in algebra at Penn State University in the fall semester of 2009.
Author: Leo Dorst
Publisher: Elsevier
ISBN: 0080553109
Category : Juvenile Nonfiction
Languages : en
Pages : 664
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Book Description
Until recently, almost all of the interactions between objects in virtual 3D worlds have been based on calculations performed using linear algebra. Linear algebra relies heavily on coordinates, however, which can make many geometric programming tasks very specific and complex-often a lot of effort is required to bring about even modest performance enhancements. Although linear algebra is an efficient way to specify low-level computations, it is not a suitable high-level language for geometric programming. Geometric Algebra for Computer Science presents a compelling alternative to the limitations of linear algebra. Geometric algebra, or GA, is a compact, time-effective, and performance-enhancing way to represent the geometry of 3D objects in computer programs. In this book you will find an introduction to GA that will give you a strong grasp of its relationship to linear algebra and its significance for your work. You will learn how to use GA to represent objects and perform geometric operations on them. And you will begin mastering proven techniques for making GA an integral part of your applications in a way that simplifies your code without slowing it down. * The first book on Geometric Algebra for programmers in computer graphics and entertainment computing * Written by leaders in the field providing essential information on this new technique for 3D graphics * This full colour book includes a website with GAViewer, a program to experiment with GA
Author: Judith N. Cederberg
Publisher: Springer Science & Business Media
ISBN: 1475738315
Category : Mathematics
Languages : en
Pages : 243
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Book Description
A Course in Modern Geometries is designed for a junior-senior level course for mathematics majors, including those who plan to teach in secondary school. Chapter 1 presents several finite geometries in an axiomatic framework. Chapter 2 introduces Euclid's geometry and the basic ideas of non-Euclidean geometry. The synthetic approach of Chapters 1 - 2 is followed by the analytic treatment of transformations of the Euclidean plane in Chapter 3. Chapter 4 presents plane projective geometry both synthetically and analytically. The extensive use of matrix representations of groups of transformations in Chapters 3 - 4 reinforces ideas from linear algebra and serves as excellent preparation for a course in abstract algebra. Each chapter includes a list of suggested sources for applications and/or related topics.
