Geometries and Transformations 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 Geometries and Transformations PDF full book. Access full book title Geometries and Transformations by Norman W. Johnson. Download full books in PDF and EPUB format.
Author: Norman W. Johnson
Publisher: Cambridge University Press
ISBN: 1107103401
Category : Mathematics
Languages : en
Pages : 455
Get Book
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
Get Book
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: 1108132677
Category : Mathematics
Languages : en
Pages : 455
Get Book
Book Description
Euclidean and other geometries are distinguished by the transformations that preserve their essential properties. Using linear algebra and transformation groups, this book provides a readable exposition of how these classical geometries are both differentiated and connected. Following Cayley and Klein, the book builds on projective and inversive geometry to construct 'linear' and 'circular' geometries, including classical real metric spaces like Euclidean, hyperbolic, elliptic, and spherical, as well as their unitary counterparts. The first part of the book deals with the foundations and general properties of the various kinds of geometries. The latter part studies discrete-geometric structures and their symmetries in various spaces. Written for graduate students, the book includes numerous exercises and covers both classical results and new research in the field. An understanding of analytic geometry, linear algebra, and elementary group theory is assumed.
Author: Clayton W. Dodge
Publisher: Courier Corporation
ISBN: 0486138429
Category : Mathematics
Languages : en
Pages : 306
Get Book
Book Description
This introduction to Euclidean geometry emphasizes transformations, particularly isometries and similarities. Suitable for undergraduate courses, it includes numerous examples, many with detailed answers. 1972 edition.
Author: David Gans
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 424
Get Book
Book Description
Author: Hans Schwerdtfeger
Publisher: Courier Corporation
ISBN: 0486135861
Category : Mathematics
Languages : en
Pages : 224
Get Book
Book Description
Illuminating, widely praised book on analytic geometry of circles, the Moebius transformation, and 2-dimensional non-Euclidean geometries.
Author: Reinhold Baer
Publisher: Courier Corporation
ISBN: 0486154661
Category : Mathematics
Languages : en
Pages : 338
Get Book
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: James Richard King
Publisher:
ISBN: 9781470464431
Category : Electronic books
Languages : en
Pages :
Get Book
Book Description
Many paths lead into Euclidean plane geometry. Geometry Transformed offers an expeditious yet rigorous route using axioms based on rigid motions and dilations. Since transformations are available at the outset, interesting theorems can be proved sooner; and proofs can be connected to visual and tactile intuition about symmetry and motion. The reader thus gains valuable experience thinking with transformations, a skill that may be useful in other math courses or applications. For students interested in teaching mathematics at the secondary school level, this approach is particularly useful sinc.
Author: Vaughn Climenhaga
Publisher: American Mathematical Soc.
ISBN: 1470434792
Category : Geometry
Languages : en
Pages : 420
Get Book
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: Judith N. Cederberg
Publisher: Springer Science & Business Media
ISBN: 1475738315
Category : Mathematics
Languages : en
Pages : 243
Get Book
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.
Author: Max Jager
Publisher:
ISBN:
Category : Transformations (Mathematics)
Languages : en
Pages : 152
Get Book
Book Description
