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Author : Norman W. Johnson
Publisher : Cambridge University Press
Page : 455 pages
File Size : 47,60 MB
Release : 2018-06-07
Category : Mathematics
ISBN : 1107103401
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
Page : 455 pages
File Size : 26,36 MB
Release : 2018-06-07
Category : Mathematics
ISBN : 1108132677
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 : Răzvan Gelca
Publisher : Springer Nature
Page : 581 pages
File Size : 34,46 MB
Release : 2022-02-16
Category : Mathematics
ISBN : 3030891178
This textbook teaches the transformations of plane Euclidean geometry through problems, offering a transformation-based perspective on problems that have appeared in recent years at mathematics competitions around the globe, as well as on some classical examples and theorems. It is based on the combined teaching experience of the authors (coaches of several Mathematical Olympiad teams in Brazil, Romania and the USA) and presents comprehensive theoretical discussions of isometries, homotheties and spiral similarities, and inversions, all illustrated by examples and followed by myriad problems left for the reader to solve. These problems were carefully selected and arranged to introduce students to the topics by gradually moving from basic to expert level. Most of them have appeared in competitions such as Mathematical Olympiads or in mathematical journals aimed at an audience interested in mathematics competitions, while some are fundamental facts of mathematics discussed in the framework of geometric transformations. The book offers a global view of the geometric content of today's mathematics competitions, bringing many new methods and ideas to the attention of the public. Talented high school and middle school students seeking to improve their problem-solving skills can benefit from this book, as well as high school and college instructors who want to add nonstandard questions to their courses. People who enjoy solving elementary math problems as a hobby will also enjoy this work.
Author : Clayton W. Dodge
Publisher : Courier Corporation
Page : 306 pages
File Size : 43,75 MB
Release : 2012-04-26
Category : Mathematics
ISBN : 0486138429
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 : George E. Martin
Publisher : Springer Science & Business Media
Page : 251 pages
File Size : 27,71 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 1461256801
Transformation Geometry: An Introduction to Symmetry offers a modern approach to Euclidean Geometry. This study of the automorphism groups of the plane and space gives the classical concrete examples that serve as a meaningful preparation for the standard undergraduate course in abstract algebra. The detailed development of the isometries of the plane is based on only the most elementary geometry and is appropriate for graduate courses for secondary teachers.
Author : James Richard King
Publisher :
Page : pages
File Size : 23,42 MB
Release : 2021
Category : Electronic books
ISBN : 9781470464431
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 : Hans Schwerdtfeger
Publisher : Courier Corporation
Page : 228 pages
File Size : 39,94 MB
Release : 2012-05-23
Category : Mathematics
ISBN : 0486135861
Illuminating, widely praised book on analytic geometry of circles, the Moebius transformation, and 2-dimensional non-Euclidean geometries.
Author : David Gans
Publisher :
Page : 424 pages
File Size : 33,57 MB
Release : 1969
Category : Mathematics
ISBN :
Author : Reinhold Baer
Publisher : Courier Corporation
Page : 338 pages
File Size : 26,40 MB
Release : 2012-06-11
Category : Mathematics
ISBN : 0486154661
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
Page : 240 pages
File Size : 37,92 MB
Release : 2005-08-09
Category : Mathematics
ISBN : 0387255303
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