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Author : Norman W. Johnson
Publisher : Cambridge University Press
Page : 455 pages
File Size : 16,54 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 : 32,76 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 : 13,22 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 : 17,71 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 : 29,18 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 : 20,83 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 : 43,61 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 : Shoshichi Kobayashi
Publisher : Springer Science & Business Media
Page : 192 pages
File Size : 34,22 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 3642619819
Given a mathematical structure, one of the basic associated mathematical objects is its automorphism group. The object of this book is to give a biased account of automorphism groups of differential geometric struc tures. All geometric structures are not created equal; some are creations of ~ods while others are products of lesser human minds. Amongst the former, Riemannian and complex structures stand out for their beauty and wealth. A major portion of this book is therefore devoted to these two structures. Chapter I describes a general theory of automorphisms of geometric structures with emphasis on the question of when the automorphism group can be given a Lie group structure. Basic theorems in this regard are presented in §§ 3, 4 and 5. The concept of G-structure or that of pseudo-group structure enables us to treat most of the interesting geo metric structures in a unified manner. In § 8, we sketch the relationship between the two concepts. Chapter I is so arranged that the reader who is primarily interested in Riemannian, complex, conformal and projective structures can skip §§ 5, 6, 7 and 8. This chapter is partly based on lec tures I gave in Tokyo and Berkeley in 1965.
Author : I. M. Yaglom
Publisher : MAA
Page : 302 pages
File Size : 29,90 MB
Release : 2009-10-15
Category : Mathematics
ISBN : 9780883856482
A comprehensive treatment of the geometry of circular transformations.
Author : David Gans
Publisher :
Page : 424 pages
File Size : 26,92 MB
Release : 1969
Category : Mathematics
ISBN :