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Author : Clayton W. Dodge
Publisher : Courier Corporation
Page : 306 pages
File Size : 50,14 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 : James Richard King
Publisher :
Page : pages
File Size : 26,33 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 : Roger A. Johnson
Publisher : Courier Corporation
Page : 338 pages
File Size : 38,34 MB
Release : 2013-01-08
Category : Mathematics
ISBN : 048615498X
This classic text explores the geometry of the triangle and the circle, concentrating on extensions of Euclidean theory, and examining in detail many relatively recent theorems. 1929 edition.
Author : George E. Martin
Publisher : Springer Science & Business Media
Page : 251 pages
File Size : 38,16 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 : Răzvan Gelca
Publisher : Springer Nature
Page : 581 pages
File Size : 11,60 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 : Hans Schwerdtfeger
Publisher : Courier Corporation
Page : 228 pages
File Size : 15,51 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 : Norman W. Johnson
Publisher : Cambridge University Press
Page : 455 pages
File Size : 10,97 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 : Owen Byer
Publisher : American Mathematical Soc.
Page : 461 pages
File Size : 34,57 MB
Release : 2010-12-31
Category : Mathematics
ISBN : 0883857634
Euclidean plane geometry is one of the oldest and most beautiful topics in mathematics. Instead of carefully building geometries from axiom sets, this book uses a wealth of methods to solve problems in Euclidean geometry. Many of these methods arose where existing techniques proved inadequate. In several cases, the new ideas used in solving specific problems later developed into independent areas of mathematics. This book is primarily a geometry textbook, but studying geometry in this way will also develop students' appreciation of the subject and of mathematics as a whole. For instance, despite the fact that the analytic method has been part of mathematics for four centuries, it is rarely a tool a student considers using when faced with a geometry problem. Methods for Euclidean Geometry explores the application of a broad range of mathematical topics to the solution of Euclidean problems.
Author : M. N. Aref
Publisher : Courier Corporation
Page : 274 pages
File Size : 10,31 MB
Release : 2010-01-01
Category : Mathematics
ISBN : 0486477207
Based on classical principles, this book is intended for a second course in Euclidean geometry and can be used as a refresher. Each chapter covers a different aspect of Euclidean geometry, lists relevant theorems and corollaries, and states and proves many propositions. Includes more than 200 problems, hints, and solutions. 1968 edition.
Author : Robin Hartshorne
Publisher : Springer Science & Business Media
Page : 535 pages
File Size : 42,90 MB
Release : 2013-11-11
Category : Mathematics
ISBN : 0387226761
This book offers a unique opportunity to understand the essence of one of the great thinkers of western civilization. A guided reading of Euclid's Elements leads to a critical discussion and rigorous modern treatment of Euclid's geometry and its more recent descendants, with complete proofs. Topics include the introduction of coordinates, the theory of area, history of the parallel postulate, the various non-Euclidean geometries, and the regular and semi-regular polyhedra.