Geometric transformations / Razvan Gelca, Ionut Onisor, Carlos Yuzo Shine.
Gelca, Rǎzvan, 1967- author.; Onisor, Ionut, author.; Shine, Carlos Yuzo, author.
2022
QA445 .G45 2022
Available Online

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Title Geometric transformations / Razvan Gelca, Ionut Onisor, Carlos Yuzo Shine.
Author Gelca, Rǎzvan, 1967- author.
ISBN 9783030891176 (electronic bk.)
3030891178 (electronic bk.)
9783030891169
303089116X
DOI https://doi.org/10.1007/978-3-030-89117-6
Published Cham : Springer, [2022]
Copyright ©2022
Language English
Description 1 online resource : illustrations.
Other Standard Identifiers 10.1007/978-3-030-89117-6 doi
Call Number QA445 .G45 2022
Dewey Decimal Classification 516
Summary 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.
Note Includes index.
Access Note Access limited to authorized users.
Source of Description Description based on print version record.
Added Author Onisor, Ionut, author.
Shine, Carlos Yuzo, author.
Series Problem books in mathematics.
Available in Other Form Geometric transformations.
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Introduction
Part I: Problems - 1. Isometries
2. Homotheties and Spiral Similarities
3. Inversions
4. A Synthesis
Part II: Hints - 5. Isometries
6. Homotheties and Spiral Similarities
7. Inversions
8. A Synthesis
Part III: Solutions - 9. Isometries
10. Homotheties and Spiral Similarities
11. Inversions
12. A Synthesis.

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