Geometric Transformations

Răzvan Gelca, Ionuţ Onişor, Carlos Yuzo Shine

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English

Springer Nature Switzerland AG
16 November 2023

Groups & group theory; Geometry

Series: Problem Books in Mathematics

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.

By: Răzvan Gelca, Ionuţ Onişor, Carlos Yuzo Shine
Imprint: Springer Nature Switzerland AG
Country of Publication: Switzerland
Edition: 2022 ed.
Dimensions: Height: 235mm, Width: 155mm,
Weight: 896g
ISBN: 9783030978488
ISBN 10: 3030978486
Series: Problem Books in Mathematics
Pages: 578
Publication Date: 16 November 2023
Audience: College/higher education , A / AS level
Format: Paperback
Publisher's Status: Active

Razvan Gelca is a Professor at Texas Tech University, USA, and holds a PhD in Mathematics from the University of Iowa, USA (1997). He coached the US International Mathematical Olympiad Team and co-authored, with Titu Andreescu, the books “Putnam and Beyond,” published by Springer, and “Mathematical Olympiad Challenges” (Birkhäuser), both now in their 2nd edition. Ionut Onisor is a Professor at the Colegiul National de Informatica Tudor Vianu, Romania. Carlos Yuzo Shine teaches at the Colégio Etapa, Brazil. He studied Production Engineering at the University of São Paulo, Brazil, and holds a Master’s degree (2018) from Texas A&M University, USA. He has been coordinating and coaching Mathematical Olympiad teams in Brazil since 2002.

Reviews for Geometric Transformations

“This book … is a nice addition to the literature. … for instructors teaching geometry courses in which these are a topic, this book should provide an excellent source of interesting examples and problems. The large number of solved problems should also make useful reading for people preparing for mathematical contests and Olympiads.” (Mark Hunacek, MAA Reviews, October 4, 2022)