03946nam 22006615 450 99646641800331620240215144404.03-030-89117-810.1007/978-3-030-89117-6(MiAaPQ)EBC6891234(Au-PeEL)EBL6891234(CKB)21250894500041(DE-He213)978-3-030-89117-6(PPN)260825956(EXLCZ)992125089450004120220216d2022 u| 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierGeometric Transformations[electronic resource] /by Răzvan Gelca, Ionuţ Onişor, Carlos Yuzo Shine1st ed. 2022.Cham :Springer International Publishing :Imprint: Springer,2022.1 online resource (581 pages)Problem Books in Mathematics,2197-8506Includes index.Print version: Gelca, Răzvan Geometric Transformations Cham : Springer International Publishing AG,c2022 9783030891169 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.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.Problem Books in Mathematics,2197-8506GeometryGroup theoryMathematicsStudy and teaching GeometryGroup Theory and GeneralizationsMathematics EducationGeometriathubProblemes i exercicisthubLlibres electrònicsthubGeometry.Group theory.MathematicsStudy and teaching .Geometry.Group Theory and Generalizations.Mathematics Education.Geometria516Gelca Rǎzvan1967-731262Onisor IonutShine Carlos YuzoMiAaPQMiAaPQMiAaPQBOOK996466418003316Geometric transformations2920271UNISA