LEADER 03946nam 22006735 450 001 9910547289603321 005 20240215144404.0 010 $a3-030-89117-8 024 7 $a10.1007/978-3-030-89117-6 035 $a(MiAaPQ)EBC6891234 035 $a(Au-PeEL)EBL6891234 035 $a(CKB)21250894500041 035 $a(DE-He213)978-3-030-89117-6 035 $a(PPN)260825956 035 $a(EXLCZ)9921250894500041 100 $a20220216d2022 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aGeometric Transformations /$fby R?zvan Gelca, Ionu? Oni?or, Carlos Yuzo Shine 205 $a1st ed. 2022. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2022. 215 $a1 online resource (581 pages) 225 1 $aProblem Books in Mathematics,$x2197-8506 300 $aIncludes index. 311 08$aPrint version: Gelca, R?zvan Geometric Transformations Cham : Springer International Publishing AG,c2022 9783030891169 327 $aIntroduction -- 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. 330 $aThis textbook teaches the transformations of plane Euclidean geometry through problems, offering a transformation-based perspective on problems that have appeared in recent years at mathematics competitions around the globe, as well as on some classical examples and theorems. It is based on the combined teaching experience of the authors (coaches of several Mathematical Olympiad teams in Brazil, Romania and the USA) and presents comprehensive theoretical discussions of isometries, homotheties and spiral similarities, and inversions, all illustrated by examples and followed by myriad problems left for the reader to solve. These problems were carefully selected and arranged to introduce students to the topics by gradually moving from basic to expert level. Most of them have appeared in competitions such as Mathematical Olympiads or in mathematical journals aimed at an audience interested in mathematics competitions, while some are fundamental facts of mathematics discussed in the framework of geometric transformations. The book offers a global view of the geometric content of today's mathematics competitions, bringing many new methods and ideas to the attention of the public. Talented high school and middle school students seeking to improve their problem-solving skills can benefit from this book, as well as high school and college instructors who want to add nonstandard questions to their courses. People who enjoy solving elementary math problems as a hobby will also enjoy this work. 410 0$aProblem Books in Mathematics,$x2197-8506 606 $aGeometry 606 $aGroup theory 606 $aMathematics$xStudy and teaching  606 $aGeometry 606 $aGroup Theory and Generalizations 606 $aMathematics Education 606 $aGeometria$2thub 608 $aProblemes i exercicis$2thub 608 $aLlibres electrònics$2thub 615 0$aGeometry. 615 0$aGroup theory. 615 0$aMathematics$xStudy and teaching . 615 14$aGeometry. 615 24$aGroup Theory and Generalizations. 615 24$aMathematics Education. 615 7$aGeometria 676 $a516 676 $a516.0076 700 $aGelca$b Ra?zvan$f1967-$0731262 702 $aOnisor$b Ionut 702 $aShine$b Carlos Yuzo 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910547289603321 996 $aGeometric transformations$92920271 997 $aUNINA