TY - BOOK ID - 103609879 TI - Geometric Transformations AU - Gelca, Rǎzvan AU - Onisor, Ionut AU - Shine, Carlos Yuzo PY - 2022 SN - 303089116X 3030891178 PB - Cham : Springer International Publishing : Imprint: Springer, DB - UniCat KW - Mathematics. KW - Geometry. KW - Geometry KW - Mathematics KW - Euclid's Elements KW - Math KW - Science KW - Geometria KW - Matemàtica KW - Congruències (Geometria) KW - Dibuix lineal KW - Envolupants (Geometria) KW - Esfera KW - Geometria algebraica KW - Geometria computacional KW - Geometria conforme KW - Geometria convexa KW - Geometria de l'espai KW - Geometria diferencial KW - Geometria euclidiana KW - Porismes KW - Programació geomètrica KW - Ràtio i proporció KW - Similitud (Geometria) KW - Teorema de Pitàgores KW - Transformacions (Matemàtica) KW - Trigonometria KW - Geometria en l'art KW - Group theory. KW - Group Theory and Generalizations. KW - Mathematics Education. KW - Study and teaching . KW - Groups, Theory of KW - Substitutions (Mathematics) KW - Algebra UR - https://www.unicat.be/uniCat?func=search&query=sysid:103609879 AB - 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. ER -