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.
