Mathematics via Problems: Part 2: Geometry (MSRI Mathematical Circles Library, 26)

Mathematics via Problems: Part 2: Geometry (MSRI Mathematical Circles Library, 26)

This book is a translation from Russian of Part II of the book Mathematics Through Problems: From Olympiads and Math Circles to Profession. Part I, Algebra, was recently published in the same series. Part III, Combinatorics, will be published soon. The main goal of this book is to develop important parts of mathematics through problems. The authors tried to put together sequences of problems that allow high school students (and some undergraduates) with strong interest in mathematics to discover and recreate much of elementary mathematics and start edging into more sophisticated topics such as projective and affine geometry, solid geometry, and so on, thus building a bridge between standard high school exercises and more intricate notions in geometry. Definitions and/or references for material that is not standard in the school curriculum are included. To help students that might be unfamiliar with new material, problems are carefully arranged to provide gradual introduction into each subject. Problems are often accompanied by hints and/or complete solutions. The book is based on classes taught by the authors at different times at the Independent University of Moscow, at a number of Moscow schools and math circles, and at various summer schools. It can be used by high school students and undergraduates, their teachers, and organizers of summer camps and math circles. In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession. Zaslavsky and Skopenkov's 'Mathematics via Problems Part 2: Geometry' is not your average textbook. Though it touches upon most high school geometry topics, it does go beyond the level required by the standards. In fact, it is not an instructive book for students' first time engaging with relevant geometry content; rather, it is a collection of relevant problems meant to be pondered and discussed. The book serves as a problem-solving agenda for mathematics clubs and communities of practice called 'math circles.' Math circles are vertical clubs of mathematicians, from elementary-aged students to professionals and researchers, that support engagement with mathematics via problems. --Jasmine Sourwine, Iowa State University, MAA Reviews Alexey A. Zaslavsky: Central Economical and Mathematical Institute, Moscow, Russia and Moscow Power Energetic Institute, Moscow, Russia, Mikhail B. Skopenkov: National Research University Higher School of Economics, Moscow, Russia and Institute for Information Transmission Problems RAS, Moscow, Russia