Challenges in Geometry For Mathematical Olympians Past and Present
J. Bradley has been, for many years, deeply involved in training the United Kingdom teams for the International Mathematical Olympiad. This book contains a number of topics of geometric nature, in which lengths, areas, etc., have integer values. About 3500 years ago geometers were aware of the existence of right-angled triangles having integer sides (Pythagorean triangles) and may have had some methods for constructing them. Problems involving integers have always been considered fascinating (e.g. Fermat last theorem). In this book, the reader will also find problems concerning triangles and circles (circumcircle, incircle, nine-point-circle, etc.) It contains the proof of Pick’s theorem and also deals with rational points on curves and with polygons and solids. It is recommended for students who are interested in geometry and number theory and it is good preparation for competitions. The book contains numerous exercises, hints and solutions.