Preface; Preliminaries; Part I. Fundamentals: 1. Angle chasing; 2. Circles; 3. Lengths and rules; 4. Assorted configurations; Part II. Analytic Techniques: 5. Computational geometry; 6. Complex numbers; 7. Barycentric coordinates; Part III. Farther from Kansas: 8. Inversion; 9. Projective geometry; 10. Complete quadrilaterals; 11. Personal favorites; Part IV. Appendices: Appendix A. An ounce of linear algebra; Appendix B. Hints; Appendix C. Selected solutions; Appendix D. List of contests and abbreviations; Bibliography; Index; About the author.
A problem-solving book on Euclidean geometry, providing carefully chosen worked examples and over 300 practice problems from contests around the world.
Evan Chen is currently an undergraduate studying at the Massachusetts Institute of Technology. He won the 2014 USA Mathematical Olympiad, earned a gold medal at the IMO 2014 for Taiwan, and acts as a Problem Czar for the Harvard-MIT Mathematics Tournament.
The book is divided into four parts. Part I (""Fundamentals"") discusses a number of basic ideas that will be used repeatedly in the sequel. I hesitate to call this part of the book a ""review,"" because many of the topics covered here (e.g., Ceva's theorem, the power of a point) might well be new to a student who has not taken a college course in geometry. Part II (""Analytic Techniques"") does not, its name notwithstanding, involve analysis, but does cover a variety of useful techniques for tackling geometric problems: computational formulas, complex numbers, and barycentric coordinates. Part III (""Further from Kansas"") brings in more advanced ideas, with chapters on inversion with respect to a circle, the extended Euclidean plane (projective geometry), and complete quadrilaterals. Part IV contains a series of appendices, mostly consisting of hints and/or solutions to some of the problems in the earlier parts. A good understanding of high school geometry, and a fondness for solving problems, should be sufficient background for this book. There are topics covered here that are not generally covered in a high school course, but definitions are provided for these. The heart of a book like this is, of course, the problems. As I noted earlier, there are a great many of them, and by and large, they struck me as very difficult and involved. Even the diagrams for some of them can be a bit daunting. They should provide a good challenge for prospective test-takers, though the large number of unsolved problems might prove frustrating for some. Even if not used as the text for a geometry course, an instructor of such a course might want to keep the book handy as a potential source of challenging problems. And, as previously noted, students preparing for mathematics competitions, and their faculty coaches, should find this book very valuable."" - Mark Hunacek, MAA Reviews