Euclidean Geometry in Mathematical Olympiads

Problem Books

by Evan Chen

This is a challenging problem-solving book in Euclidean geometry, assuming nothing of the reader other than a good deal of courage. Topics covered included cyclic quadrilaterals, power of a point, homothety, triangle centers; along the way the reader will meet such classical gems as the nine-point circle, the Simson line, the symmedian and the mixtilinear incircle, as well as the theorems of Euler, Ceva, Menelaus, and Pascal. Another part is dedicated to the use of complex numbers and barycentric coordinates, granting the reader both a traditional and computational viewpoint of the material. The final part consists of some more advanced topics, such as inversion in the plane, the cross ratio and projective transformations, and the theory of the complete quadrilateral. The exposition is friendly and relaxed, and accompanied by over 300 beautifully drawn figures. The emphasis of this book is placed squarely on the problems. Each chapter contains carefully chosen worked examples, which explain not only the solutions to the problems but also describe in close detail how one would invent the solution to begin with. The text contains as selection of 300 practice problems of varying difficulty from contests around the world, with extensive hints and selected solutions. This book is especially suitable for students preparing for national or international mathematical olympiads, or for teachers looking for a text for an honor class.

Genres: Mathematics

326 pages, Paperback

Published October 31, 2016

Reviews

[MAHIR LABIB · Rating 5 out of 5]

This book is full of problems One can first read theories and then do the Problems or reverse I a big thanks is given to Evan Chen(web: https://web.evanchen.cc/olympiad.html) I want a similar book on algebra

[Charles · Rating 5 out of 5]

While Euclidean geometry was codified almost 2,500 years ago, the field has been anything but stagnant since then. This book is an existence proof of how dynamic it is. The problems are original, challenging and have that achievable level of difficulty that makes them worthy Mathematical Olympiad material.
Each chapter opens with some explanation of the material needed to understand and work through the problems. Theorems and proofs are stated, followed by example problems with detailed solutions. Each chapter ends with a set of Olympiad-style problems. Brief hints to the methods used to solve the end-of-chapter problems appear in appendix B with selected solutions given in appendix C.
If you are a coach of budding Mathematical Olympians or an instructor looking for challenging problems in Euclidean geometry, this book contains what you are looking for. The material is hard, yet so revealing of the beauty that is geometry.

[Indranil]

Great

[Ym.R.]

כשהתחלתי לקרוא את הספר הזה רציתי משהו יחסית עקבי, שמתחיל מהאקסיומות וכו', מהבחינה הזו הספר לא ממש סיפק אותי. כמובן שהוא ספר מצוין שכולל הרבה מאוד ידע מעבר לבעיה זו

[Juan Belza · Rating 5 out of 5]

Great book. Gradual increase in difficulty while slowly introducing new concepts. Great reading experience and selection of problems.

[Emmett · Rating 5 out of 5]

pretty cool

[Yong Joon Kim · Rating 5 out of 5]

Undoubtedly one of the best olympiad books ever written.

[Andy Zhang · Rating 5 out of 5]

"This is your last chance. After this, there is no turning back. You take the blue pill--the story ends, you wake up in your bed and believe whatever you want to believe. You take the red pill--you stay in Wonderland and I show you how deep the rabbit-hole goes."