Challenging Problems in Geometry (Dover Books on Mathematics)

This book is suitable for anyone who want to learn advanced high school geometry or want to participate in any mathematical contest and have to learn much though not really new on it. The problems are set from the quite easy to advanced, with many of them are quite simple so you don't get frustrated because you can't do any of the problems. It covers the basic and common problems in math contest. Unfortunately, it don't have good set of theorems. Sure, it's written on the back but they're not easy to navigate. Also, many of them are not really basic even for contest geometry. Like its title, 'Challenging' is sure quite challenging, since many of the problems, though not really hard, need deeper thinking and you need to draw the 'help line' to solve the problem. The hints written on the back is not really helpful. Overall, for those who want to improve skills, participate in contest, or teacher who wants to make a surprise test, this book is a really good source of information.

It's late at night, hard day's night :) The girl is sleeping already, the dogs snoring quietly in the kitchen, I'm about to go to sleep. But before that - just one look in this book, just one problem to fall asleep with. Ah, hour an a half later when the problem is solved I really off to bed :) It's such a fun book. Some of the problems are unimaginary hard. Some are easier. All of them are enjoyable, challenging and satisfying. For whom who loves geometry and loves to play with proofs and theorems - You will love it.

Posamentiers' book is a little bit unbalanced. It contains around 200 problems with solutions. The easy problems are just what you would expect in the exercises sections of an introduction to Euclidean geometry like Kiselev's Geometry / Book I. Planimetry . The the harder problems you will find as classical theorems and examples in more advanced texts like Altshiller Courts' College Geometry: An Introduction to the Modern Geometry of the Triangle and the Circle (Dover Books on Mathematics) . A more balanced text would have contained more intermediate problems and the harder ones would have been more "original". The methods used are purely synthetic, no analytic geometry. The book is aimed at an advanced high school level audience. Prerequisite is the stuff you find in a book like kiselev I mentioned above. If you need a book to train your geometric problem solving abilities I think that Altshiller Courts' book is a better choice although there are no solutions to the exercises in that book. But what use are the solutions? Problems should be solved and not looked up! For many problems, especially the hard ones, several solutions are provided. To me this is what makes the book attractive.

Instead of doing what most other geometry problem books do - pose problems and give shortened answers - Posamentier has chosen a different tack. This book has 45 pages of Problems, 175 pages of Solutions, and 18 pages of Hints. This enables the reader to get a Hint instead of the full solution. So far, the Hints are spot on. At the end is a numbered list of all the Definitions, Postulates and Theorems used as well as a list of Selected Formulae. The book is structured into two sections: the first is suitable for use as exam questions in a standard high school geometry course while the second section covers advanced Euclidean topics. The chapters in the second section are: A Geometric Potpourri, Ptolomy and the Cyclic Quadrilateral, Menelaus and Ceva: Collinearity and Concurrency, The Simson Line, and The Theorem of Stewart. This book is certain to satisfy anyone who wants to continue their Euclidean geometry education.

I liked this book very much. I solved every single problem in the book with two students that I tutor for International Math Olympiads and carefully read the hints and solutions proposed at the end of the book. They really teach how to "attack" geometry problems using simple stuff like angle chasing, drawing parallel lines etc. I cannot recommend this book more to the readers with some mathematical sophistication. I even have a suggestion for parents that have some sort of mathematical background (engineers, bankers, doctors, etc.): If you want to spend quality time with your children, get this book and enjoy solving the problems together. I cannot imagine a more amusing pastime. I am looking forward to seeing new titles from the authors.

I bought this book trying to teach Geometry to my daughter in 9th grade. The collection of problems is exceptional. Only a third of the book lists the problems. Rest of the book has the solutions. Several problems have multiple solutions. I learned just by reading through several solutions. And I re-learned explaining them to my daughter. Most of the problems are not for the faint of heart. But the hours spent discovering the solutions with your student will be very rewarding. It was for me.

This books presents a lot of problems to solve. One challenge after another, you can find several problems and better still if you get stuck, you have hints that really help in solving the problems, and one, sometime two or even three different ways of solving it. As written at Plato's academy, for geometers only, you have to be willing to spend sometime doing geometry.

Fine book, but not good for what I wanted it for, which was to pull challenge problems for HS Geometry students.

This book provides a well chosen, intriguing and challenging collection of geometry problems for the young minds and for those who would like to reignite their mental powers. In general, geometry problems demand more of logical reasoning than dry calculations. Sadly, Euclidean geometry is hardly taught beyond secondary school curricula. The contents of this book therefore fill up the gaping chasm that exists in most modern mathematics programs of higher education. Historical theorems of Ptolemy, Menelaus and Ceva are explained lucidly enough to be understood even by secondary school students. Solutions provided make the book ideal for self study. A really cheap price for a great book that makes one feel nostalgic. I am thankful to amazon for its great service in making this book available to me.

Excellent

Very challenging yet interesting problems! I love this book so much!

If you are looking for something to prepare for mathematical games or problem-solving this book is for you. Comprehends a long list of problems with detailed step by step solutions.

Excelente livro, com vários níveis de exercícios, pouco explorados pelos livros didáticos.