Challenging Problems in Geometry

by Charles T. Salkind and Alfred S. Posamentier

Book Overview

Designed for high school students and teachers with an interest in mathematical problem-solving, this volume offers a wealth of nonroutine problems in geometry that stimulate students to explore unfamiliar or little-known aspects of mathematics. Included are nearly 200 problems dealing with congruence and parallelism, the Pythagorean theorem, circles, area relationships, Ptolemy and the cyclic quadrilateral, collinearity and concurrency, and many...

• Format: Paperback
• Language: English
• ISBN: 0486691543
• ISBN13: 9780486691541
• Release Date: May 1996
• Publisher: Dover Publications
• Length: 272 Pages
• Weight: 0.68 lbs.
• Dimensions: 0.5" x 5.4" x 8.5"

Customer Reviews

Learning geometry from the principles

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.

Very good after the basics

This is a great book! But, don't buy it if you don't know the basics well. You'll get frustrated easily and leave geometry. For beginning this is what I recommend: [...] Firstly, don't try a problem for 10 minutes and then just look at the solution. This way, you'll gain nothing from the book. You HAVE to try these problems for at least an hour (some may even take up to 2-3 hours)if you can't solve them. You can, however, break this up into pieces. For example, sit for about 15-25 minutes with one line of attack and then if couldn't solve it, then come back when you have time and give a try with another line of attack. And, let me tell you, when you do solve a problem after trying it for 1-2 hours, it'll be motivation enough to move on to the next problem. I especially like this book because I can hide it under my desk at school :) Also recommended is Geometry Revisited (buy it with this if you can).

Great Problems for Pondering the Greatness of Geometry

In a very well organized fashion the authors have amassed a fabulous collection of geometry problems that are quite challenging indeed. Although most high schoolers will likely have difficulty it can be used wisely as a study tool since they have sections for hints and finally a solutions section. It should be noted that other solutions are possible but the ones given are very easy to follow. A fun time for all geometry teachers (like me) and good students.

Great book on geometry.

Geometry problems are my favorite sort of math problems to do, because many geometry problems require, literally looking at the problem in a different way; a slight twist on the facts that you are using and the problem becomes much easier. It's usually a simple, yet ingenious insight that often solves the problem.To that end, this book does not disappoint. I highly recommend this book, for it contains such problems, and at the end of the first section of problems, I had developed a sort of intuition for Euclidean 'way' of thinking. I am far from finishing this book, but I think it would take me a few years to do so. The book is broken down into several chapters. The first chapter contains the problems, the next are the solutions, the next are hints to the problem, and finally an appendix of useful theorems and formulas. The useful theorems are mostly the results of Euclid's Book 1 and 3, and the immediate consequences of those theorems, e.g., the sum of the angles of a convex quadrilateral is 360. The hint chapter may be too helpful for it usually outlines the steps you need. I would have preferred several hint chapters that are progressively more helpful. The solution section may show more than one solution to a problem. There were a few times my solution was not found in the back of the book, but that's not a fault of the book, but a delight if you can come up with an original solution!The problem chapter is broken down into what I would call fundamentals and advanced sections. There are over 200 problems.The fundamental section is further broken down into parts, either by method, e.g., similar triangles/pythagorean's theorem, or theme, e.g., problems concerning 'circles' and problems concerning 'areas'. Many the problems can be solved in different ways. The first section of problems can be done with a purely Euclidean style approach. But lots of problems require a *little* algebra, mainly to economize on thought, e.g., a variable place holder for proportions, and a simple formula or two, and of course Euclid's theorems. Each section is not isolated, they sort of build on the first part of this section.The advanced section has a part containing a 'mixture' of techniques to use, and again themes which may not be familiar to the beginner, e.g., Simson lines, and Ceva's theorem.The problems are of proof, or finding the measure of a line, angle, area, or finding the algebraic formula for a collection of objects. So far, I have not encountered a single construction problem. Some of these problems may be quite easy to solve, and some can be quite hard! For instance, one of the problems asks you to prove Heron's formula. The Euclidean proof takes several pages, and I would say is beyond that for a math olympiad. Most problems, are of course, not this hard.You may have a tendency to want to 'angle-chase' or plug and play a formula. Such thinking will cause you to go mad! You'll endlessly try to some up combinations of angles, and co

Superb book

This book is a great one. Invaluable as a supplement to a basic geometry textbook. It includes approximately 200 problems dealing with congruence and parallelism, circles, area relationships, collinearity and concurrency and many other subjects. Detailed solutions and hints are provided for all problems, and specific answers for most. I highly recommend this book to anyone looking for a great book at an affordable price. Buy it. You won't regret it.