Challenging Problems in Geometry (Dover Books on Mathematics) by Alfred S. Posamentier (PDF)

Description

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 other subjects. Within each topic, the problems are arranged in approximate order of difficulty. Detailed solutions (as well as hints) are provided for all problems, and specific answers for most.Invaluable as a supplement to a basic geometry textbook, this volume offers both further explorations on specific topics and practice in developing problem-solving techniques.

User’s Reviews

Editorial Reviews: About the Author Al Posamentier is currently Dean of the School of Education and Professor of Mathematics Education at Mercy College, New York. He is Professor Emeritus of Mathematics Education at The City College of the City University of New York, and former Dean of the School of Education, where he was for 40 years. He is the author and co-author of more than 55 mathematics books for teachers, secondary and elementary school students, and the general readership. Dr. Posamentier is also a frequent commentator in newspapers and journals on topics relating to education. Alfred S. Posamentier: Math’s Champion Dr. Alfred S. Posamentier, Professor Emeritus of Mathematics Education at New York’s City College and, from 1999 to 2009, the Dean of City College’s School of Education, has long been a tireless advocate for the importance of mathematics in education. He is the author or co-author of more than 40 mathematics books for teachers, students, and general readers including The Fascinating Fibonacci Numbers (Prometheus, 2007) and Mathematical Amazements and Surprises: Fascinating Figures and Noteworthy Numbers (Prometheus, 2009) His incisive views on aspects of mathematics education may often be encountered in the Letters columns and on the op-ed pages of The New York Times and other newspapers and periodicals. For Dover he provided, with co-author Charles T. Salkind, something very educational and also fun, two long-lived books of problems: Challenging Problems in Geometry and Challenging Problems in Algebra, both on the Dover list since 1996. Why solve problems? Here’s an excerpt from a letter Dr. Posamentier sent to The New York Times following an article about Martin Gardner’s career in 2009: “Teachers shouldn’t think that textbook exercises provide problem-solving experiences — that’s just drill. Genuine problem solving is what Mr. Gardner has been espousing. Genuine problem solving provides a stronger command of mathematics and exhibits its power and beauty. Something sorely lacking in our society.”

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐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

⭐. The the harder problems you will find as classical theorems and examples in more advanced texts like Altshiller Courts’

⭐. 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.

⭐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.

⭐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.

⭐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.

⭐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.

⭐”Challenging Problems in Geometry” is exactly that – presenting problems in plane geometry with detailed answers. In addition to the problems the book offers “challenges” to the reader, which may be viewed as tangent topics to the problems. It is clearly written and with instructive diagrams.

⭐Excellent

⭐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 problems! I am a mathematics teacher with deep interest in advanced problems. So I can say for sure that this book is not for a beginner at all. Those who are preparing for Olympiads can try.

⭐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.

⭐Possui vários exemplos e exercícios, abrange toda geometria plana e possui a resolução de todos os exercícios. Muito bom para consolidar os conhecimentos em Geometria Plana .

⭐

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