Customer Reviews

Geometric Transformations I (Number 8) (Bk. 1)

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This is an excellent introduction to geometric transformations. It is very useful for Competitions such as the AIME USAMO and IMO. Also, it is a great book for those interested in Mathematics.

This book (first of three) is an excellent step-by-step introduction to some geometric transformations (in this volume: translations, reflections, and rotations) in the synthetic style (i.e., no algebra). The exercises are very good and full solutions are given to all. Lots of drawings to make everything easy to understand.

I'm using this book to 'reintroduce' myself to geometry after being away from the study of mathematics for many years and it is great fun.

As part of the New Mathematical Library it is ideal for the advanced high school student or the enthusiast/amateur (like me).

UPDATE December 2009: Great news! Volume 4, on inversions in a circle was just published and is excellent! Geometric Transformations IV: Circular Transformations (New Mathematical Library)

The Yaglom geometric transformation books are aimed at a mathematical Olympiad audience. The books are not primarily about transformations, they are mainly about how to use transformations to solve problems. Yaglom wrote the book in Russian back in the fifties, presenting geometrical transformations techniques to geometric problem solving. He introduces transformation types and then shows how they can be used to solve problems that otherwise would sometimes be almost unsolvable using elementary (synthetic) methods. Then he presents a set of problems that vary from difficult to fiendish. Full solutions are provided, you will need them. The Russian book has chapters on congruence, similarity and projective transformations that are contained in the three English translations published by the MAA. It continues with sections on inversion transformations that are not (yet?) translated into English.

This is the first of three books, it deals with congruence transformations. Examples of congruence transformations are reflections in a line or in a point and translations (parallel movements). One could make up a set of problems that can be solved by simply applying a convenient transformation, but that is not how Yaglom works. Most problems use one ore more other themes (tricks) besides a transformation. So let this not be your first geometry problem book.

These are great books for problem solving.

book arrived timely, it is a bit higher level than expected, but satisfactory. I am certain I will be able to use this in my high school classes.