Geometric Transformations I (Number 8) (Bk. 1) First Thus Edition

by I. M. Yaglom (Author)

5 customer reviews

ISBN-13: 978-0883856086

ISBN-10: 0883856085

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Almost everyoneis acquainted with plane Euclidean geometry as it is usually taught in high school. This book introduces the reader to a completely different way of looking at familiar geometrical facts. It is concerned with transformations of the plane that do not alter the shapes and sizes of geometric figures. Such transformations play a fundamental role in the group theoretic approach to geometry.

The treatment is direct and simple. The reader is introduced to new ideas and then is urged to solve problems using these ideas. The problems form an essential part of this book and the solutions are given in detail in the second half of the book.

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

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Product Details

Series: Number 8 (Book 8)
Paperback: 140 pages
Publisher: Mathematical Assn of Amer; First Thus edition (June 1962)
Language: English
ISBN-10: 0883856085
ISBN-13: 978-0883856086
Product Dimensions: 0.5 x 6.2 x 9 inches
Shipping Weight: 8.8 ounces
Average Customer Review: 4.8 out of 5 stars See all reviews (5 customer reviews)
Amazon Best Sellers Rank: #1,886,952 in Books (See Top 100 in Books)
- #1053 in Books > Textbooks > Science & Mathematics > Mathematics > Geometry
- #2013 in Books > Science & Math > Mathematics > Geometry & Topology

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Most Helpful Customer Reviews

10 of 10 people found the following review helpful

Problem solving for Olympians

By J. Bogaarts on December 3, 2007

Format: Paperback Verified Purchase

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.

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6 of 6 people found the following review helpful

Excellent step-by-step introduction to transformations

By David Bakin on April 20, 2006

Format: Paperback Verified Purchase

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)

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10 of 12 people found the following review helpful

Transformations Review.

By gautam on June 17, 2000

Format: Paperback

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.

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A Wonderful Book

By Dr S Muralidharan on December 29, 2012

Format: Paperback

Geometric Transformations is a wonderful book teaching geometry from a modern perspective - using Geometric transformations. The three construction problems author mentions in the Introduction appear to be very different but he shows that there is a unifying theme connecting them - he solves all the three problems in a most natural way with very a few lines of proof. You are amazed at the beauty of the argument and wonder why you are not introduced to Geometry in this natural way.
On the whole a very enjoyable book. I wish every school teacher teaching Geometry should read - better - master this book. Then he/she can tranmit the joy of Geometry to the students.

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0 of 1 people found the following review helpful

excellent

By Michael Seyller on December 28, 2011

Format: Paperback Verified Purchase

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.

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