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Geometric Transformations I (Number 8) (Bk. 1), by I. M. Yaglom
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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.
- Sales Rank: #535407 in Books
- Brand: Brand: Mathematical Assn of Amer
- Published on: 1962-06
- Original language: English
- Number of items: 1
- Dimensions: 9.00" h x 6.25" w x .50" l, .35 pounds
- Binding: Paperback
- 140 pages
- Used Book in Good Condition
About the Author
Issac Moisevitch Yaglom graduated from Sverdlovsk University in 1942 and received his Candidate's Degree in 1945. He then moved onto the Moscow State Pedagogical Institute since 1957 and is the author of many scientific publications.
Most helpful customer reviews
12 of 12 people found the following review helpful.
Problem solving for Olympians
By J. Bogaarts
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.
6 of 6 people found the following review helpful.
Excellent step-by-step introduction to transformations
By David Bakin
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)
10 of 12 people found the following review helpful.
Transformations Review.
By gautam
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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