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Geometric Transformations IV: Circular Transformations (Anneli Lax New Mathematical Library), by I. M. Yaglom
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The familiar plane geometry of high school figures composed of lines and circles takes on a new life when viewed as the study of properties that are preserved by special groups of transformations. No longer is there a single, universal geometry: different sets of transformations of the plane correspond to intriguing, disparate geometries.
This book is the concluding Part IV of Geometric Transformations, but it can be studied independently of Parts I, II, and III, which appeared in this series as Volumes 8, 21, and 24. Part I treats the geometry of rigid motions of the plane (isometries); Part II treats the geometry of shape-preserving transformations of the plane (similarities); Part III treats the geometry of transformations of the plane that map lines to lines (affine and projective transformations) and introduces the Klein model of non-Euclidean geometry.
The present Part IV develops the geometry of transformations of the plane that map circles to circles (conformal or anallagmatic geometry). The notion of inversion, or reflection in a circle, is the key tool employed. Applications include ruler-and-compass constructions and the Poincaré model of hyperbolic geometry.
The straightforward, direct presentation assumes only some background in high-school geometry and trigonometry. Numerous exercises lead the reader to a mastery of the methods and concepts. The second half of the book contains detailed solutions of all the problems.
- Sales Rank: #2205852 in Books
- Published on: 2009-09-14
- Original language: English
- Dimensions: 8.98" h x .59" w x 5.98" l, 1.10 pounds
- Binding: Paperback
- 285 pages
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
8 of 8 people found the following review helpful.
Long time waited....
By Francisco Bellot
The last volume of the Yaglom's serie about geometric transformations has been long time waited (the english version, of course), but it worth the time!
An excellent monography about inversion (or reflection in a circle, to follow the taste of the author)with many well chosen exercises and problems.
So, the non russian speaking mathematicians have the opportunity of complete the saga of geometric transformations, thanks of the work of Abe Shenitzer as translator and the MAA as publishers. Strongly recommended
2 of 2 people found the following review helpful.
Brilliant exposition
By Dr S Muralidharan
These days, Geometry is making a come back in the school curriculum in many parts of the world. 20 years ago, Feurbach's theoerm used to be taught in schools/colleges. Inversion as a technique of problem solving helped students to appreciate many beautiful theorems of Geometry. Alas, the last few years saw the demise of geometry from schools. With that,the ability to visualize also diminished and students found it difficult to appreciate Calculus. Fortunately, the four volumes Geometric Transformations are still available - and a keen student would get a very solid understanding of the methods of proof through the beautiful problems in these books. Particularly, the Volume 4 is about circular transformations. Inversion as a technique would also help students to appreciate Mobius transformations when they encounter the same as part of Complex Analysis course. Highly recommended for lovers of Geometry.
1 of 1 people found the following review helpful.
Yaglom's book in Geometry are true gems. I'm not ...
By Luis Ferroni
Yaglom's book in Geometry are true gems. I'm not saying too much about this book, just because it is long enough that I haven't finished it. However, there are some characteristics that could be very helpful for the buyers: the paperback is a bit weak, so treat the book carefully. It is not similar to the previous volumes of the collection at all. It is a bit different (even inside, where there are some restructuration with respect to the others). The book deserves each penny, but I can't say the same about the work that the editorial made with the softcover.
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