Geometric Transformations: Volume 4, Circular Transformations (Anneli Lax New Mathematical Library) by I. M. Yaglom (PDF)

Description

The familiar plane geometry of secondary 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. 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 elementary geometry and trigonometry.

User’s Reviews

Editorial Reviews: Book Description This is the fourth volume of Yaglom’s Geometric Transformations. This volume develops the geometry of transformations of the plane that map circles to circles (conformal or anallagmatic geometry). The latter part of the book consists of detailed solutions of the problems posed throughout the text. From the Back Cover 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. About the Author I. M. Yaglom authored many books which have since become academic standards of reference. These include Complex Numbers in Geometry, Geometric Transformations, A Simple Non-Euclidean Geometry and its Physical Basis, and Probability and Information. He was Professor of Mathematics at Yaroslavl State University from 1974-83 and a technical consultant at the Academy of Pedagogical Sciences from 1984-88.Abe Shenitzer has translated many mathematics classics (from German, Polish and Russian into English). He retired in 1989 from York University, where he had been Professor of Mathematics since 1969. Read more

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

⭐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.

⭐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

⭐Great shape as described.

⭐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.

⭐Une perle!Du niveau de Altshiller-Court.Non amoureux de la géométrie: s’abstenir. Géomètres calculatoires: s’abstenir également.Ce tome est indépendant, largement, des trois autres précédents, mais l’ensemble est un monument.

⭐

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