In this post, we will see the book Geometric Transformations Volume 1 Euclidean And Affine Transformations by P.S. Modenov; A.S. Parkhomenko.

About the book

This is the first volume of a two-volume translation of the Russian book Geometric Transformations, by Modenov and Parkhomenko. This volume embraces Chapters I—IV; Vol­ume 2 (Projective Transformations) contains the translation of the original Chapters V and VI.

The treatment is elementary, and should be accessible to the high school senior. The prerequisites amount to some famil­ iarity with Euclidean geometry, including the use of coordi­ nates, elementary trigonometry, and linear equations (up to determinants). A little knowledge of vectors and conics might also be helpful. However, the material covered or referred to ranges much further, and should be of interest to a very broad spectrum of readers, from high school senior to college teacher.

This book is not designed to be a standard text. As will be seen from the introduction, the material covered is not usually included in the curriculum, and its style is more suitable for browsing than for systematic class study. The purpose of the book is rather to introduce the reader to a fascinating and not at all difficult area of geometry, at the same time acquainting him painlessly with some of the simpler methods and concepts of advanced mathematics. Since the topic is one for which everyone will have some intuitive feeling, and the exposition is consistently straightforward, there is no danger that the reader will find himself suddenly out of his depth.

This book is intended for use in geometry seminars in universities and teacher-training colleges. It may also be used as supplementary reading by high school teachers who wish to extend their range of knowledge. Finally, many sections may be used as source material for school mathematics clubs under the guidance of a teacher.

The subject matter is those transformations of the plane that preserve the fundamental figures of geometry: straight lines and circles. In particular, we discuss orthogonal, affine, pro­ jective, and similarity transformations, and inversions.

The treatment is elementary, though in a number of in­ stances (where a synthetic treatment seems more cumbersome) coordinate methods are used. A little use is also made of vec­ tor algebra, but the text here is self-contained.

In order to clarify a number of points, we give some elemen­ tary facts from projective geometry; also, in the addendum to Chapter I of Volume 2 (the topology of the projective plane), the structure of the projective plane is examined in greater detail.

You can get the book here.
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