تحولات هندسی، جلد دوم: تحولات پروژه‌ای

This is the second volume of a two-volume translation of theRussianbookGeometricTransformations,byModenovandParkhomenko. It contains a translationofChapters V(withAppendix) and VI of the original, here Chapters I and II, respectively.The greater portion of this volume is concerned with projective transformations. These are the collinearity-preserving transformations of the projective plane. It turns out that many of themappings of the ordinary plane that preserve collinearitymaybest be regarded as defined on an extended object, calledtheprojective plane. In particular, the affine transformationsthatwere considered in Chapter IV of the first volume(EuclideanandAffineTransformations)may very conveniently be regarded asthose projective transformations which fix theideal line. Geometric Transformations, Volume 2: Projective Transformations focuses on collinearity-preserving transformations of the projective plane. The book first offers information on projective transformations, as well as the concept of a projective plane, definition of a projective mapping, fundamental theorems on projective transformations, cross ratio, and harmonic sets. Examples of projective transformations, projective transformations in coordinates, quadratic curves in the projective plane, and projective transformations of space are also discussed. The text then examines inversion, including the power of a point with respect to a circle, definition and properties of inversion, and circle transformations and the fundamental theorem. The manuscript elaborates on the principle of duality. The manuscript is designed for use in geometry seminars in universities and teacher-training colleges. The text can also be used as supplementary reading by high school teachers who want to extend their range of knowledge on projective transformations. Content: ACADEMIC PAPERBACKS, Page ii Front Matter, Page iii Copyright, Page iv Preface to Volume 2 of the English Edition, Pages v-vi Translator's Note, Page vii Preface to the Russian Edition, Page ix CHAPTER I - Projective Transformations, Pages 1-110 CHAPTER II - Inversion, Pages 111-132 Subject Index, Pages 133-136