Geometric Transformations Volume 2 Projective Transformations pdf

Geometric Transformations Volume 2 Projective Transformations

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Description of the Book:

This is the second volume of a two-volume translation of the Russian book Geometric Transformations, by Modenov and Parkhomenko. It contains a translation of Chapters V (with Appendix) and VI of the original, here Chapters I and II, respec­ tively.The greater portion of this volume is concerned with projec­ tive transformations. These are the collinearity-preserving trans­ formations of the projective plane.

It turns out that many of the mappings of the ordinary plane that preserve collinearity may best be regarded as defined on an extended object, called the projective plane. In particular, the affine transformations that were considered in Chapter IV of the first volume (Euclidean and Affine Transformations) may very conveniently be regarded as those projective transformations which fix the ideal line.Chapter I therefore starts with the motivation of the construc­ tion of the projective plane, followed by a number of alternative constructions for it. Later most of the basic facts are proved, and some of the applications outlined.Chapter II deals with an independent topic, but at the same level of sophistication. However, the appendices to Chapter I refer to more advanced concepts, and these are not motivated or treated in detail. The unprepared reader should not be afraid to read through them, picking up what he can, and taking the rest on faith.

They serve as distant glimpses of some of the methods and concerns of modern geometry and algebra, respectively.
In general, this book is probably at about the right level for an undergraduate reader. However, interest and ability are more relevant for profiting from it than is quantity of previous know­ ledge.

• Creator/s: P.S. Modenov, A.S. Parkhomenko
• Date: 1965
• Book Topics/Themes: geometry, projections, projective mapping, harmonic sets, projective transformations, geometric inversion, circle transformation, principle of duality

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