[PDF] Geometric Transformations Iv eBook

Author : I. M. Yaglom
Publisher : MAA
Page : 302 pages
File Size : 14,39 MB
Release : 2009-10-15
Category : Mathematics
ISBN : 9780883856482

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A comprehensive treatment of the geometry of circular transformations.

Author : P. S. Modenov
Publisher : Academic Press
Page : 149 pages
File Size : 35,87 MB
Release : 2014-05-12
Category : Mathematics
ISBN : 1483261492

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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.

Author : I. M. Yaglom
Publisher : Mathematical Association of America
Page : 293 pages
File Size : 41,9 MB
Release : 2009-10-15
Category : Mathematics
ISBN : 9780883856482

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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.

Author : Castellani Leonardo
Publisher : World Scientific Publishing Company
Page : 2216 pages
File Size : 21,7 MB
Release : 1991-06-11
Category :
ISBN : 9814590738

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This book provides a self-contained presentation of supergravity theories from its fundamentals to its most recent union with string and superstring theories, which are also reviewed in a self-contained manner. The subject is presented consistently in a unified geometric formalism, relying on the calculus of exterior forms and the mathematics needed to develop the theory is explained in appropriate chapters.