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Geometric Transformations: Volume 4, Circular Transformations

Name: Geometric Transformations: Volume 4, Circular Transformations
Brand: Mathematical Association of America
SKU: 01400426
Price: 63.79 EUR
Availability: InStock
Author: I. M. Yaglom
ISBN: 9780883856482

I. M. Yaglom

Lingua

Inglese

Libro In brossura

Codice Libristo: 01400426

Casa editrice Mathematical Association of America, ottobre 2009

The familiar plane geometry of secondary school - figures composed of lines and circles - takes on a... Descrizione completa

Codice Libristo: 01400426

156 b

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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.