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Geometric Transformations IV : Circular Transformations Circular Transformations. /
The familiar plane geometry of high 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 cor...
| Clasificación: | Libro Electrónico |
|---|---|
| Otros Autores: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge :
Cambridge University Press,
2011.
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| Colección: | Anneli Lax new mathematical library.
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| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 245 | 0 | 0 | |a Geometric Transformations IV : |b Circular Transformations |p Circular Transformations. / |c I.M. Yaglom, Translated by Abe Shenitzer. |
| 260 | |a Cambridge : |b Cambridge University Press, |c 2011. | ||
| 300 | |a 1 online resource | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a Anneli Lax New Mathematical Library ; |v v. 44 | |
| 500 | |a Title from publishers bibliographic system (viewed on 30 Jan 2012). | ||
| 505 | 0 | |a Cover -- Title page -- Contents -- 1 Reflection in a circle (inversion) -- 2 Application of inversionsto the solution of constructions -- Problems. Constructions with compass alone -- Problems involving the construction of circles -- Notes to Section 2 -- 3 Pencils of circles. The radical axis of two circles -- Notes to Section 3 -- 4 Inversion (concluding section) -- Notes to Section 4 -- 5 Axial circular transformations -- A. Dilatation -- B. Axial inversion -- Notes to Section 5 -- Supplement | |
| 505 | 8 | |a Non-Euclidean Geometry of Lobachevski-Bolyai, or Hyperbolic GeometryNotes to Supplement -- Solutions -- Section 1 -- Section 2 -- Section 3 -- Section 4 -- Notes to Section 4 -- Section 5 -- Notes to Section 5 -- Supplement -- Notes to Supplement -- About the Author | |
| 520 | |a The familiar plane geometry of high 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, which appeared in this series as Volumes 8, 21, and 24. Part I treats the geometry of rigid motions of the plane (isometries); Part II treats the geometry of shape-preserving transformations of the plane (similarities); Part III treats the geometry of transformations of the plane that map lines to lines (affine and projective transformations) and introduces the Klein model of non-Euclidean geometry. 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 high-school geometry and trigonometry. Numerous exercises lead the reader to a mastery of the methods and concepts. The second half of the book contains detailed solutions of all the problems. | ||
| 590 | |a ProQuest Ebook Central |b Ebook Central Academic Complete | ||
| 650 | 0 | |a Inversions (Geometry) | |
| 650 | 0 | |a Geometry, Modern. | |
| 650 | 6 | |a Inversions (Géométrie) | |
| 650 | 6 | |a Géométrie moderne. | |
| 650 | 7 | |a Geometry, Modern |2 fast | |
| 650 | 7 | |a Inversions (Geometry) |2 fast | |
| 700 | 1 | |a Yaglom, I. M. | |
| 700 | 1 | |a Shenitzer, Abe. | |
| 776 | 0 | 8 | |i Print version: |a Yaglom, I.M. |t Geometric Transformations Vol. 4 : Circular Transformations. |d Washington : Mathematical Association of America, ©2014 |z 9780883856482 |
| 830 | 0 | |a Anneli Lax new mathematical library. | |
| 856 | 4 | 0 | |u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=3330414 |z Texto completo |
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