Geometric transformations [[electronic resource] ] . IV Circular transformations / / I.M. Yaglom ; translated by A. Shenitzer

• Autore: I͡Aglom I. M (Isaak Moiseevich), <1921-1988.>
• Pubblicazione: Washington, D.C., : Mathematical Association of America, c2009
• Descrizione fisica: 1 online resource (294 p.)
• Disciplina: 516
• Soggetto topico: Inversions (Geometry); Geometry, Modern
• Soggetto genere / forma: Electronic books.
• Altri autori: ShenitzerAbe
• Note generali: Description based upon print version of record.
• Nota di contenuto: ""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"" ; ""Non-Euclidean Geometry of Lobachevski-Bolyai, or Hyperbolic Geometry""""Notes 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""
• Sommario/riassunto: 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.
• Titolo autorizzato: Geometric transformations
• ISBN: 0-88385-958-0
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910461924803321
• Lo trovi qui: Univ. Federico II
• Serie: Anneli Lax new mathematical library ; ; v. 44.