Geometric Transformations IV
Mathematical Association of America (Verlag)
9780883856482 (ISBN)
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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 Poincar 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.
I. M. Yaglom authored many books which have since become academic standards of reference. These include Complex Numbers in Geometry, Geometric Transformations, A Simple Non-Euclidean Geometry and its Physical Basis, and Probability and Information. He was Professor of Mathematics at Yaroslavl State University from 1974–83 and a technical consultant at the Academy of Pedagogical Sciences from 1984–88. Abe Shenitzer has translated many mathematics classics (from German, Polish and Russian into English). He retired in 1989 from York University, where he had been Professor of Mathematics since 1969.
1. Reflection in a circle (inversion); Notes to Section 1; 2. Application of inversions to the solution of construction; 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 I; Non-euclidean geometry of Lobachevskii-Bolyai, or hyperbolic geometry; Notes to Supplement I; Solutions; Section 1; Section 2; Section 3; Circular transformations; Section 4; Section 5; Supplement II; Notes to Supplement II.
| Reihe/Serie | New Mathematical Library ; Vol.44 |
|---|---|
| Sprache | englisch |
| Maße | 152 x 229 mm |
| Gewicht | 408 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Geometrie / Topologie |
| ISBN-13 | 9780883856482 / 9780883856482 |
| Zustand | Neuware |
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