Circles: A Mathematical View - Brossura

Pedoe, Dan

Brossura

ISBN 10: 0883855186 ISBN 13: 9780883855188

Casa editrice: The Mathematical Association of America, 1997

Riassunto

Illuminates the fundamental aspects of geometry where the circle plays an important role.

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Descrizione del libro

Armed with paper, pencil, compass, and straightedge, readers of Circles will find great pleasure in following the constructions and theorems, not only from ancient Greece, but also interesting results which were only discovered in modern times. Novices and experts alike will find much to enlighten them in this mathematical classic.

Contenuti

Preface; 1. The nine-point circle, inversion, Feuerbach's theorem, extension of Ptolemy's theorem, Fermat's problem, the centres of similitude of two circles, coaxal systems of circles, canonical form for coaxal system, further properties, problem of Apollonius, compass geometry; 2. Representation of a circle, Euclidean three-space, first properties of the representation, coaxal systems, deductions from the representation 0, conjugacy relations, circles cutting at a given angle, representation of inversion, the envelope of a system, some further applications, some anallagmatic curves; 3. Complex numbers, the Argand diagram, modulus and argument, circles as level curves, the cross-ratio of four complex numbers, Moebius transformations of the s-plane, a Moebius transformation dissected, the group property, special transformations, the fundamental theorem, the Poincare model, the parallel axiom, non-Euclidean distance; 4. Steiner's enlarging process, existence of a solution, method of solution, area of a polygon, regular polygons, rectifiable curves, approximation by polygons, area enclosed by a curve; Exercises; Solutions; Appendix: Karl Wilhelm Feuerbach, Mathematician, by Laura Guggenbuhl.

Dettagli dell?edizione

• Editore: The Mathematical Association of America
• Data di pubblicazione: 1997
• Lingua: Inglese
• ISBN 10: 0883855186
• ISBN 13: 9780883855188
• Rilegatura: Copertina flessibile
• Numero edizione: 2
• Numero di pagine: 138
• Contatto del produttore: non disponibile