Circles : a mathematical view
著者
書誌事項
Circles : a mathematical view
Mathematical Association of America, 1995
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注記
Includes bibliography and index
Originally published in 1957 by Pergamon Press
A corrected and enlarged edition was first published in 1979 by Dover Publication, Inc
内容説明・目次
内容説明
This revised edition of a mathematical classic originally published in 1957 will bring to a new generation of students the enjoyment of investigating that simplest of mathematical figures, the circle. The author has supplemented this new edition with a special chapter designed to introduce readers to the vocabulary of circle concepts with which the readers of two generations ago were familiar. Readers of Circles need only be armed with paper, pencil, compass, and straight edge to find great pleasure in following the constructions and theorems. Those who think that geometry using Euclidean tools died out with the ancient Greeks will be pleasantly surprised to learn many interesting results which were only discovered in modern times. Novices and experts alike will find much to enlighten them in chapters dealing with the representation of a circle by a point in three-space, a model for non-Euclidean geometry, and the isoperimetric property of the circle.
目次
- 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.
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