Advanced Euclidean Geometry

Advanced Euclidean Geometry

Paperback Dover Books on Mathematics

By (author) Roger A. Johnson

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  • Publisher: Dover Publications Inc.
  • Format: Paperback | 336 pages
  • Dimensions: 135mm x 211mm x 18mm | 318g
  • Publication date: 30 November 2007
  • Publication City/Country: New York
  • ISBN 10: 0486462374
  • ISBN 13: 9780486462370
  • Illustrations note: 107 Figs.
  • Sales rank: 378,736

Product description

For many years, this elementary treatise on advanced Euclidean geometry has been the standard textbook in this area of classical mathematics; no other book has covered the subject quite as well. It explores the geometry of the triangle and the circle, concentrating on extensions of Euclidean theory, and examining in detail many relatively recent theorems. Several hundred theorems and corollaries are formulated and proved completely; numerous others remain unproved, to be used by students as exercises. The author makes liberal use of circular inversion, the theory of pole and polar, and many other modern and powerful geometrical tools throughout the book. In particular, the method of "directed angles" offers not only a powerful method of proof but also furnishes the shortest and most elegant form of statement for several common theorems. This accessible text requires no more extensive preparation than high school geometry and trigonometry.

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Table of contents

IntroductionSimilar FiguresCoaxal Circles and InversionTriangles and PolygonsGeometry of CirclesTangent CirclesThe Theorem of MiquelTheorems of Ceva and MenelausThree Notable PointsInscribed and Escribed CirclesThe Nine Point CircleSymmedian Point and Other Notable PointsTriangles in PerspectivePedal Triangles and CirclesShorter TopicsThe Brocard ConfigurationEquibrocardal TrianglesThree Similar FiguresIndex