Advanced Euclidean Geometry (Paperback)

Roger A. Johnson

ISBN 10: 0486462374 / ISBN 13: 9780486462370

Editore: Dover Publications Inc., New York, 2007

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Paperback. This classic text explores the geometry of the triangle and the circle, concentrating on extensions of Euclidean theory, and examining in detail many relatively recent theorems. 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. This classic text explores the geometry of the triangle and the circle, concentrating on extensions of Euclidean theory, and examining in detail many relatively recent theorems. 1929 edition. Shipping may be from our UK warehouse or from our Australian or US warehouses, depending on stock availability.

Codice articolo 9780486462370

Dati bibliografici

• Titolo: Advanced Euclidean Geometry (Paperback)
• Editore: Dover Publications Inc., New York
• Data di pubblicazione: 2007
• Lingua: Inglese
• ISBN 10: 0486462374
• ISBN 13: 9780486462370
• Rilegatura: Paperback
• Condizione: new

Descrizione articolo

Riassunto

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.

Contenuti

Introduction Similar Figures Coaxal Circles and Inversion Triangles and Polygons Geometry of Circles Tangent Circles The Theorem of Miquel Theorems of Ceva and Menelaus Three Notable Points Inscribed and Escribed Circles The Nine Point Circle Symmedian Point and Other Notable Points Triangles in Perspective Pedal Triangles and Circles Shorter Topics The Brocard Configuration Equibrocardal Triangles Three Similar Figures Index