The top and bottom of the book show signs of wear with slight additional wear along the edges of the front cover . These imperfections are mostly cosmetic and do not affect the overall structure or readability of the book. ; "Advanced Euclidean Geometry" (Dover Books on Mathematics) delves into the classical geometry of the triangle and circle, extending traditional Euclidean principles. The book covers topics such as the nine-point circle, geometric transformations, and notable theorems like Ceva's and Menelaus' theorems. Ideal for students and geometry enthusiasts, it offers a deeper understanding of Euclidean concepts through rigorous proofs and geometric insight. ; 13.5 x 21.3 x 1.7 cm; xiii, 319 pages.

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Dati bibliografici

Titolo: Advanced Euclidean Geometry - Dover Books on Mathematcs
Editore: Dover Publications Inc, New York
Data di pubblicazione: 2007
Lingua: Inglese
ISBN 10: 0486462374
ISBN 13: 9780486462370
Rilegatura: Softcover
Edizione: Second Edition; (?).
Condizione: Very Good
Condizione della sovraccoperta: No Dust Jacket

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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

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