Advanced Euclidean Geometry

 
 
Dover Publications (Verlag)
erschienen am 8. Januar 2013 | 336 Seiten
 
E-Book | ePUB mit Adobe DRM | Systemvoraussetzungen
978-0-486-15498-5 (ISBN)
 
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.
Dover Publications
Englisch
New York
107 Figs.
Höhe: 216 mm | Breite: 137 mm
15,00 MB
376 gr
978-0-486-15498-5 (9780486154985)
048615498X (048615498X)
weitere Ausgaben werden ermittelt
Roger A. Johnson
  • Cover
  • Title Page
  • Copyright Page
  • Editor's Introduction
  • Preface
  • Contents
  • I. Introduction
  • 1. Prerequisites
  • 2. Positive and Negative Quantities
  • 8. Points at Infinity
  • 13. Notation
  • 16. Directed Angles
  • II. Similar Figures
  • 21. Homothetic Figures
  • 25. Centers of Similitude of Two Circles
  • 31. Similar Figures in General
  • III. Coaxal Circles and Inversion
  • 40. The Radical Axis
  • 50. Coaxal Circles
  • 63. Inversion
  • IV. Triangles and Polygons
  • 84. Ratios in the Triangle
  • 89. Quadrangles and Quadrilaterals
  • 92. The Theorem of Ptolemy
  • 96. Triangle and Quadrangle Theorems
  • 101. Polygon Theorems and Exercises
  • 107. Theorems Concerning Areas
  • V. Geometry of Circles
  • 113. The Power Theorem of Casey
  • 126. Circles of Antisimilitude
  • 134. Poles and Polars
  • 144. Stereographic Projection
  • VI. Tangent Circles
  • 150. Circles Tangent to Two Circles
  • 158. Steiner Chains
  • the Arbelos
  • 166. The Problem of Apollonius
  • 172. Four Circles Touching a Circle
  • VII. The Theorem of Miquel
  • 184. The Miquel Theorem
  • 189. Pedal Triangles and Circles
  • Simson Lines
  • VIII. Theorems of Ceva and Menelaus
  • 213. The Theorems of Ceva and Menelaus
  • Applications
  • 231. Isogonal Conjugates
  • IX. Three Notable Points
  • 249. Fundamental Properties of Orthocenter and Circumcenter
  • 259. The Orthocentric System
  • 271. Properties of the Median Point
  • 278. The Polar Circle
  • X. Inscribed and Escribed Circles
  • 287. Fundamental Properties
  • 298. Algebraic Formulas
  • Principle of Transformation
  • XI. The Nine Point Circle
  • 308. Properties of the Nine Point Circle
  • 320. The Theorem of Feuerbach
  • 326. Further Properties of Simson Lines
  • XII. Symmedian Point and Other Notable Points
  • 341. Symmedians and the Symmedian Point
  • 352. The Isogonic Centers
  • 361. Nagel Point, Spieker Circle, Fuhrmann Circle
  • XIII. Triangles in Perspective
  • 373. The Theorem of Desargues
  • 385. The Theorems of Pascal and Brianchon
  • XIV. Pedal Triangles and Circles
  • 394. Pedal Triangles and Circles of a Quadrangle
  • 401. Fontené's Theorems
  • the Theorem of Feuerbach
  • 406. The Orthopole
  • XV. Shorter Topics
  • 408. Statical Theorems: Center of Gravity, Resultant of Vectors
  • 417. The Cyclic Quadrangle and its Orthocenters
  • 420. The Theorem of Morley
  • 424. Circles of Droz-farny
  • 428. Miscellaneous Exercises
  • XVI. The Brocard Configuration
  • 433. The Brocard Points and their Properties
  • 448. The Tucker Circles
  • 461. The Brocard Triangles and the Brocard Circle
  • 469. Steiner Point and Tarry Point
  • 473. Related Triangles
  • XVII. Equibrocardal Triangles
  • 480. The Neuberg Circles
  • 486. Vertical Projection of Triangles
  • 490. Circles of Apollonius and Isodynamic Points
  • 497. The Circles of Schoute
  • 499. Generalizations of Brocard Geometry
  • XVIII. Three Similar Figures
  • 506. Similar Figures on the Sides of a Triangle
  • 516. Three Similar Figures in General
  • Index

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