Geometry Revisited /

Among the many beautiful and nontrivial theorems in geometry found here are the theorems of Ceva, Menelaus, Pappus, Desargues, Pascal, and Brianchon. A nice proof is given of Morley's remarkable theorem on angle trisectors. The transformational point of view is emphasized: reflections, rotation...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Otros Autores: Coxeter, H. S. M., Greitzer, Samuel L.
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Cambridge : Cambridge University Press, 2012.
Colección:Anneli Lax new mathematical library.
Temas:
Geometry.
Mathematics.
Mathematics
Géométrie.
Mathématiques.
geometry.
Geometry
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Front Cover
  • Geometry Revisited
  • Copyright Page
  • Contents
  • Preface
  • Chapter 1. Points and Lines Connected with a Triangle
  • 1.1 The extended Law of Sines
  • 1.2 Cevaâ€?s theorem
  • 1.3 Points of interest
  • 1.4 The incircle and excircles
  • 1.5 The Steiner-Lehmus theorem
  • 1.6 The orthic triangle
  • 1.7 The medial triangle and Euler line
  • 1.8 The nine-point Circle
  • 1.9 Pedal triangles
  • Chapter 2. Some Properties of Circles
  • 2.1 The power of a point with respect to a circle
  • 2.2 The radical axis of two circles
  • 2.3 Coaxal circles
  • 2.4 More on the altitudes and orthocenter of a triangle2.5 Simson lines
  • 2.6 Ptolemyâ€?s theorem and its extension
  • 2.7 More on Simson lines
  • 2.8 The Butterfly
  • 2.9 Morleyâ€?s theorem
  • Chapter 3. Collinearity and Concurrence
  • 3.1 Quadrangles; Varignonâ€?s theorem
  • 3.2 Cyclic quadrangles; Brahmaguptaâ€?s formula
  • 3.3 Napoleon triangles
  • 3.4 Menelausâ€?s theorem
  • 3.5 Pappusâ€?s theorem
  • 3.6 Perspective triangles; Desarguesâ€?s theorem
  • 3.7 Hexagons
  • 3.8 Pascalâ€?s theorem
  • 3.9 Brianchonâ€?s theorem
  • Chapter 4. Transformations4.1 Translation
  • 4.2 Rotation
  • 4.3 Half-turn
  • 4.4 Reflection
  • 4.5 Fagnanoâ€?s problem
  • 4.6 The three jug problem
  • 4.7 Dilatation
  • 4.8 Spiral similarity
  • 4.9 A genealogy of transformations
  • Chapter 5. An Introduction to Inversive Geometry
  • 5.1 Separation
  • 5.2 Cross ratio
  • 5.3 Inversion
  • 5.4 The inversive plane
  • 5.5 Orthogonality
  • 5.6 Feuerbachâ€?s theorem
  • 5.7 Coaxal circles
  • 5.8 Inversive distance
  • 5.9 Hyperbolic functions
  • Chapter 6. An Introduction to Projective Geometry
  • 6.1 Reciprocation6.2 The polar circle of a triangle
  • 6.3 Conics
  • 6.4 Focus and directrix
  • 6.5 The projective plane
  • 6.6 Central conics
  • 6.7 Stereographic and gnomonic projection
  • Hints and Answers to Exercises
  • References
  • Glossary
  • Index
  • Back Cover

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