Episodes in Nineteenth and Twentieth Century Euclidean Geometry /

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Euclidean geometry was worked out by Euclid and his predecessors more than 2300 years ago and is studied today mostly as a background to other branches of mathematics. In fact, however, as Professor Honsberger masterfully demonstrates, geometry in the style of Euclid is still alive and well. Mathema...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Honsberger, Ross
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Cambridge : Cambridge University Press, 2012.
Colección:Anneli Lax new mathematical library.
Temas:
Geometry, Projective.
Géométrie projective.
MATHEMATICS > Geometry > General.
Geometry, Projective
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Cover
  • Title page
  • copyright page
  • 1. Cleavers and Splitters
  • 2. The Orthocenter
  • 3. On Triangles
  • 4. On Quadrilaterals
  • Exercise Set 4
  • 5. A Property of Triangles
  • 1. The Property
  • 2. The Simson Line
  • 3. The Proof of the Property (John Rigby)
  • 4. A Corollary
  • 5. A Property of Parabolas
  • 6. The Fuhrmann Circle
  • 7. The Symmedian Point
  • Section 1
  • 2. Isogonal Lines and Points
  • Exercise
  • 3. The Symmedians and the Symmedian Point K
  • 4. Applications and Further Developments
  • References
  • Exercise Set 78. The Miquel Theorem
  • Section 1
  • 2. The Theorem of Miquel
  • 3. The Case of P_1, P_2, P_3 Collinear
  • 4. Simson Lines
  • 5. A Curious Angle Property
  • 9. The Tucker Circles
  • 1. Parallels and antiparallels
  • 2. The Lemoine circles
  • 3. The Tucker circles
  • 4. The center of a Tucker circle lies on the line KO
  • 5. The first Lemoine circle
  • 6. The Taylor Circle
  • Exercise Set 9
  • 10. The Brocards Points
  • 1. The Brocard Points
  • 2. The Brocard Angle
  • Exercise
  • Exercise
  • 3. The Brocard Circle
  • 4. The Brocard triangles5. The Steiner point and the Tarry point
  • 6. A property relating K, G, Omega, Omega'
  • 11. The Orthopole
  • Section 1
  • Section 2
  • 3. The Rigby Point
  • Exercise
  • 12. On Cevians
  • 1. Cevaâ€?s Theorem
  • Section 2
  • Section 3
  • 4. Harukiâ€?s Cevian theorem for circles
  • 13. The Theorem of Menelaus
  • Section 1
  • 2. Applications
  • Suggested Reading
  • Solutions to the Exercises
  • 1. Cleavers and Splitters
  • 2. The Orthocenter
  • 3. On Triangles
  • 4. On Quadrilaterals
  • 7. The Symmedian Point
  • 9. The Tucker Circles11. The Orthopole
  • Index

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