Euclidean Geometry and its Subgeometries

In this monograph, the authors present a modern development of Euclidean geometry from independent axioms, using up-to-date language and providing detailed proofs. The axioms for incidence, betweenness, and plane separation are close to those of Hilbert. This is the only axiomatic treatment of Eucli...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Specht, Edward John (Autor), Jones, Harold Trainer (Autor), Calkins, Keith G. (Autor), Rhoads, Donald H. (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Cham : Springer International Publishing : Imprint: Birkhäuser, 2015.
Edición:1st ed. 2015.
Temas:
Geometry.
Mathematics.
History.
History of Mathematical Sciences.
Acceso en línea:Texto Completo
Tabla de Contenidos:
  • Preface
  • Preliminaries and Incidence Geometry (I)
  • Affine Geometry: Incidence with Parallelism (IP)
  • Collineations of an Affine Plane (CAP)
  • Incidence and Betweenness (IB)
  • Pasch Geometry (PSH)
  • Ordering a Line in the Pasch Plane (ORD)
  • Collineations Preserving Betweenness (COBE)
  • Neutral Geometry (NEUT)
  • Free Segments of a Neutral Plane (FSEG)
  • Rotations about a Point of a Neutral Plane (ROT)
  • Euclidean Geometry Basics (EUC)
  • Isometries of a Euclidean Plane (ISM)
  • Dilations of a Euclidean Plane (DLN)
  • Every Line in a Euclidean Plane is an Ordered Field (OF)
  • Similarity on a Euclidean Plane (SIM)
  • Axial Affinities of a Euclidean Plane (AX)
  • Rational Points on a Line (QX)
  • A Line as Real Numbers (REAL); Coordinatization of a Plane (RR)
  • Belineations on a Euclidean/LUB Plane (AA)
  • Ratios of Sensed Segments (RS)
  • Consistency and Independence of Axioms; Other Matters Involving Models
  • References
  • Index.

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