Euclidean Geometry and its Subgeometries

• Κύριοι συγγραφείς: Specht, Edward John (Συγγραφέας), Jones, Harold Trainer (Συγγραφέας), Calkins, Keith G. (Συγγραφέας), Rhoads, Donald H. (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Cham : Springer International Publishing : Imprint: Birkhäuser, 2015.
• Έκδοση: 1st ed. 2015.
• Θέματα: Mathematics.; Geometry.; History.; History of Mathematical Sciences.

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...

Πίνακας περιεχομένων:

• 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.