Euclidean Geometry and its Subgeometries

Euclidean Geometry and its Subgeometries

Paperback(Softcover reprint of the original 1st ed. 2015)

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Product Details

ISBN-13: 9783319795331
Publisher: Springer International Publishing
Publication date: 03/31/2018
Edition description: Softcover reprint of the original 1st ed. 2015
Pages: 527
Product dimensions: 6.10(w) x 9.25(h) x (d)

Table of Contents

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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