A Background to Geometry: Natural, Synthetic and Algebraic

by T. G. Room

Overview

The central theme of the book is the development of the idea of congruence, that relation between geometric figures which is basic to ordinary Euclidean geometry. The text is divided into four books corresponding to stages in the development of a geometrical system from simple axioms: 1. 'Geometry without numbers': the relations of order and sense. 2. 'Geometry and counting': properties of the systems obtained by repetitions of the operation of displacement. 3. 'Geometry and algebra': the consequences of adjoining new points to the system developed in Book 2. In particular the properties of an algebraic field are deduced from the geometric axioms. 4. 'Congruence': properties derived from the operation of reflexion. An early introduction of parallels makes possible the drawing of diagrams which resemble those of Euclid's geometry so that the reader may see the broad outline of a proof from observable properties of these diagrams. Particular geometrical systems are explored and some general topics investigated in detail in appendices following each section of the book.

Product Details

ISBN-13:	9780521090636
Publisher:	Cambridge University Press
Publication date:	11/27/2008
Edition description:	Reissue
Pages:	352
Product dimensions:	6.00(w) x 9.00(h) x 0.90(d)

Table of Contents

1. Geometry without numbers; 2. Geometry and Counting; 3. Geometry and Algebra; 4. Congruence.