A Background to Geometry: Natural, Synthetic and Algebraic - Softcover

Room, T. G.

Softcover

ISBN 10: 0521090636 ISBN 13: 9780521090636

Publisher: Cambridge University Press, 2009

Synopsis

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.

About this title

Book Description

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.

Edition details

• Publisher: Cambridge University Press
• Publication date: 2009
• Language: English
• ISBN 10: 0521090636
• ISBN 13: 9780521090636
• Binding: Paperback
• Number of pages: 352