A Background to Geometry

Natural, Synthetic and Algebraic

T. G. Room (Autor)

Buch | Softcover

352 Seiten

2008
Cambridge University Press (Verlag)
978-0-521-09063-6 (ISBN)

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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.

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

Erscheint lt. Verlag	27.11.2008
Zusatzinfo	Worked examples or Exercises
Verlagsort	Cambridge
Sprache	englisch
Maße	152 x 229 mm
Gewicht	520 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
ISBN-10	0-521-09063-6 / 0521090636
ISBN-13	978-0-521-09063-6 / 9780521090636
Zustand	Neuware