An Introduction to the Study of Projective Planes
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Miniquaternion Geometry by T.G. Room
Book DescriptionThis tract provides an introduction to four finite geometrical systems and to the theory of projective planes. Of the four geometries, one is based on a nine-element field and the other three can be constructed from the nine-element 'miniquaternion algebra', a simple system which has many though not all the properties of a field. The three systems based on the miniquaternion algebra have widely differing properties; none of them has the homogeneity of structure which characterizes geometry over a field. While these four geometries are the main subject of this book, many of the ideas developed are of much more general significance. The authors have assumed a knowledge of the simpler properties of groups, fields, matrices and transformations (mappings), such as is contained in a first course in abstract algebra. Development of the nine-element field and the miniquaternion system from a prescribed set of properties of the operations of addition and multiplication are covered in an introductory chapter. Exercises of varying difficulty are integrated with the text.
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Book DetailsISBN: 9780521090643
(216mm x 140mm x 11mm)
Imprint: Cambridge University Press
Publisher: Cambridge University Press
Publish Date: 27-Nov-2008
Country of Publication: United Kingdom
Books By Author T.G. Room
Background to Geometry, Paperback (November 2008)» View all books by T.G. Room
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.
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