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About this product
- DescriptionThis book examines the geometrical tion of orthogonality, and shows how to use it as the primitive concept on which to base a metric structure in affine geometry. The subject has a long history, and an extensive literature, but whatever velty there may be in the study presented here comes from its focus on geometries hav- ing lines that are self-orthogonal, or even singular (orthogonal to all lines). The most significant examples concern four-dimensional special-relativistic spacetime (Minkowskian geometry), and its var- ious sub-geometries, and these will be prominent throughout. But the project is intended as an exercise in the foundations of geome- try that does t presume a kwledge of physics, and so, in order to provide the appropriate intuitive background, an initial chapter has been included that gives a description of the different types of line (timelike, spacelike, lightlike) that occur in spacetime, and the physical meaning of the orthogonality relations that hold between them. The coordinatisation of affine spaces makes use of constructions from projective geometry, including standard results about the ma- trix represent ability of certain projective transformations (involu- tions, polarities). I have tried to make the work sufficiently self- contained that it may be used as the basis for a course at the ad- vanced undergraduate level, assuming only an elementary kwledge of linear and abstract algebra.
- Author(s)Robert Goldblatt
- PublisherSpringer-Verlag New York Inc.
- Date of Publication13/05/1987
- Series TitleUniversitext
- Place of PublicationNew York, NY
- Country of PublicationUnited States
- ImprintSpringer-Verlag New York Inc.
- Content Notebiography
- Weight317 g
- Width156 mm
- Height234 mm
- Spine10 mm
- Format DetailsTrade paperback (US)
- Edition StatementSoftcover reprint of the original 1st ed. 1987
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