K. N. P. Singh
eBook, ePUB

Concepts In Coordinate Geometry (eBook, ePUB)

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The reduction of geometry to algebra requires the notion of a transformation group. The transformation group supplies two essential ingredients. First it is used to define the notion of equivalence in the geometry in question. For example, in Euclidean geometry, two triangles are congruent if there is distance preserving transformation carrying one to the other and they are similar if there is a similarity transformation carrying one to the other. Secondly, in each kind of geometry there are normal form theorems which can be used to simplify coordinate proofs. In analytic geometry, the plane i...

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