Abstract
At some point between high school and college we first make the transition between Euclidean (or synthetic) geometry and co-ordinate (or analytic) geometry. Later, during graduate studies we are introduced to differential geometry of many dimensions. The justification given in the first instance is that coordinates are a natural outcome of the axioms of Euclidean geometry; and in the second case because Riemannian geometry is much more general than axiomatic non-Euclidean geometry. In this expository account we examine these two justifications.
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References
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© 1996 Hindustan Book Agency
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Paranjape, K. (1996). Axiomatic and Coordinate Geometry. In: Bhatia, R. (eds) Analysis, Geometry and Probability. Texts and Readings in Mathematics, vol 10. Hindustan Book Agency, Gurgaon. https://doi.org/10.1007/978-93-80250-87-8_8
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DOI: https://doi.org/10.1007/978-93-80250-87-8_8
Publisher Name: Hindustan Book Agency, Gurgaon
Print ISBN: 978-81-85931-12-8
Online ISBN: 978-93-80250-87-8
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