Abstract
Euclidean geomeltry and the geometry of surfaces in E3 that we looked at in the preceeding chapter turn out to be quite unsatisfactory for many reasons. We will review some of them here; they are not all logically related.
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Recall that Euclid introduced ten axioms for his geometry, five of which were called postulates while the other five were called common notions. The significance of this distinction is a matter of conjecture, but the postulates are clearly geometric, while the common notions are concerned with the nature of equations and inequalities generally, essentially defining = and <. The common notions are assumed in any geometry.
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© 2003 Springer-Verlag Berlin Heidelberg
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Berger, M. (2003). Transition: The Need for a More General Framework. In: A Panoramic View of Riemannian Geometry. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18245-7_2
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DOI: https://doi.org/10.1007/978-3-642-18245-7_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-65317-2
Online ISBN: 978-3-642-18245-7
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