Abstract
Ernest Nagel argued in 1939 that the principle of duality, by putting points and lines on a par, was an important stimulus for abstract, non-intuitive geometry, because it is intuitive that a plane is made up of points but not that it is made up of lines. One can go further: projective geometry made up spaces whose elements (points) were curves somewhere else (the space of all conic sections, for example).
More extracts are given from Hilbert’s Grundlagen der Geometrie.
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© 2011 Springer-Verlag London Limited
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Gray, J. (2011). What is Geometry? The Formal Side. In: Worlds Out of Nothing. Springer Undergraduate Mathematics Series. Springer, London. https://doi.org/10.1007/978-0-85729-060-1_28
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DOI: https://doi.org/10.1007/978-0-85729-060-1_28
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