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Did Lobachevsky have a model of his Imaginary geometry?

Rodin, Andrei (2008) Did Lobachevsky have a model of his Imaginary geometry? [Preprint]

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    Abstract

    Lobachevsky's Imaginary geometry in its original form involved an extension of rather than a radical departure from Euclidean intuition. It wasn't anything like a formal theory in Hilbert's sense and hence didn't require anything like a model. However, rather surprisingly, Lobachevsky uses what in modern terms can be called a non-standard model of Euclidean plane, namely as a specific surface (a horisphere) in a Hyperbolic space. In this paper I critically review some popular accounts of the discovery of Non-Euclidean geometries and suggest a revision of the epistemic view on the issue dating back to Hilbert's Grundlagen.


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    Item Type: Preprint
    Keywords: Lobachevsky, Hilbert, Hyperbolic space, Horisphere, Horicircle
    Subjects: Specific Sciences > Mathematics
    Depositing User: Andrei Rodin
    Date Deposited: 07 Jul 2008
    Last Modified: 07 Oct 2010 11:16
    Item ID: 4099
    URI: http://philsci-archive.pitt.edu/id/eprint/4099

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