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
Creators:	Creators Email ORCID Rodin, Andrei
Keywords:	Lobachevsky, Hilbert, Hyperbolic space, Horisphere, Horicircle
Subjects:	Specific Sciences > Mathematics
Depositing User:	Dr. Andrei Rodin
Date Deposited:	07 Jul 2008
Last Modified:	07 Oct 2010 15:16
Item ID:	4099
Subjects:	Specific Sciences > Mathematics
Date:	June 2008
URI:	https://philsci-archive.pitt.edu/id/eprint/4099

Available Versions of this Item

• Did Lobachevsky have a model of his Imaginary geometry? (deposited 07 Jul 2008) [Currently Displayed]
  • DID LOBACHEVSKY HAVE A MODEL OF HIS "IMAGINARY GEOMETRY"? (deposited 12 Aug 2010)

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