PhilSci Archive

DID LOBACHEVSKY HAVE A MODEL OF HIS "IMAGINARY GEOMETRY"?

Rodin, Andrei (2010) DID LOBACHEVSKY HAVE A MODEL OF HIS "IMAGINARY GEOMETRY"? [Preprint]

This is the latest version of this item.

[img]
Preview
PDF
Download (496Kb) | Preview

    Abstract

    The invention of non-Euclidean geometries is often seen through the optics of Hilbertian formal axiomatic method developed later in the 19th century. However such an anachronistic approach fails to provide a sound reading of Lobachevsky's geometrical works. Although the modern notion of model of a given theory has a counterpart in Lobachevsky's writings its role in Lobachevsky's geometrical theory turns to be very unusual. Lobachevsky doesn't consider various models of Hyperbolic geometry, as the modern reader would expect, but uses a non-standard model of Euclidean plane (as a particular surface in the Hyperbolic 3-space). In this paper I consider this Lobachevsky's construction, and show how it can be better analyzed within an alternative non-Hilbertian foundational framework, which relates the history of geometry of the 19th century to some recent developments in the field.


    Export/Citation:EndNote | BibTeX | Dublin Core | ASCII/Text Citation (Chicago) | HTML Citation | OpenURL
    Social Networking:

    Item Type: Preprint
    Keywords: Lobachevsky, Hilbert, geometry
    Subjects: Specific Sciences > Mathematics
    Depositing User: Andrei Rodin
    Date Deposited: 12 Aug 2010
    Last Modified: 07 Oct 2010 11:14
    Item ID: 2883
    URI: http://philsci-archive.pitt.edu/id/eprint/2883

    Available Versions of this Item

    Actions (login required)

    View Item

    Document Downloads