Beltrami’s Models of Non-Euclidean Geometry

Nicola Arcozzi ()
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Nicola Arcozzi: Università di Bologna, Dipartimento di Matematica

A chapter in Mathematicians in Bologna 1861–1960, 2012, pp 1-30 from Springer

Abstract: Abstract In two articles published in 1868 and 1869, Eugenio Beltrami provided three models in Euclidean plane (or space) for non-Euclidean geometry. Our main aim here is giving an extensive account of the two articles’ content. We will also try to understand how the way Beltrami, especially in the first article, develops his theory depends on a changing attitude with regards to the definition of surface. In the end, an example from contemporary mathematics shows how the boundary at infinity of the non-Euclidean plane, which Beltrami made intuitively and mathematically accessible in his models, made non-Euclidean geometry a natural tool in the study of functions defined on the real line (or on the circle).

Keywords: Constant Curvature; Euclidean Plane; Projective Transformation; Length Element; Disc Model (search for similar items in EconPapers)
Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-0348-0227-7_1

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DOI: 10.1007/978-3-0348-0227-7_1

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