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Beltrami’s Models of Non-Euclidean Geometry

In: Mathematicians in Bologna 1861–1960

Author

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  • Nicola Arcozzi

    (Università di Bologna, Dipartimento di Matematica)

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).

Suggested Citation

  • Nicola Arcozzi, 2012. "Beltrami’s Models of Non-Euclidean Geometry," Springer Books, in: Salvatore Coen (ed.), Mathematicians in Bologna 1861–1960, edition 127, pages 1-30, Springer.
    • Handle: RePEc:spr:sprchp:978-3-0348-0227-7_1
    DOI: 10.1007/978-3-0348-0227-7_1
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