Beltrami
# Eugenio Beltrami

### Born: 16 Nov 1835
in Cremona, Lombardy, Austrian Empire (now Italy)

Died: 4 June 1899
in Rome, Italy

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**Eugenio Beltrami** studied at Pavia (1853-56), then Milan, before being appointed to the University of Bologna in 1862 as a visiting professor of algebra and analytic geometry. In 1866 he was appointed professor of rational mechanics. Beltrami also worked at universities in Pisa, Rome, and Pavia.
Influenced by Cremona, Lobachevsky, Gauss and Riemann, Beltrami contributed to work in differential geometry on curves and surfaces. He is best known, however, for his 1868 paper Essay on an interpretation of non-euclidean geometry which gives a concrete realisation of the non-euclidean geometry of Lobachevsky and Bolyai and connects it with Riemann's geometry. The concrete realisation uses the surface generated by the revolution of a tractrix about its asymptote.

Beltrami also worked on optics, thermodynamics, elasticity, electricity and magnetism. His contributions to these topics appeared in the four-volume work, Opere Matematiche (1902-20), published posthumously.

**References (9 books/articles)**

**References elsewhere in this archive:**

Tell me about Beltrami's work on non-Euclidean geometry

Beltrami worked on the Tractrix

JOC/EFR December 1996