Eugenio Beltrami

Infobox_Scientist
name = Eugenio Beltrami


image_width = 170px
caption = Eugenio Beltrami
birth_date = birth date|1835|11|16|df=y
birth_place = Cremona, Lombardy, Austrian Empire
death_date = death date and age|1899|6|4|1835|11|16|df=y
death_place = Rome, Italy
residence =
nationality =
field = Mathematician
work_institution = University of Bologna
University of Pisa
University of Rome
alma_mater = University of Pavia
doctoral_advisor = Francesco Brioschi
doctoral_students =
known_for = Laplace-Beltrami operator
religion =
footnotes=

Eugenio Beltrami (16 November, 1835 - 4 June, 1899) was an Italian mathematician notable for his work on non-Euclidean geometry, electricity, and magnetism.

He was born in Cremona in Lombardy, then a part of the Austrian Empire, and now part of Italy. Beltrami first began studying mathematics at University of Pavia in 1853, but was forced to discontinue his studies in 1856 because of financial hardship. He was appointed to the University of Bologna as a professor in 1862, the year he published his first paper. Beltrami later taught at universities in Pisa, Rome and Pavia. He died in Rome in 1899.

Hyperbolic geometry

In 1868, (in "Essay on an interpretation of non-Euclidean geometry") Beltrami gave the first model of hyperbolic geometry. In Beltrami's model, lines of hyperbolic geometry are represented by geodesics on the pseudosphere. Thus, Beltrami attempted to prove that Euclid's parallel postulate could not be derived from the other axioms of Euclidean geometry; this proof fails however since the pseudosphere is only a small portion of the hyperbolic plane.

In the same year, however, Beltrami went much farther and gave a correct proof of the equiconsistency of hyperbolic and Euclidean geometry, by defining what are now known as the Klein model, the Poincaré disk model, and the Poincaré half-plane model, in his paper "Teoria fondamentale degli spazii di curvatura costante". For the half-plane model, Beltrami cited a note by Liouville in a book by Monge on differential geometry.

Works

* [http://gallica.bnf.fr/notice?N=FRBNF31790864 Opere matematiche di Eugenio Beltrami publicate per cura della Facoltà di scienze della r. Università di Roma (volumes 1-2)] (U. Hoepli, Milano, 1902-1920)
* [http://name.umdl.umich.edu/AAN9527 Same edition, vols. 1-4]

ee also

*Beltrami's theorem
*Klein model
*Laplace-Beltrami operator
*Poincaré disk model
*Poincaré half-plane model
*Beltrami equation

External links

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Persondata
NAME= Beltrami, Eugenio
ALTERNATIVE NAMES=
SHORT DESCRIPTION= Italian Mathematician
DATE OF BIRTH= 16 November, 1835
PLACE OF BIRTH= Cremona, Lombardy, Austrian Empire
DATE OF DEATH= 4 June, 1899
PLACE OF DEATH= Rome, Italy