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Topic: Eugenio Beltrami

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	Eugenio Beltrami Encyclopedia
		Beltrami first began studying mathematics at University of Pavia in 1853, but was forced to discontinue his studies in 1856 because of financial hardship.
		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.
	www.hallencyclopedia.com /topic/Eugenio_Beltrami.html (349 words)

	Beltrami biography
		Beltrami studied at Pavia from 1853 to 1856, and there he was taught by Brioschi who had been appointed as professor of applied mathematics at the University of Pavia the year before Beltrami began his studies.
		Beltrami would have liked to continue his mathematical studies but he was suffering financial hardship so in 1856 he had to stop his studies and take up a job.
		Beltrami showed that not all geodesics could be represented in this way and he then went on to consider the natural question of which surfaces had the property that geodesics on the surface could be represented as straight lines on the plane.
	www-history.mcs.st-andrews.ac.uk /Biographies/Beltrami.html (1061 words)

	Eugenio Beltrami -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-11-03)
		Beltrami first began studying mathematics at (Click link for more info and facts about University of Pavia) University of Pavia in 1853, but was forced to discontinue his studies in 1856 because of financial hardship.
		Beltrami later taught at universities in (A city in Tuscany; site of the famous Leaning Tower) Pisa, (Capital and largest city of Italy; on the Tiber; seat of the Roman Catholic Church; formerly the capital of the Roman Republic and the Roman Empire) Rome and Pavia.
		In Beltrami's model, lines of hyperbolic geometry are represented by ((mathematics) the shortest line between two points on a mathematically defined surface (as a straight line on a plane or an arc of a great circle on a sphere)) geodesics on the (Click link for more info and facts about pseudosphere) pseudosphere.
	www.absoluteastronomy.com /encyclopedia/e/eu/eugenio_beltrami.htm (281 words)

	Eugenio Beltrami Summary
		In his later work in applied mathematics, on fluid theory and elasticity, Beltrami remained interested in the underlying conceptions of space in these theories.
		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 Theoria fondamentale delgi spazil di curvatura constanta.
		Eugenio Beltrami at the MacTutor History of Mathematics archive.
	www.bookrags.com /Eugenio_Beltrami (335 words)

	Eugenio Beltrami -- Britannica Concise Encyclopedia - The online encyclopedia you can trust! (Site not responding. Last check: 2007-11-03)
		Beltrami was a member of the scientific Accademia dei Lincei, serving as president in 1898; he was elected to the Italian Senate a year before his death.
		In the 1930s and 1940s the Italian poet, prose writer, editor, and translator Eugenio Montale was considered to be a leader of the literary movement known as Hermeticism.
		An educator, writer, and political leader, Eugenio Maria de Hostos y Bonilla was an early advocate of self-government for the island of Puerto Rico.
	www.britannica.com /ebc/article-9015326 (797 words)

	AllRefer.com - Eugenio Beltrami (Mathematics, Biography) - Encyclopedia
		AllRefer.com - Eugenio Beltrami (Mathematics, Biography) - Encyclopedia
		Eugenio Beltrami[AOOje´nyO bAltrA´mE] Pronunciation Key, 1835–99, Italian mathematician.
		More articles from AllRefer Reference on Eugenio Beltrami
	reference.allrefer.com /encyclopedia/B/Beltrami.html (122 words)

	References for Beltrami (Site not responding. Last check: 2007-11-03)
		F Palladino and R Tazzioli, Letters of Eugenio Beltrami to Ernesto Cesàro, Archive for History of Exact Science 49 (4) (1996), 321-353.
		M J Scanlan, Beltrami's model and the independence of the parallel postulate, Hist.
		E Valabrega Gibellato, The papers of Eugenio Beltrami, Corrado Segre and Giovanni Vailati on the "forgotten Saccheri" (Italian), Pietro Riccardi (1828-1898) and the historiography of mathematics in Italy, Modena, 1987 (Modena, 1989), 297-303.
	www-gap.dcs.st-and.ac.uk /~history/References/Beltrami.html (183 words)

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