21. Beltrami, Eugenio beltrami, eugenio (18351899). Italian mathematician who pioneeredmodern non-Euclidean geometry. His work ranged over almost the http://www.cartage.org.lb/en/themes/Biographies/MainBiographies/B/Beltrami/1.htm

Beltrami, Eugenio Italian mathematician who pioneered modern non-Euclidean geometry. His work ranged over almost the whole field of pure and applied mathematics, but especially theories of surfaces and space of constant curvature. Beltrami was born in Cremona, Lombardy, and studied mathematics at Pavia. He held academic posts at Bologna, Pisa, Pavia, and Rome. In 1862 he published his first paper, an analysis of the differential geometry of curves, to which he would return in his most important paper, 'Saggio di interpretazione della geometria non-euclidia' 1868. This advanced a theory of hyperbolic space that laid the analytical base for the development of non-Euclidean geometry. Beltrami demonstrated that the concepts and formulae of Russian mathematician Nikolai Lobachevsky's geometry are realized for geodesics on surfaces of constant negative curvature. He showed also that there are rotation surfaces of this kind - he called them 'pseudospherical surfaces'. He also demonstrated the usefulness of employing differential parameters in surface theory, thereby beginning the use of invariant methods in differential geometry. After 1872 Beltrami switched his attention to questions of applied mathematics, especially problems in elasticity and electromagnetism.

22. Beltrami, Eugenio Encyclopædia Britannica. beltrami, eugenio. Encyclopædia Britannica Article http://kids.infoplease.lycos.com/ce6/people/A0806941.html

Search For: Lycos Zone Home Family Zone Teachers Zone Encyclopedia Beltrami, Eugenio A OO O b A E Pronunciation Key Beltrami, Eugenio , Italian mathematician. He is famous for his work on non-euclidean geometry, electricity, and magnetism. Belteshazzar Beltsville swine Awards and Press Citing Fact Monster Lycos Worldwide Lycos Zone Privacy Statement

23. Mathematicians Translate this page Babbage, Charles Baker, Alan Balmer, Johann Jakob Banneker, Benjamin Banu, MusaBarrow, Isaac Bayes, Reverend Thomas beltrami, eugenio Bernoulli, Daniel http://www.cartage.org.lb/en/themes/Biographies/Categories/Scientists/Mathematic

Babbage, Charles Baker, Alan Balmer, Johann Jakob Banneker, Benjamin Babbage, Charles Baker, Alan Balmer, Johann Jakob Banneker, Benjamin ... Byron, Augusta Ada

24. La Matematica Italiana 1800-1950 Translate this page eugenio beltrami. (1835-1900). Nacque a Cremona il 16 - 11 - 1835 emorì a Roma il 18 - 2 - 1900. Ebbe gioventù movimentata a causa http://www.dm.unito.it/sism/m_italiani/biografie/tricomi/beltrami.html

Eugenio BELTRAMI Necr.: Rend. Circ. Mat. Palermo 14 (1900), 275-289 (L. Cremona), Annali di Matem. (3) 4 (1900) 151-160 (U. Dini); Rend. Semin. Milano 9 (1935), 75-85 (G. A. Maggi); ecc. Opere: 4 voll. a cura dell'Univ. di Roma. Milano, Hoepli, 1902-1920. Tricomi, 1962

25. Beltrami, Eugenio beltrami, eugenio 183599, Italian mathematician. He is famous for his work on non-euclideangeometry, electricity, and magnetism. Bea - Bei. beltrami, eugenio. http://www.slider.com/enc/6000/Beltrami_Eugenio.htm

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27. Encyclopædia Britannica Encyclopædia Britannica, beltrami, eugenio Encyclopædia Britannica Article. MLAstyle beltrami, eugenio. 2003 Encyclopædia Britannica Premium Service. http://www.britannica.com/eb/article?eu=15522

28. Beltrami, Eugenio beltrami, eugenio. (b. Nov. 16, 1835, Cremona, Lombardy, AustrianEmpire now in Italyd. Feb. 18, 1900, Rome, Italy), Italian http://www.phy.bg.ac.yu/web_projects/giants/beltrami.html

Britannica CD Index Articles Dictionary Help Beltrami, Eugenio (b. Nov. 16, 1835, Cremona, Lombardy, Austrian Empire [now in Italy]d. Feb. 18, 1900, Rome, Italy), Italian mathematician known for his concepts of non-Euclidean geometry, especially his theories of surfaces of constant curvature. Following his studies at the University of Pavia (1853-56) and later in Milan, Beltrami was invited to join the faculty at the University of Bologna in 1862 as a visiting professor of algebra and analytic geometry; four years later he was appointed professor of rational mechanics. He also held professorships at universities in Pisa, Rome, and Pavia. Influenced by N.I. Lobachevsky, C.F. Gauss, and Bernhard Riemann, Beltrami's work on the differential geometry of curves and surfaces removed any doubts about the validity of non-Euclidean geometry, and his method was soon followed by the German mathematician Felix Klein. Beltrami's four-volume work, Opere Ma te ma tiche (1902-20), published posthumously, contains his comments on a broad range of physical and mathematical subjects, including thermodynamics, elasticity, magnetism, optics, and electricity. Beltrami was a member of the Accademia dei Lincei, serving as president in 1898; he was elected senator a year before his death. Related Propaedia Topics: The 19th and 20th centuries: development of non-Euclidean geometry by Bolyai, Lobachevsky, and others; contributions to the theories of groups, functions, and complex variables; development of algebraic geometry; influence of physical science on analysis; study of the foundations of mathematics

29. Biografie - Eugenio Beltrami Translate this page eugenio beltrami Cremona 1835 - Roma 1900. Professore di algebrae geometria analitica all’Università di Bologna dal 1862, fu http://galileo.imss.firenze.it/milleanni/cronologia/biografie/beltrami.html

Eugenio Beltrami Cremona 1835 - Roma 1900 Indietro Indice Biografie Inizio

30. Browse UM Historical Math Collection bookbag beltrami, eugenio, 1835-1900. Opere matematiche di eugenio beltrami. http://www.dlxs.org/products/archive-by-CDROM/8/TextClass/src/web/u/umhistmath/b

Multiple collection search Authorized user login View bookbag simple search ... help " width="1" height="1" border="0"> " width="1" height="1" border="0"> " width="1" height="1" border="0"> " width="1" height="1" border="0"> " width="1" height="1" border="0"> " width="1" height="1" border="0"> " width="1" height="1" border="0"> Books are displayed in alphabetical order by author. 1 to 100 of 460 records Abel, Niels Henrik, 1802-1829.: Abhandlung über eine besondere Klasse algebraisch auflösbarer Gleichungen. Von N. H. Abel (1829). Hrsg. von Alfred Loewy. Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg. Abhandlungen zur Geschichte der Mathematik. Abhandlungen zur Geschichte der Mathematik. Abhandlungen zur Geschichte der Mathematik. Abhandlungen zur Geschichte der mathematischen Wissenschaften mit Einschluss ihrer Anwendungen. Abhandlungen zur Geschichte der mathematischen Wissenschaften mit Einschluss ihrer Anwendungen. Abhandlungen zur Geschichte der mathematischen Wissenschaften mit Einschluss ihrer Anwendungen. Abhandlungen zur Geschichte der mathematischen Wissenschaften mit Einschluss ihrer Anwendungen.

31. Sistema Museale Di Ateneo, Università Di Pavia Translate this page eugenio beltrami Nacque a Cremona nel 1835. Dopo aver ricoperto lacattedra di algebra e geometria analitica all’Università di http://ppp.unipv.it/musei/pagine/Biografie/biobeltra.htm

Cerca nel sito: Almeno una parola Tutte le parole Frase intera Biografie Personaggi: Eugenio Beltrami Alessandro Brambilla Luigi Valentino Brugnatelli Luigi Brusotti Galileo Ferraris ... Alessandro Volta Eugenio Beltrami http://dimat.unipv.it/~cornalba/lezioni/beltrami.pdf

32. Vita Di Beltrami Translate this page eugenio beltrami. Cremona 16/11/1835-Roma 18/2/1900. Per approfondire Articolodi Maurizio Cornalba del 20 maggio 2000 eugenio beltrami un sito in inglese. http://www.rccr.cremona.it/beltrami/beltra.htm

33. Math Curiosities A Brief Look at The Life and Works of eugenio beltrami By Dr. MarkHughes. eugenio beltrami was an Italian mathematician who played http://www.frostburg.edu/dept/math/Bio_Beltrami.htm

A Brief Look at The Life and Works of Eugenio Beltrami By Dr. Mark Hughes Eugenio Beltrami was an Italian mathematician who played an important role in improving our understanding of non-Euclidean geometry. Beltrami was born on November 16, 1835 in Cremona. He was a student at universities in Pavia and Milan. His first academic position was at the University of Bologna. During his career, he was also associated with universities in Pisa, Rome and Pavia. Among Beltrami's non-mathematical activities was his service as a senator in the kingdom of Italy during his last year of life. He died on June 4, 1899 in Rome. Beltrami's life as a mathematician can be divided into two main stages. His earlier and more important work was in the field of geometry. Later, his interests turned towards applied mathematics, including works on elasticity, Maxwell's theory of electromagnetism and other topics of mathematical physics. Beltrami's 1868 paper, "Saggio di interpretazione della geometria non-euclidea" is considered to be his most important work. In this paper, Beltrami provided an important key towards the understanding of Hyperbolic Geometry, namely a model developed within the framework of Euclidean Geometry.

34. Cannizzaro List Of Correspondents Translate this page Bellini, Ranieri -. Bellucci, Giuseppe -. Bellucci, Italo -. beltrami, eugenio-. Beltrani, Vito -. Beretta, Antonio -. Bertagnini, Cesare -. Bertani, Agostino-. http://www.accademiaxl.it/Archivi/Cannizzaro/CorrInd.asp?Lat=B

35. Cannizzaro Documents Look Up Translate this page beltrami, eugenio. Dati anagrafici Cremona,1835-Roma,1900 NotizieMatematico,fu prof. di Geometria analitica a Bologna (1862), di http://www.accademiaxl.it/Archivi/Cannizzaro/Corr.asp?String=51

36. Jacques Maritain Center: William A. Wallace, OP (2) Jacques Maritain Center Thomistic Institute From DSB 1599600 (beltrami,eugenio) In a paper of 1865 beltrami had shown that http://www.nd.edu/Departments/Maritain/ti/wallace2.htm

Jacques Maritain Center: Thomistic Institute From DSB 1:599-600 (Beltrami, Eugenio): ...In a paper of 1865 Beltrami had shown that on surfaces of constant curvature, and only on them, the line elements ds can be written in such a form that the geodesics, and only these, are represented by linear expressions in u and v . For positive curvature R this form is . . . The geodesics in this case behave, locally speaking, like the great circles on a sphere. It now occurred to Beltrami that, by changing R to iR and a to ia , the line element thus obtained . . ., which defines surfaces of constant curvature -R , offers a new type of geometry for its geodesics inside the region u v a . This geometry is exactly that of the so-called non-Euclidean geometry of Lobachevski, if geodesics on such a surface are identified with the "straight lines" of non-Euclidean geometry.

37. Scientists Math of Perga; Archimedes; Babbage, Charles; Banach, Stefan; Barrow, Isaac;beltrami, eugenio; Benedetti, Giovanni Battista; Bhaskara; Birkhoff http://www.infoplease.com/spot/scibio5.html

38. Beltrami, Eugenio Help Site Map. encyclopediaEncyclopedia beltrami, eugenio, AOOje'nyO bAlträ'mEPronunciation Key. beltrami, eugenio , 1835–99, Italian mathematician. http://www.infoplease.com/ce6/people/A0806941.html

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39. Un Largo Camino -- Indice Biografico Translate this page Un Largo Camino Índice Biográfico Índice Biográfico. beltrami,eugenio (1835-1900) Nació en Cremona, Italia, y murió en Roma. http://mural.uv.es/beaco/bio.htm

BELTRAMI, Eugenio (1835-1900): BOLYAI, Farkas Wolfgang (1775-1856): axioma de las paralelas. Sus intentos por impedir que su hijo estudiara el axioma postulado BOLYAI, Janos (1802-1860): axioma D'ALEMBERT, Jean le Rond (1717-1783): EUCLIDES: GAUSS, Carl F. (1777-1855): , basada en axioma GIRARD, Albert (1595-1632): KLEIN, Felix Christian (1849-1925): LAMBERT Johann Heinrich (1728-1777): LEGENDRE, Adrien-Marie (1752-1833): LOBATCHEVSKY, Nicolai Ivanovich (1793-1856): axioma , el de las rectas paralelas. Lovachevski dio un paso gigantesco al preguntarse si dicho axioma MENELAO DE ALEJANDRIA: PLAYFAIR, John (1748-1819): RIEMANN, Georg Friedrich Bernhard (1826-1866): SACCHERI, Giovanni Girolamo (1667-1733): TAURINUS, Franz Adolph (1794-1874): postulado de Euclides. WALLIS, John (1616-1703):

40. Un Largo Camino -- El Significado Real De La Geometria De Lobatchevsky Translate this page En 1868 el italiano eugenio beltrami publicó Ensayo sobre la interpretación dela Geometría no euclídea, que proporcionó un modelo para la geometría no http://mural.uv.es/beaco/tr3.htm

En 1868 el italiano Eugenio Beltrami de Lobatchevsky dentro de la FIGURA 5: Tractriz y seudoesfera Beltrami hizo notar que la Lobatchevsky . De este modo, esta Pero, como hemos mencionado con anterioridad, Beltrami Lobatchevsky Klein Klein ... cuerdas en cuerdas Lobatchevsky Euclides Lobatchevsky FIGURA 6: La Esfera de Klein Una recta se interpreta como una cuerda cuerda cuerda s en cuerda s. Lobatchevsky Lobatchevsky Lobatchevsky en el espacio).

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