81. Bernoulli, Jakob [Jacques] Catalog of the Scientific Community. bernoulli, Jakob Jacques Note the creators of the Galileo Project and this catalogue cannot answer email on genealogical questions. 1. Dates http://es.rice.edu/ES/humsoc/Galileo/Catalog/Files/bernouli_jak.html

Catalog of the Scientific Community Bernoulli, Jakob [Jacques] Note: the creators of the Galileo Project and this catalogue cannot answer email on genealogical questions. 1. Dates Born: Died: Basel, Switzerland 16 Aug 1705 Dateinfo: Dates Certain Lifespan: 2. Father Occupation: Drug Merchant Clearly prosperous. 3. Nationality Birth: Swiss Career: Swiss Death: Swiss 4. Education Schooling: Bas?, M.A., D.D. University: MA philosophy 1671. Licentiate in theology 1676. Also studied math and astronomy. 5. Religion Affiliation: evangelicali.e, Lutheran 6. Discipline: mathematics. Subordinate: mechanics, astronomy. 6. Scientific Disciplines Primary: None 7. Means of Support Primary: Academic Position Secondary: Personal Means, Schoolmaster 1676, went as a tutor to Geneva. Then 2 years in France. 1683, returned to Basel, gave lectures as MA on mechanics (Experimentalphysik). 1687, became prof of mathematics at U. of Basel. 8. Patronage Type: City Magistrates His father was a Ratsherr of Basel. 9. Technological Involvement Types: None 10. Scientific Societies

82. Bernoulli, Jakob (1654-1705) -- From Eric Weisstein's World Of Scientific Biogra Mathematicians. Nationality. Swiss. Gender or Minority Status. Scientific Families. bernoulli, Jakob (16541705) Swiss mathematician (also known as Jacque I or James I) who was the brother of Johann http://www.treasure-troves.com/bios/BernoulliJakob.html

Branch of Science Mathematicians Nationality Swiss ... Scientific Families Bernoulli, Jakob (1654-1705) Swiss mathematician (also known as Jacque I or James I) who was the brother of Johann Bernoulli . With his brother, he is considered the most important founder of calculus with the exception of Newton . Nonetheless, the two had bitter arguments about the quality of each other's work. In his Ars conjectandi (1713), which was published posthumously, he developed the properties of Bernoulli numbers It has still not been determined how Bernoulli was able to derive many of the properties of Bernoulli numbers he discovered (Smith 1994, p. 85). In a paper of sums, he remarks how useless Bullialdus's voluminous work Opus novum ad arithmeticum infinitorum (1682) was, which "did nothing more that compute with immense labor the sums of the first six powers, which is only a part of what we have accomplished in the space of a single page" (Smith 1994, p. 90). Ars conjectandi was also the first substantial treatise on probability It contained the general theory of permutation and combination the weak law of large numbers as well as the binomial theorem (for which the first adequate proof for positive integers was given) and multinomial theorem He solved the Bernoulli differential equation independently of Leibniz and Johann Bernoulli . The lemniscate of Bernoulli, described by the polar equation

83. Bernoulli Numbers And The Pascal Triangle The relation between bernoulli numbers and the Pascal triangle. Fibonacci numbers and Golden Section.Lucas numbers and Golden Section. The relation between Fibonacci numbers and Lucas numbers. http://milan.milanovic.org/math/english/bernoulli/bernoulli.html

Bernoulli numbers and the Pascal triangle The Bernoulli numbers plays an important role in mathematics.They first appeard in Ars Conjectandi , a famous (and posthumous) published treatise in 1713, by Jakob Bernoulli. Bernoulli`s numbers appears in analysis, number theory and differential topology. Perheps one of the most important result is Euler - Maclaurin summation formula, where Bernoulli`s numbers are contained and which allows to accelerate the computation of slow converging series. There is surprising connection with Bernoulli`s numbers and Pascal`s triangle. To ilustrate this we shall now consider the function Taking advantage of the familiar expansion we can write From this it is clear that the function f(x) can be expanded in a power series about x=0 ; for the sake of convenience in subsequent computations, we represent this series as where B =f(0)=1. In order to determine the other coefficients B n (n=1,2, ... ) of the expansion, which are called Bernoulli numbers, we make use of the identity Multiplying together the power series and equating to zero the coefficients of the positive powers of the variable x, we obtain an infinite system of linear equations :

84. Nicolaus Bernoulli Nicolaus bernoulli. 16871759. Nicolaus bernoulli was a nephew of Jacobbernoulli and Johann bernoulli, two other famous mathematicians. http://www.stetson.edu/~efriedma/periodictable/html/Bi.html

Nicolaus Bernoulli Nicolaus Bernoulli was a nephew of Jacob Bernoulli and Johann Bernoulli, two other famous mathematicians. His early education involved studying mathematics with his uncles. In fact it was Jacob Bernoulli who supervised Nicolaus's Master's degree at the University of Basel, which he was awarded in 1704. Five years later he was received a doctorate for a dissertation which studied the application of probability theory to certain legal questions. In 1712, Bernoulli toured Europe visiting Holland, England and France. It was in France that he met Montmort and the two mathematicians became close friends and collaborated on mathematical questions in a long correspondence. Bernoulli was appointed to Galileo's chair at Padua in 1716. There he worked on geometry and differential equations. In 1722, he left Italy and returned to his home town to take up the chair of logic at the University of Basel. After 9 years, he was appointed to he chair of law. In addition to these academic appointments, he did 4 periods as rector of the university. Bernoulli was a gifted but not very productive mathematician. As a result, his most important achievements are hidden throughout his correspondence, which comprises about 560 items. From Montmort's work we can see that Bernoulli formulated certain problems in the theory of probability, in particular the problem which today is known as the St. Petersburg problem. Nicolaus also corresponded with Leibniz during the years 1712 to 1716. In these letters Nicolaus discussed questions of convergence.

85. The Mathematics Genealogy Project - Update Data For Jacob Bernoulli The Mathematics Genealogy Project http://www.genealogy.ams.org/html/php/submit-update.php?id=54440

86. Bernoulli, Jakob (1654-1705) -- From Eric Weisstein's World Of Scientific Biogra bernoulli, Jakob (16541705), Swiss mathematician (also known as JacqueI or James I) who was the brother of Johann bernoulli. With http://scienceworld.wolfram.com/biography/BernoulliJakob.html

Branch of Science Mathematicians Nationality Swiss ... Scientific Families Bernoulli, Jakob (1654-1705) Swiss mathematician (also known as Jacque I or James I) who was the brother of Johann Bernoulli . With his brother, he is considered the most important founder of calculus with the exception of Newton . Nonetheless, the two had bitter arguments about the quality of each other's work. In his Ars conjectandi (1713), which was published posthumously, he developed the properties of Bernoulli numbers It has still not been determined how Bernoulli was able to derive many of the properties of Bernoulli numbers he discovered (Smith 1994, p. 85). In a paper of sums, he remarks how useless Bullialdus's voluminous work Opus novum ad arithmeticum infinitorum (1682) was, which "did nothing more that compute with immense labor the sums of the first six powers, which is only a part of what we have accomplished in the space of a single page" (Smith 1994, p. 90). Ars conjectandi was also the first substantial treatise on probability It contained the general theory of permutation and combination the weak law of large numbers as well as the binomial theorem (for which the first adequate proof for positive integers was given) and multinomial theorem He solved the Bernoulli differential equation independently of Leibniz and Johann Bernoulli . The lemniscate of Bernoulli, described by the polar equation

87. Bernoulli Jakob bernoulli (16541705). Last modified, September9, 2003. suchii@bun.kyoto-u.ac.jp. http://www.bun.kyoto-u.ac.jp/phisci/Gallery/bernoulli.html

Jakob Bernoulli Last modified, September 9, 2003. suchii@bun.kyoto-u.ac.jp

88. Bernoulli pero la abandonó en cuanto pudo, en favor de su amor por las ciencias. http://es.geocities.com/fisicas/cientificos/matematicos/bernoulli.htm

La familia BERNOULLI Jacob Bernoulli En su libro Ars Conjectandi Johann Bernoulli Los hermanos Bernoulli trabajaron a veces en los mismos problemas, lo que era lamentable, debido a sus naturalezas celosas y quisquillosas. Este hijo, Daniel Bernoulli En su famoso libro Hydrodynamica Teorema de Bernoulli r g h + r v / 2 = cte http://es.geocities.com/fisicas Los autores: e fisicas@yahoo.es

89. Imago Mundi - Bernoulli. http://www.cosmovisions.com/Bernoulli.htm

Dictionnaire biographique Les gens Bernouilli et mieux Bernoulli , famille suisse; originaire d'Anvers a produit dans les XVII e et XVIII e Bernoulli Leibniz Ars conjectandi Jacobi Bernoulli Opera Bernoulli Hartsœker Opera omnia , Lausanne, 1742, 4, vol. in-4. Il faut y joindre son Commercium philosophicum et mathematicum avec Leibniz, 2 v. in-4, Lausanne, 1745. Il forma Euler Bernoulli (Daniel), 2 e Hydrodynamica (Strasbourg, 1738, in-4) est le plus important de ses ouvrages. Un 2 e A B C D ... Z

90. Bernoulli, Hans Translate this page bernoulli, Hans. Archivi -Fondo presso ETH-GTA Bibliografia -K. e M. Nägelin-Gschwind,H. bernoulli, Architekt und Städtebauer, 1993 (con elenco delle op.). http://www.lexhist.ch/externe/protect/textes/i/I6178.html

Bernoulli, Eva Bernoulli, Jacob No 6 Bernoulli, Hans 17.2.1876 Basilea, 12.9.1959 Basilea, rif., di Basilea. Figlio di Theodor, impiegato presso l'ufficio notarile; fratello di Elisabeth ( -> No 4 Werk . Tornato a Basilea, fu insegnante di bozzetto alla scuola professionale industriale (1930-42) e, per il movimento dei Freiwirtschafter , Granconsigliere (1935-38); fu inoltre redattore di Archiv , "trimestrale per un ordine economico naturale" (1941-44). Ricevette il dottorato h.c. dall'Univ. di Basilea (1947), e per l'Anello degli indipendenti fece parte del Consiglio nazionale (1947-51). Convinto sostenitore delle idee economiche dei Freiwirtschafter , si occupò di diritto fondiario e di legislazione edilizia ("suolo e terreno alla città, proprietà immobiliare ai privati"). Le sue concezioni urbanistiche denotano influssi del movimento delle città giardino; nella sua architettura si rileva l'impronta di Friedrich Ostendorf e del classicismo Biedermeier del movimento di "ritorno all'Ottocento". Nello sviluppo di abitazioni tipo creò, partendo dai modelli tradizional, piccoli appartamenti e piccole case per famiglie con reddito modesto. Dopo il 1945 fu attivo quale consulente nelle zone di ricostruzione di Ungheria, Polonia, Germania e Austria. Archivi -Fondo presso ETH-GTA Bibliografia -K. e M. Nägelin-Gschwind

91. BiblioDb http://aleasrv.cs.unitn.it/bibliodb.nsf/0/9084ebd76a57112ec1256951002afdf4?OpenD

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