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Topic: Nicholas I Bernoulli


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  Jakob Bernoulli
Jakob Bernoulli was born in Switzerland and received his degree in 1671 after studying philosophy and theology at the request of his father and mathematics and astronomy against the will of his father.
Bernoulli showed his mastery of the calculus with his analysis of the solutions given by Huygens in 1687 and by Gottfried Wilhelm Leibniz in 1689 to the problem of the curve of constant descent in a gravitational field.
He was the first mathematician of the Bernoulli family, which became the most famous family in the history of mathematics.
www.economyprofessor.com /theorists/jakobbernoulli.php   (282 words)

  
  Jakob Bernoulli Summary
Bernoulli's pamphlet on parallels of logic and algebra appeared in 1685, again furthering his reputation, and in 1687 he was offered a post at the University of Basel as a professor of mathematics.
Bernoulli was fascinated by the mathematical properties of curves, especially the logarithmic spiral, a figure similar to the chambered nautilus mollusk shell in nature with its perfectly symmetrical spirals.
Bernoulli formulated an equation to refute the traditional hypothesis among mathematicians that the catenary is a parabola.
www.bookrags.com /Jakob_Bernoulli   (3052 words)

  
 Jean d'Alembert   (Site not responding. Last check: 2007-11-06)
The Petersburg problem was introduced by Nicholas Bernoulli in correspondence to Montmort which occurred in September 1713.
There is also interesting correspondence between Nicholas Bernoulli and others on the problem which began with a letter from Cramer in 1728.
Daniel Bernoulli earned a share of the prize in 1734 with his paper, "Physical and astronomical researches on the problem proposed for the second time by the Academie Royale des Sciences de Paris." Here he hypothesized that the solar atmosphere was the cause.
www.cs.xu.edu /math/Sources/Dalembert/index.html   (1106 words)

  
 A comprehensive biography of the Bernoullis   (Site not responding. Last check: 2007-11-06)
The Bernoullis (or as they are sometimes called, the Bernouillis) were a family of Dutch origin, who were driven from Holland by Catholic persecutions, and finally settled at Basle in Switzerland.
Nicholas Bernoulli was not as great as his brothers --- we shall speak of him only fleetingly.
Bar his innumerable controversies, the chief discoveries of John Bernoulli were the exponential calculus, the vigorous treatment of rigonometry as a branch of analysis, the conditions for a geodesic (the curve of shortest length between between two points on a surface.
www.uz.ac.zw /science/maths/zimaths/bernoull.htm   (1135 words)

  
 The Saint Petersburg paradox
Actually, his cousin, Nicholas Bernoulli, proposed it in 1713 in a letter to Pierre Rémond de Montmort who put it in his book Essay d'analyse sur les jeux de hazard that same year (see Montmort and the Grand Jan).
In a letter to me written in 1732 he declared that he was in no way dissatisfied with my proposition on the evaluation of risky propositions when applied to the case of a man who is to evaluate his own prosepcts.
See also the link "Bernoulli family tree" near the end of the page Johann Bernoulli, which has no pictures but is a little more complete and easier to understand.
www.math.fau.edu /Richman/Ideas/petersburg.htm   (676 words)

  
 Eulogy of Euler - Condorcet   (Site not responding. Last check: 2007-11-06)
He had studied Mathematics under Jacob Bernoulli and we know that this great man accompanied his genius for the Sciences with a profound philosophy which although it may not always be coupled with genius, serves as an extension to it, to make it more useful.
The Bernoulli brothers were true to their promise and took as much trouble to have a formidable rival at their side, as most men would have taken to keep themselves free from such circumstances.
Bernoulli, that he was the only other person to share the distinction of having won the prize of the Academy of Sciences thirteen times.
www.math.dartmouth.edu /~euler/historica/condorcet.html   (7325 words)

  
 The Bernoulli Family
The Bernoulli family may sound like a Mafia family from a television show, but they were the most predominant math family of Europe.
Daniel Bernoulli, born 1700 and died 1787 in Bale.
The Bernoulli blood may be filled with fire, but they did have a passion for mathematics.
www.math.wichita.edu /history/men/bernoulli.html   (786 words)

  
 The Bernoullis
Jacob or James Bernoulli was born at Bâle on December 27, 1654; in 1687 he was appointed to a chair in mathematics in the university there; and occupied it until his death on August 16, 1705.
Nicholas Bernoulli, the eldest of the three sons of John, was born on Jan. 27, 1695, and was drowned at St. Petersburg, where he was professor, on July 26, 1726.
Bernoulli also wrote a large number of papers on various mechanical questions, especially on problems connected with vibrating strings, and the solutions given by Taylor and by D'Alembert.
www.maths.tcd.ie /pub/HistMath/People/Bernoullis/RouseBall/RB_Bernoullis.html   (1078 words)

  
 Battery History, Technology, Applications and Development
Daniel Bernoulli was also the first to explain that the pressure exerted by a gas on the walls of its container is the sum of the many collisions by individual molecules, all moving independently of each other - the basis of the gas laws and the modern kinetic theory of gases.
Daniel Bernoulli was a member of a family of Bernoullis many of whom gained international distinction in mathematics.
John (Jean/Johann) Bernoulli, James' brother and father of Daniel was clever but unscrupulous, fraudulently substituting the work of his brother James, of whom he was jealous, for his own to cover up his errors.
www.mpoweruk.com /history.htm   (17340 words)

  
 Lemniscate of Bernoulli
His cousin, Nicholas Bernoulli, was the first to pose the famous St.Petersburg paradox.
A fourth Bernoulli, Nicholas, was the first to state the St. Petersburg paradox.
The Bernoulli family of distinguished mathematicians and scientists is virtually synonymous with the city of Basel in Switzerland.
curvebank.calstatela.edu /lemniscate/lemniscate.htm   (529 words)

  
 The Expected Utility Hypothesis - Introduction
The expected utility hypothesis stems from Daniel Bernoulli's (1738) solution to the famous St. Petersburg Paradox posed in 1713 by his cousin Nicholas Bernoulli (it is common to note that Gabriel Cramer, another Swiss mathematician, also provided effectively the same solution ten years before Bernoulli).
Daniel Bernoulli's solution involved two ideas that have since revolutionized economics: firstly, that people's utility from wealth, u(w), is not linearly related to wealth (w) but rather increases at a decreasing rate - the famous idea of diminishing marginal utility, u
Channelled by Gossen (1854), Bernoulli's idea of diminishing marginal utility of wealth became a centerpiece in the Marginalist Revolution of 1871-4 in the work of Jevons (1871), Menger (1871) and Walras (1874).
cepa.newschool.edu /het/essays/uncert/bernoulhyp.htm   (457 words)

  
 James Bernoulli - Wikipedia, the free encyclopedia
James Bernoulli (also known as Jacob I) was born in Basel, Switzerland on December 27, 1654 and lived until August 16, 1705.
He is one of the eight prominent mathematicians in the Bernoulli family.
He was appointed professor of mathematics at the University of Basel in 1687, remaining in this position for the rest of his life.
en.wikipedia.org /wiki/James_Bernoulli   (310 words)

  
 Giovanni Poleni   (Site not responding. Last check: 2007-11-06)
He was appointed, at the age of twenty-five, professor of astronomy at Padua.
In 1715 he was assigned to the chair of physics, and in 1719 he succeeded Nicholas Bernoulli as professor of mathematics.
As an expert in hydraulic engineering he was charged by the Venetian Senate with the care of the waters of lower Lombardy and with the constructions necessary to prevent floods.
www.catholicity.com /encyclopedia/p/poleni,giovanni.html   (249 words)

  
 Bernoulli in the Shower? Bernoulli Effect Fluids Pressure Science Experiment of the Week 307
The shape of an airplane wing was supposed to make the air travel faster over the top of the wing, causing less downwards air pressure on the wing.
Sounds great, but in both cases the Bernoulli effect is not the whole answer.
If the inward pull was from the Bernoulli effect, then the pull would be strongest at the far end of the towel, where the air is moving the fastest.
nicholasacademy.com /scienceexperiment307bernoullieffect.html   (911 words)

  
 Nicolaus II Bernoulli - Wikipedia, the free encyclopedia
Niklaus Bernoulli, Nikolaus Bernoulli, (February 6, 1695, Basel, Switzerland – July 31, 1726, St.
Eric W. Weisstein, Bernoulli, Nicholas (1695-1726) at ScienceWorld.
This article about a mathematician is a stub.
en.wikipedia.org /wiki/Nicolaus_II_Bernoulli   (109 words)

  
 Nicolaus II Bernoulli Summary
The first and favorite son of Johann Bernoulli (1667-1748), Nikolaus Bernoulli was destined to be overshadowed by his younger brother Daniel (1700-1782).
The Bernoullis were a distinguished family of Swiss mathematicians and scientists dating back to Nikolaus's grandfather, Nikolas (1623-1708).
Nicolaus II Bernoulli at the MacTutor History of Mathematics archive.
www.bookrags.com /Nicolaus_II_Bernoulli   (559 words)

  
 Biography of Leonard Euler
Witnessing this accomplishment, the Bernoulli’s suggested he pursue a mathematics career, which met with much resistance from Euler’s father.
Daniel Bernoulli commanded the top mathematical position at the Academy, and when he left it was Euler who took over.
Thanks to his connections to the Bernoulli family, Euler was able to get a strong foundation in math, and attained a teaching position at the prestigious St.
tiger.towson.edu /~gstiff1/eulerbio.htm   (1468 words)

  
 Newsletter Volume 28, No. 3 (84) 2004
Bernoulli was born in Basel into a wealthy Protestant family that two generations earlier had fled Amsterdam to escape enforced conformity to Roman Catholicism.
Hence, Bernoulli was born on December 27, 1654, under the Julian calendar as recognized by his canton, or on January 6, 1655, under the Gregorian calendar.
Bernoulli formally introduced the idea of estimating probabilities through relative frequencies of observed outcomes and obtained an associated theorem, now known as the Bernoulli’s weak law of large numbers.
isi.cbs.nl /NLet/NLet043.htm   (13459 words)

  
 Amazon.com: "James Bernoulli": Key Phrase page   (Site not responding. Last check: 2007-11-06)
The treatise is reprinted with a commentary in James Bernoulli's Ars Conjectandi, and forms the first of the four parts...
Key Phrases: Nicholas Bernoulli, James Bernoulli, Royal Society, John Bernoulli, Ludo Aleae, Daniel Bernoulli, compound probability theorem, median remaining lifetime, reversionary annuity, figurate numbers, survivorship insurances, symmetric binomial (see more)
James Bernoulli (1705) showed that compression also occurred, and that the so-called neutral line or surface, which was neither extended nor compressed,...
www.amazon.com /phrase/James-Bernoulli   (357 words)

  
 James Lewis CU
The Bernoulli brothers are most remembered for the Bernoulli number series and their work with differential calculus.
His father, Paul, was a student of Jakob Bernoulli and during his tenure at the University of Basel, he lived in the Bernoulli house with Jakob’s brother Johann.
With the support of Bernoulli, Euler was able to convince his father that he had a career in mathematics and shifted the emphasis of his studies.
www.unm.edu /~abqteach/math2002/02-02-06.htm   (8654 words)

  
 Lady Luck
Its author, the late Dr. Warren Weaver, was a professor of mathematics, active in the Rockefeller and Sloan foundations, an authority on communications and probability, and distinguished for his work at bridging the gap between science and the average citizen.
In accessible language and drawing upon the widely diverse writings of thinkers like Kurt Godel, Susanne K. Langer and Nicholas Bernoulli, Dr. Weaver explains such concepts as permutations, independent events, mathematical expectation, the law of averages, Chebychev's theorem, the law of large numbers, and probability distributions.
He uses a probabilistic viewpoint to illuminate such matters as rare events and coincidences, and also devotes space to the relations of probability and statistics, gambling, and modern scientific research.
www.project2061.org /publications/rsl/online/TRADEBKS/REVS/LADYLUCK.HTM   (170 words)

  
 Life and Work of Statisticians
Correspondence of Nicholas Bernoulli concerning the St Petersburg game with Montmort, Daniel Bernoulli and Cramer.
Nicholas Wright Gilham, A Life of Sir Francis Galton: From African Exploration to the Birth of Eugenics, Oxford University Press 2001 (ISBN 0-19-514365-5) (information about a new biography)
A problem concerning Pharaon: To determine generally the advantage of the banker relative to the punter (extracted from Essai D'analyse sur les jeux de hazard, 2nd edn 1713, pp.
www.york.ac.uk /depts/maths/histstat/lifework.htm   (2903 words)

  
 Earliest Known Uses of Some of the Words of Mathematics (M)
May 1728 written by Gabriel Cramer; see letter 8 in Correspondence of Nicholas Bernoulli concerning the St Petersburg game with Montmort, Daniel Bernoulli and Cramer (translation by Richard J. Pulskamp.) Daniel Bernoulli published an extract from this letter in his "Specimen Theoriae Novae de Mensara Sortis," Commentarii Academiae Scientiarum Imperialis Petropolitana, 5, 175-192 (1738).
Laplace gave Bernoulli's theory plenty of attention in the Théorie Analytique des Probabilités, livre II, chapitre X, p.
That is morally certain whose probability nearly equals the whole certainty, so that a morally certain event cannot be perceived not to happen: on the other hand, that is morally impossible which has merely as much probability as renders the certainty of failure moral certainty.
members.aol.com /jeff570/m.html   (9381 words)

  
 Isaac Newton (1642 - 1727)
He also used the series to determine the areas of the circle and the hyperbola in infinite series, and he found that the results were the same as those he had arrived at by other means.
Of these Newton enumerated one seventy-two; four of the remainder were mentioned by Stirling in 1717, one by Nicole in 1731, and one by Nicholas Bernoulli about the same time.
The problem of Pappus, here alluded to, is to find the locus of a point such the rectangle under its distances from two given straight lines shall be in a given ratio to the rectangle under its distances from two other given straight lines.
www.maths.tcd.ie /pub/HistMath/People/Newton/RouseBall/RB_Newton.html   (8709 words)

  
 Amazon.com: "Jacques Bernoulli": Key Phrase page   (Site not responding. Last check: 2007-11-06)
that the ordinary harmonic series does not converge, a theorem usually attributed to Jacques Bernoulli in 1689; he also showed the convergence of the reciprocals of the triangular numbers, a result for which Huygens usually...
Or again, consider the different interpretations that have been put upon the work of Jacques Bernoulli, whose posthumous book on probability was published in 1713.
Jacques Bernoulli, a Swiss mathematician (1654-1705), a contemporary of Newton and Leibnitz, discovered the sum of several infinite...
www.amazon.com /phrase/Jacques-Bernoulli   (278 words)

  
 Consumer Decision Making by Michael Richarme   (Site not responding. Last check: 2007-11-06)
The focus of this paper is to examine the major decision-making models, strategies, and theories that underlie the decision processes used by consumers and to provide some clarity for marketing executives attempting to find the right mix of variables for their products and services.
Early economists, led by Nicholas Bernoulli, John von Neumann, and Oskar Morgenstern, puzzled over this question.
Beginning about 300 years ago, Bernoulli developed the first formal explanation of consumer decision making.
www.decisionanalyst.com /publ_art/DecisionMaking.asp   (1644 words)

  
 Nicholas Riley’s Weblog
The disk/drive separation began to break down with the introduction of high-capacity removable, desktop-mountable media (CD, Bernoulli/SyQuest, etc.) Each removable disc or cartridge could be partitioned, just like a hard drive, and it would appear on the desktop as multiple "disks".
Referring to a CD or Bernoulli cartridge as a "drive", or relying on the difference between "disc" and "disk" would be to nit-pick, but it took until Mac OS X for Apple to redefine "disk" for consistency.
What Mac OS 9 calls a drive, Mac OS X calls a disk.
web.sabi.net /log   (2699 words)

  
 History of Mathematics: Chronology of Mathematicians
Jacques Bernoulli (James, Jakob) (1654-1705) *RB *MT *W
Jean Bernoulli (John, Johann) (1667-1748) *RB *MT *W
Jean Bernoullie (1744-1807) (son of Jean 1710-1790) *MT
aleph0.clarku.edu /~djoyce/mathhist/chronology.html   (693 words)

  
 Chronology of Game Theory
In a letter dated 13 November 1713 James Waldegrave provided the first, known, minimax mixed strategy solution to a two-person game.
Waldegrave wrote the letter, about a two-person version of the card game le Her, to Pierre-Remond de Montmort who in turn wrote to Nicolas Bernoulli, including in his letter a discussion of the Waldegrave solution.
Waldegrave's solution is a minimax mixed strategy equilibrium, but he made no extension of his result to other games, and expressed concern that a mixed strategy "does not seem to be in the usual rules of play" of games of chance
www.econ.canterbury.ac.nz /personal_pages/paul_walker/gt/hist.htm   (6341 words)

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