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Topic: John Bernoulli

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	Isaac Newton's later life - Wikipedia, the free encyclopedia
		In June 1696 Bernoulli addressed a letter to the mathematicians of Europe challenging them to solve two problems—(1) to determine the brachistochrone between two given points not in the same vertical line, (2) to determine a curve such that, if a straight line drawn through a fixed point A meet it in two points P
		Six months were allowed by Bernoulli for the solution of the problem, and in the event of none being sent to him he promised to publish his own.
		Tschirnhaus were appointed on February 4, James Bernoulli and John Bernoulli on February 14, and Newton and Ole Rømer on February 21.
	en.wikipedia.org /wiki/Isaac_Newton_(in_depth,_3/3) (3179 words)

	James Bernoulli (1654-1705) (Site not responding. Last check: 2007-09-29)
		The Swiss Bernoulli brothers, James and John, were the first to achieve a full understanding of Leibniz’s presentation of the calculus.
		The Bernoulli brothers used the techniques of Leibniz’s calculus as a means for handling a wide range of astronomical and physical problems, sometimes working independently to solve the same problem.
		In 1690, James Bernoulli challenged the mathematicians of Europe to determine the shape (that is, to find the equation) of a hanging flexible cable suspended in equilibrium at two points.
	www.mhhe.com /math/calc/smithminton2e/cd/tools/timeline/bernoulli.html (342 words)

	Bernoulli. The Columbia Encyclopedia, Sixth Edition. 2001-05 (Site not responding. Last check: 2007-09-29)
		One of the chief developers both of the ordinary calculus and of the calculus of variations, he was the first to use the word integral in solving Leibniz’s problem of the isochronous curve.
		He was succeeded at Basel by his brother, Johann, Jean, or John Bernoulli, 1667–1748, who earlier had been professor at Gröningen and who was famous for his work in the field of integral and exponential calculus and was also a founder of the calculus of variations.
		His greatest work was his Hydrodynamica (1738), which included the principle now known as Bernoulli’s principle, and anticipated the law of conservation of energy and the kinetic-molecular theory of gases developed more than 100 years later.
	www.bartleby.com /65/be/BernoulFam.html (343 words)

	Johann Bernoulli - Wikipedia, the free encyclopedia
		Johann Bernoulli (Basel, July 27, 1667 - January 1, 1748) was a Swiss mathematician.
		He was the brother of Jakob Bernoulli, and the father of Daniel Bernoulli and Nicolaus II Bernoulli.
		Bernoulli proposed a fluid energy perpetual motion machine.
	en.wikipedia.org /wiki/John_Bernoulli (125 words)

	The Bernoullis
		John Bernoulli, the brother of James Bernoulli, was born at Bâle on August 7, 1667, and died there on January 1, 1748.
		Leaving out of account his innumerable controversies, the chief discoveries of John Bernoulli were the exponential calculus, the treatment of trigonometry as a branch of analysis, the conditions for a geodesic, the determination of orthogonal trajectories, the solution of the brachistochrone, the statement that a ray of light pursues such a path that
		John Bernoulli, the younger, a brother of Nicholas and Daniel, was born on May 18, 1710, and died in 1790; he also was a professor at Bâle.
	www.maths.tcd.ie /pub/HistMath/People/Bernoullis/RouseBall/RB_Bernoullis.html (1078 words)

	Bernoulli_Johann
		Bernoulli received generous payment from de l'Hôpital for these lessons, and indeed they were worth a lot for few other people would have been able to have given them.
		Bernoulli's course is virtually identical with de l'Hôpital's book but it is worth pointing out that de l'Hôpital had corrected a number of errors such as Bernoulli's mistaken belief that the integral of 1/x is finite.
		Bernoulli also made important contributions to mechanics with his work on kinetic energy, which, not surprisingly, was another topic on which mathematicians argued over for many years.
	www-groups.dcs.st-and.ac.uk /~history/Mathematicians/Bernoulli_Johann.html (2494 words)

	john - definition by dict.die.net
		John Bull, an ideal personification of the typical characteristics of an Englishman, or of the English people.
		John Doe (Law), the name formerly given to the fictitious plaintiff in an action of ejectment.
		When John the Baptist began his ministry in the wilderness of Judea, John, with many others, gathered round him, and was deeply influenced by his teaching.
	dict.die.net /john (547 words)

	Johann Bernoulli -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-09-29)
		Johann Bernoulli ((A city in northwestern Switzerland) Basel, July 27, 1667 - January 1, 1748) was a (The natives or inhabitants of Switzerland) Swiss (A person skilled in mathematics) mathematician.
		He was the brother of (Swiss mathematician (1654-1705)) Jakob Bernoulli, and the father of (Swiss physicist who contributed to hydrodynamics and mathematical physics (1700-1782)) Daniel Bernoulli and (additional info and facts about Nicolaus II Bernoulli) Nicolaus II Bernoulli.
		With his brother, Bernoulli pioneered (additional info and facts about Gottfried Leibniz) Gottfried Leibniz's (A hard lump produced by the concretion of mineral salts; found in hollow organs or ducts of the body) calculus.
	www.absoluteastronomy.com /encyclopedia/j/jo/johann_bernoulli.htm (208 words)

	A Science History Quiz
		John Tyndall (1820-1893) proposed that the blueness of the sky is due to light scattering by atmospheric dust.
		Bernoulli had sent l'Hospital this rule of calculus, and l'Hospital published it under his own name, with only an unspecific acknowledgment of help from ``the young professor at Groningen.'' This shows that immortality can sometimes be bought.
		Bernoulli, Nicolas (I) (1687-1759) Nephew of Jacques (I) Bernoulli, Nicolas (II) (1695-1726) Son of Jean (I) Williams, Henry Smith.
	www.lhup.edu /~dsimanek/scihist.htm (3941 words)

	The Columbia Encyclopedia, Sixth Edition: Bernoulli @ HighBeam Research (Site not responding. Last check: 2007-09-29)
		BERNOULLI [Bernoulli] or Bernouilli, name of a family distinguished in scientific and mathematical history.
		He was succeeded at Basel by his brother, Johann, Jean, or John Bernoulli, 1667-1748, who earlier had been professor at Gröningen and who was famous for his work in the field of integral and exponential calculus and was also a founder of the calculus of variations.
		His son, Daniel Bernoulli, 1700-1782, was a mathematician, physicist, and physician and has often been called the first mathematical physicist.
	www.highbeam.com /library/doc0.asp?DOCID=1E1:BernoulFam&refid=ip_encyclopedia_hf (353 words)

	BROOK TAYLOR - LoveToKnow Article on BROOK TAYLOR
		(1685-1731), English mathematician, was the son of John Taylor, of Bifrons House, Kent, by Olivia, daughter of Sir Nicholas Tempest, Bart., of Durham, and was born at Edmonton in Middlesex on the 18th of August 1685.
		I-Ic entered St Johns College, Cambridge, as a fellow-commoner in 1701, and took degrees of LL.B. and LL.D. respectively in 1709 and 1714.
		Having studied mathematics under John Machin and John Keill, he obtained in 1708 a remarkable solution of the problem of the centre of oscillation, which, however, remaining unpublished until May 1714 (Phil.
	www.1911encyclopedia.org /T/TA/TAYLOR_BROOK.htm (604 words)

	Lemniscate of Bernoulli (Site not responding. Last check: 2007-09-29)
		John taught L'Hôpital the famous rule, but John's best known student was another native of Basel, Leonhard Euler.
		John's name is also associated with two other famous curves, the brachystochrome and the catenary.
		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)

	Leonhard Euler (1707 - 1783)
		When, in 1725, the younger Bernoullis went to Russia, on the invitation of the empress, they procured a place there for Euler, which in 1733 he exchanged for the chair of mathematics, then vacated by Daniel Bernoulli.
		John Bernoulli represented the number by c; Euler in 1734 denoted by p, and in a letter of 1736 (in which he enunciated the theorem that the sum of the squares of the reciprocals of the natural numbers is
		The classic problems on isoperimetrical curves, the brachistochrone in a resisting medium, and the theory of geodesics (all of which had been suggested by his master, John Bernoulli) had engaged Euler's attention at an early date; and in solving them he was led to the calculus of variations.
	www.maths.tcd.ie /pub/HistMath/People/Euler/RouseBall/RB_Euler.html (1819 words)

	10.3. Bernoulli, Johan (1667-1748)
		Johann Bernoulli was one of the pioneers in the field of calculus and helped apply the new tool to real problems.
		Johann (also known as Johannes, Jean or John, depending on the translation) Bernoulli was born in Basel, Switzerland, on August 6, 1667.
		Bernoulli was obviously enraged by the theft and ceased helping his freeloading friend.
	web01.shu.edu /projects/reals/history/bernoull.html (833 words)

	SCIENCE OF SPORTS: Better Baseball
		The curve ball phenomenon described in the preceding paragraph occurs partly because of the relationship between the pressure of a fluid and its velocity.
		It was determined by 18th-century Swiss scientist and mathematician Daniel Bernoulli and is known as the Bernoulli principle.
		John Garver holds eight patents for his inventions, which include a Christmas tree ornament and a ball-throwing machine, and he has a secret weapon for any baseball player -- if coaches would only listen.
	www.pbs.org /safarchive/4_class/45_pguides/pguide_405/4545_bb.html (1078 words)

	The Helen of Geometers
		Incidentally, the Bernoulli's were partisans on the side of Leibniz in the famous priority dispute between Leibniz and Newton over the invention of calculus.
		Bernoulli supposedly said he knew who the anonymous author must be, "as the lion is recognized by his print".
		It's interesting that Jean Bernoulli apparently arrived at his result from his studies of the path of a light ray through a non-uniform medium.
	www.mathpages.com /rr/s8-03/8-03.htm (1364 words)

	A comprehensive biography of the Bernoullis (Site not responding. Last check: 2007-09-29)
		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.
		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.
		John III earned a doctorate in philosophy at the age of 13 and was appointed astronomer-royal, and director of mathematical studies at Berlin, while Jacob II was a professor with a very bright future before he was accidentally drowned, like his uncle Nicholas III.
	www.uz.ac.zw /science/maths/zimaths/bernoull.htm (1135 words)

	Bernoulli and Leibniz test Newton (Site not responding. Last check: 2007-09-29)
		Bernoulli allowed six months for the solutions but no solutions were received during this period.
		Following Bernoulli's suggestion the curve which solves the problem is called the `brachistochrone', which is the Greek for `the shortest time'.
		Bernoulli's problem was an early example of a class of problems called Calculus of Variations now.
	www.math.purdue.edu /~eremenko/bernoulli.html (522 words)

	[No title]
		Bernoulli's attack on this problem began with what he called "Fermat's metaphysical principle", that light always seeks out the path of least time.
		Bernoulli's approach was to follow the light, so to speak, to the path of least time.
		Bernoulli shows, that if the density of the medium is changing according to the rate at which a body falls under its own weight, (specifically, that the velocity changes according to the square root of the vertical distance) then the resulting curve is a cycloid.
	www.wlym.com /antidummies/part09.html (1561 words)

	Daniel Bernoulli -- Encyclopædia Britannica
		Bernoulli's theorem (q.v.), which he derived, is named after him.
		First derived (1738) by the Swiss mathematician Daniel Bernoulli, the theorem states, in effect, that the total mechanical energy of the flowing...
		He developed the Bernoulli numbers, by which he derived the exponential series, and he introduced the term...
	www.britannica.com /eb/article-9078863 (748 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.
		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.
		John's three sons Nicholas, Daniel and John Bernoulli the younger and his two sons John and James all achieved distinction in mathematics in their own right.
	www.mpoweruk.com /history.htm (17339 words)

	FUNCTION - Online Information article about FUNCTION
		Bernoulli were able by 1690 to begin to make substantial contributions to the development of the new calculus, and Leibnitz adopted their word " integral " in 1695, they at the same time adopting his symbol " f." In 1696 the See also:
		logarithm and an exponential, and John Bernoulli was the first to recognize the property possessed by an exponential (az) of becoming infinitely great in comparison with any power (20°) when xis increased indefinitely.
		Great indignation was aroused; and John Keill took occasion, in a memoir on central forces which was printed in the Philosophical Transactions for 1708, to affirm that Newton was without doubt the first inventor of the calculus, and that Leibnitz had merely changed the name and mode of notation.
	encyclopedia.jrank.org /FRA_GAE/FUNCTION.html (8019 words)

	CATENARY - LoveToKnow Article on CATENARY (Site not responding. Last check: 2007-09-29)
		It was investigated by Galileo, who erroneously determined it to be a parabola; Jungius detected Galileos error, but the true form was not discovered until 1691, when James Bernoulli published it as a problem in the Ada Erudiorum.
		Bernoulli also considered the cases when (I) the chain was of variable density, (2) extensible, (3) acted upon at each point by a force directed to a fixed centre.
		These curves attracted much attention and were discussed by John Bernoulli, Leibnitz, Huygens, David Gregory and others.
	14.1911encyclopedia.org /C/CA/CATENARY.htm (126 words)

	The INfamous Bernoulli Trials [rec.humor.funny] (Site not responding. Last check: 2007-09-29)
		John and his brother Jacob Bernoulli, both Professors of Mathematics at he University of Basel, Switzerland in the late 1600's.
		Their interests turned to the Theory of Probability, and in 1694 they were accused of organized gambling.
		In a well-publicized courtroom appearance, John Bernoulli accused the judge of bias, but was overruled.
	www.netfunny.com /rhf/jokes/92q3/bertrial.html (80 words)

	Bernoulli
		Bernoulli's principle - Bernoulli's principle, physical principle formulated by Daniel Bernoulli that states that as the...
		Bernoulli, Jacques (1654-1705 and Bernoulli, Jean 1667-1748) (The Hutchinson Dictionary of Scientific Biography)
		Bernoulli Cartridge This is an example of a third-generation Bernoulli cartridge.
	www.infoplease.com /ce6/people/A0807243.html (382 words)

	References for Bernoulli_Jacob (Site not responding. Last check: 2007-09-29)
		T Boswell, The brothers James and John Bernoulli on the parallelism between logic and algebra, Hist.
		G Fenaroli, The regularity of case in the 'Pars Quarta' of the 'Ars coniectandi' of Jacob Bernoulli, Physis - Riv.
		A P Yushkevich, Nikolas Bernoulli and the publication of 'Ars conjectandi' by Jacob Bernoulli (Russian), Teor.
	www-history.mcs.st-and.ac.uk /history/References/Bernoulli_Jacob.html (251 words)

	The research notebook of a beleaguered hack.: dynamics Archives (Site not responding. Last check: 2007-09-29)
		Euler (1707-1783) "The classic problem on isoperimetrical curves, the barchistochrone in a resisting medium, and the theory of geodesics (all of which had been suggested by his master; John Bernoulli) had engaged Euler's attention at an early date; and in solving them he was led to the calculus of variations.
		Johann Bernoulli is credited with the invention of the calculus of variations because of his brachystochrone problem which is solved by the cycloid.
		John Landen, who worked on a theory of elliptic integrals, tried to overcome calculus' problems in a different manner.
	arsenal.media.mit.edu /notebook/archives/cat_dynamics.html (11954 words)

	The Bernoulli Effect
		The sum effect of her appearances hawking her new book is to leave me floundering for a word that combines pathetic with evil.
		The interview is rather rambling in its course (I would have dearly loved to see a sharp attorney like John Hindraker do the questioning) and O'Reilley fails to stay focused on the important points.
		Think of Al Gore and John Kerry--both guys were touted as being "brilliant', yet it was clear to anyone who heard them speak that they were anything but.
	www.thebernoullieffect.com (3249 words)

	bernstein
		But more importantly, they anticipated Bernoulli, by understanding that risk is valued differently by different people.
		He covers the development of Bernoulli's Law of Large numbers, the Benthamites, Gauss's Bell Curve and the concept of the regression to the mean.
		Bernstein suggests that some of these answers may be found in psychology, in the work of Kahneman and Tversky (an exciting chapter, 16!) demonstrating the strongly patterned loss-aversion responses of their subjects.
	www.lehigh.edu /~cmp8/worksinprogress/summary/bernstein.html (702 words)

	ELOGIUM OF EULER
		Nay, he had the felicity of getting into the good graces of the severe John Bernoulli himself, who carried his condescension to far as to give him a private lesson, once a week, in the view of removing any difficulties which might occur in the course of reading and study.
		EULER felt the sincerest regret at parting with the friends of his youth, and engaged them to promise their utmost exertions to procure him a similar invitation, which he was eager to participate.
		The brothers, Bernoulli, were conscientiously faithful to their promise, and exerted themselves as strenuously, to bring forward a competitor so formidable, as ordinary men would have done to keep a rival out of sight.
	www-groups.dcs.st-and.ac.uk /history/Miscellaneous/Euler_elogium.html (4925 words)

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