Daniel Bernoulli

Daniel Bernoulli (February 8, 1700 – March 17, 1782) was a Dutch-born mathematician who spent much of his life in Basel, Switzerland where he died. A member of a talented family of mathematicians, physicists and philosophers, he is particularly remembered for his applications of mathematics to mechanics, especially fluid mechanics, and for his pioneering work in probability and statistics. This image is in the public domain because its copyright has expired in the United States and those countries with a copyright term of life of the author plus 100 years. ... This image is in the public domain because its copyright has expired in the United States and those countries with a copyright term of life of the author plus 100 years. ... is the 39th day of the year in the Gregorian calendar. ... Events January 1 - Russia accepts Julian calendar. ... is the 76th day of the year (77th in leap years) in the Gregorian calendar. ... 1782 was a common year starting on Tuesday (see link for calendar). ... Leonhard Euler, considered one of the greatest mathematicians of all time A mathematician is a person whose primary area of study and research is the field of mathematics. ... For other uses, see Basel (disambiguation). ... Fluid mechanics is the subdiscipline of continuum mechanics that studies fluids, that is, liquids and gases. ... Probability is the likelihood that something is the case or will happen. ... This article is about the field of statistics. ...

Early life

Bernoulli family tree

Born in Groningen, the son of Johann Bernoulli, nephew of Jakob Bernoulli, younger brother of Nicolaus II Bernoulli, and older brother of Johann II, Daniel Bernoulli has been described as "by far the ablest of the younger Bernoullis".^[1] He is said to have had a bad relationship with his father. Upon both of them entering and tying for first place in a scientific contest at the University of Paris, Johann, unable to bear the "shame" of being compared to his offspring, banned Daniel from his house. Johann Bernoulli also tried to steal Daniel's book Hydrodynamica and rename it Hydraulica. Despite Daniel's attempts at reconciliation, his father carried the grudge until his death.^[2] Image File history File links No higher resolution available. ... Image File history File links No higher resolution available. ... Coordinates: Country Netherlands Province Groningen Area (2006)  - Municipality 83. ... Johann Bernoulli (Basel, July 27, 1667 - January 1, 1748) was a Swiss mathematician. ... To meet Wikipedias quality standards, this article or section may require cleanup. ... Nicolaus II Bernoulli (February 6, 1695, Basel, Switzerland – July 31, 1726, Saint Petersburg, Russia) was a Swiss mathematician. ... The Sorbonne, Paris, in a 17th century engraving The historic University of Paris (French: ) first appeared in the second half of the 12th century, but was in 1970 reorganised as 13 autonomous universities (University of Paris I–XIII). ...

When Daniel was five, his younger brother Johann II Bernoulli was born. Around schooling age, his father, Johann Bernoulli, encouraged him to study business, there being poor rewards awating a mathematician. However, Daniel refused, because he wanted to study mathematics. He later gave in to his father's wish and studied business. His father then asked him to study in medicine, and Daniel agreed under the condition that his father would teach him mathematics privately, which they continued for some time.^[2] Medicine is the science and art of maintaining andor restoring human health through the study, diagnosis, and treatment of patients. ...

He was a contemporary and intimate friend of Leonard Euler. He went to St. Petersburg in 1724 as professor of mathematics, but was unhappy there, and a temporary illness in 1733 gave him an excuse for leaving.^[2] He returned to the University of Basel, where he successively held the chairs of medicine, metaphysics and natural philosophy until his death.^[3] Leonhard Euler aged 49 (oil painting by Emanuel Handmann, 1756) Leonhard Euler (April 15, 1707 - September 18, 1783) (pronounced oiler) was a Swiss mathematician and physicist. ... Saint Petersburg (Russian: Санкт-Петербу́рг, English transliteration: Sankt-Peterburg), colloquially known as Питер (transliterated Piter), formerly known as Leningrad (Ленингра́д, 1924–1991) and... Events January 14 - King Philip V of Spain abdicates the throne February 20 - The premiere of Giulio Cesare, an Italian opera by George Frideric Handel, takes place in London June 23 - Treaty of Constantinople signed. ... Events February 12 - British colonist James Oglethorpe founds Savannah, Georgia. ... The University of Basel (German: Universität Basel) is located at Basel, Switzerland. ... Medicine is the science and art of maintaining andor restoring human health through the study, diagnosis, and treatment of patients. ... Plato (Left) and Aristotle (right), by Raphael (Stanza della Segnatura, Rome) Metaphysics is the branch of philosophy concerned with explaining the ultimate nature of reality, being, and the world. ... Natural philosophy or the philosophy of nature, known in Latin as philosophia naturalis, is a term applied to the objective study of nature and the physical universe that was regnant before the development of modern science. ...

Mathematical work

His earliest mathematical work was the Exercitationes (Mathematical Exercises), published in 1724 (the Riccati equation). Two years later he pointed out for the first time the frequent desirability of resolving a compound motion into motions of translation and motions of rotation. His chief work is his Hydrodynamique (Hydrodynamica), published in 1738; it resembles Joseph Louis Lagrange's Méchanique Analytique in being arranged so that all the results are consequences of a single principle, namely, in this case, the conservation of energy. This was followed by a memoir on the theory of the tides, to which, conjointly with the memoirs by Euler and Colin Maclaurin, a prize was awarded by the French Academy: these three memoirs contain all that was done on this subject between the publication of Isaac Newton's Philosophiae Naturalis Principia Mathematica and the investigations of Pierre-Simon Laplace. Bernoulli also wrote a large number of papers on various mechanical questions, especially on problems connected with vibrating strings, and the solutions given by Brook Taylor and by Jean le Rond d'Alembert.^[1] Events January 14 - King Philip V of Spain abdicates the throne February 20 - The premiere of Giulio Cesare, an Italian opera by George Frideric Handel, takes place in London June 23 - Treaty of Constantinople signed. ... In mathematics, a Riccati equation is any ordinary differential equation that has the form It is named after Count Jacopo Francesco Riccati (1676-1754). ... Events February 4 - Court Jew Joseph Suss Oppenheimer is executed in Württenberg April 15 - Premiere in London of Serse, an Italian opera by George Frideric Handel. ... Joseph-Louis Lagrange, comte de lEmpire (January 25, 1736 – April 10, 1813; b. ... Colin Maclaurin Colin Maclaurin (February, 1698 - June 14, 1746) was a Scottish mathematician. ... Sir Isaac Newton FRS (4 January 1643 – 31 March 1727) [ OS: 25 December 1642 – 20 March 1727][1] was an English physicist, mathematician, astronomer, natural philosopher, and alchemist. ... Newtons own copy of his Principia, with handwritten corrections for the second edition. ... To meet Wikipedias quality standards, this article or section may require cleanup. ... Brook Taylor (August 18, 1685 – November 30, 1731) was an English mathematician. ... Jean le Rond dAlembert, pastel by Maurice Quentin de La Tour Jean le Rond dAlembert (November 16, 1717 – October 29, 1783) was a French mathematician, mechanician, physicist and philosopher. ...

Statistics

Daniel Bernoulli was also the author in 1738 of Specimen theoriae novae de mensura sortis (Exposition of a New Theory on the Measurement of Risk),^[4] in which the St. Petersburg paradox was the base of the economic theory of risk aversion, risk premium and utility.^[5] Events February 4 - Court Jew Joseph Suss Oppenheimer is executed in Württenberg April 15 - Premiere in London of Serse, an Italian opera by George Frideric Handel. ... In probability theory and decision theory the St. ... Risk aversion is a concept in economics and finance theory explaining the behaviour of consumers and investors under uncertainty. ... A risk premium is the minimum difference between the expected value of an uncertain bet that a person is willing to take and the certain value that he is indifferent to. ... In economics, utility is a measure of the relative happiness or satisfaction (gratification) gained. ...

One of the earliest attempts to analyse a statistical problem involving censored data was Bernoulli's 1766 analysis of smallpox morbidity and mortality data to demonstrate the efficacy of vaccination.^[6] In statistics, censoring occurs when the value of an observation is only partially known. ... 1766 was a common year starting on Wednesday (see link for calendar). ... Smallpox (also known by the Latin names Variola or Variola vera) is a contagious disease unique to humans. ... A vial of the vaccine against influenza. ...

Physics

He is the earliest writer who attempted to formulate a kinetic theory of gases, and he applied the idea to explain Boyle's law.^[1] The kinetic theory of gases is a theory that explains the macroscopic properties of gases by consideration of their composition at a molecular level. ... Boyles law (sometimes referred to as the Boyle-Mariotte law) is one of the gas laws and basis of derivation for the Ideal gas law, which describes relationship between the product pressure and volume within a closed system as constant when temperature remains at a fixed measure; both entities...

He worked with Euler on elasticity and the development of the Euler-Bernoulli beam equation.^[7] Bernoulli's principle is of critical use in aerodynamics.^[3] Elasticity has meanings in two different fields: In physics and mechanical engineering, the theory of elasticity describes how a solid object moves and deforms in response to external stress. ... The elementary Euler-Bernoulli beam theory is a simplification of the linear isotropic theory of elasticity which allows quick calculation of the load-carrying capacity and deflection of common structural elements called beams. ... -1... This article does not cite any references or sources. ...

References

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Bibliography

Original entry based on the public domain Rouse History of Mathematics The public domain comprises the body of all creative works and other knowledge—writing, artwork, music, science, inventions, and others—in which no person or organization has any proprietary interest. ... See also: wikipedia:history One of Wikipedias public domain resources! There are a series of articles transcribed by Dr. David R. Wilkins (dwilkins@maths. ...

• [Anon.] (1911) "Bernoulli, Encyclopaedia Britannica
• [Anon.] (2001) "Daniel Bernoulli", Encyclopaedia Britannica
• Blower, S. (2004), D, Bernoulli's "An attempt at a new analysis of the mortality caused by smallpox and of the advantages of inoculation to prevent itPDF", Reviews of Medical Virolology, 14: 275–288
• Cardwell, D.S.L. (1971). From Watt to Clausius: The Rise of Thermodynamics in the Early Industrial Age. Heinemann: London. ISBN 0-435-54150-1. 
• Martin, R. M. (2004). The St. Petersburg Paradox. Stanford Encyclopedia of Philosophy. Stanford University. Retrieved on 2007-09-07.
• O'Connor, John J; Edmund F. Robertson "Daniel Bernoulli". MacTutor History of Mathematics archive.   (1998)
• Pacey, A.J. & Fisher, S.J. (1967) "Daniel Bernoulli and the vis viva of compressed air", British Journal for the History of Science 3, 388-92
• Rouse Ball, W. W. [1908] (2003) "The Bernoullis", in A Short Account of the History of Mathematics, 4th ed., Dover, ISBN 0486206300
• Timoshenko, S. P. [1953] (1983). History of Strength of Materials. New York: Dover Publications. ISBN 0486611876. 

... ... “PDF” redirects here. ... The Stanford Encyclopedia of Philosophy (hereafter SEP) is a free online encyclopedia of philosophy run and maintained by Stanford University. ... “Stanford” redirects here. ... Year 2007 (MMVII) is the current year, a common year starting on Monday of the Gregorian calendar and the AD/CE era. ... is the 250th day of the year (251st in leap years) in the Gregorian calendar. ... The MacTutor history of mathematics archive is a website hosted by University of St Andrews in Scotland. ... Walter William Rouse Ball (1850 August 14–1925 April 4) was a Brtish mathematician, and a fellow at Trinity College, Cambridge from 1878 to 1905. ... Stephen Timoshenko Stephen P. Timoshenko or Stepan Prokofyevich Timoshenko (Ukrainian: , Russian: , December 23, 1878 – May 29, 1972), is reputed to be the father of modern engineering mechanics. ...

External links

• Bernoulli Daniel. Mathematik.ch. Retrieved on 2007-09-07.
• Eric W. Weisstein, Bernoulli, Daniel (1700-1782) at ScienceWorld.