Daniel Bernoulli was born inGroningen, in the Netherlands, into afamily of distinguished mathematicians.[5] The Bernoulli family came originally from Antwerp, at that time in theSpanish Netherlands, but emigrated to escape the Spanish persecution of theProtestants. After a brief period in Frankfurt the family moved to Basel, in Switzerland.
He is said to have had a bad relationship with his father. Both of them entered and tied for first place in a scientific contest at theUniversity of Paris. Johann banned Daniel from his house, allegedly being unable to bear the "shame" of Daniel being considered his equal. Johann allegedly plagiarized key ideas from Daniel's bookHydrodynamica in his bookHydraulica and backdated them to beforeHydrodynamica.[citation needed] Daniel's attempts at reconciliation with his father were unsuccessful.[7]
When he was in school, Johann encouraged Daniel to study business citing poor financial compensation for mathematicians. Daniel initially refused but later relented and studied both business andmedicine at his father's behest under the condition that his father would teach him mathematics privately.[7] Daniel studied medicine atBasel,Heidelberg, andStrasbourg, and earned a PhD in anatomy and botany in 1721.
His earliest mathematical work was theExercitationes (Mathematical Exercises), published in 1724 with the help ofGoldbach. Two years later he pointed out for the first time the frequent desirability of resolving a compound motion into motions of translation and motion of rotation. In 1729, he published apolynomial root-finding algorithm which became known asBernoulli's method.[14] His chief work isHydrodynamica, published in 1738. It resemblesJoseph Louis Lagrange'sMécanique Analytique in being arranged so that all the results are consequences of a single principle, namely, the conservation ofvis viva, an early version of theconservation of energy. This was followed by a memoir on the theory of the tides, to which, conjointly with the memoirs by Euler andColin Maclaurin, a prize was awarded by theFrench Academy: these three memoirs contain all that was done on this subject between the publication ofIsaac Newton'sPhilosophiae Naturalis Principia Mathematica and the investigations ofPierre-Simon Laplace. Bernoulli also wrote a large number of papers on various mechanical questions, especially on problems connected withvibrating strings, and the solutions given byBrook Taylor and byJean le Rond d'Alembert.[6]
A 1738 copy of Bernoulli'sHydrodynamica
First page of the first section of a 1738 copy ofHydrodynamica
In his 1738 bookSpecimen theoriae novae de mensura sortis (Exposition of a New Theory on the Measurement of Risk),[15] Bernoulli offered a solution to theSt. Petersburg paradox as the basis of the economic theory ofrisk aversion,risk premium, andutility.[16] Bernoulli often noticed that when making decisions that involved some uncertainty, people did not always try to maximize their possible monetary gain, but rather tried to maximize "utility", an economic term encompassing their personal satisfaction and benefit. Bernoulli realized that for humans, there is a direct relationship between money gained and utility, but that it diminishes as the money gained increases. For example, to a person whose income is $10,000 per year, an additional $100 in income will provide more utility than it would to a person whose income is $50,000 per year.[17]
According toLéon Brillouin, theprinciple of superposition was first stated by Daniel Bernoulli in 1753: "The general motion of a vibrating system is given by a superposition of its proper vibrations."[20]
^Anderson, John David (1997).A History of Aerodynamics and its Impact on Flying Machines. New York, NY: Cambridge University Press. p. 47.ISBN0-521-45435-2.
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