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Daniel Bernoulli

 
Statistics Dictionary: Daniel Bernoulli
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(1700–82; b. Gröningen, Netherlands; d. Basel, Switzerland) Swiss mathematical physicist. Daniel Bernoulli is best known to statisticians for his solution of the St Petersburg paradox posed by his cousin Nicolaus Bernoulli. Daniel, a famous prodigy, was the son of Johann Bernoulli and the nephew of Jacob Bernoulli, both being Professors of Mathematics. He gained a succession of degrees from U Basel whilst still a teenager: BA in philosophy and logic in 1715, MA in 1716, Doctor of Medicine in 1720. In 1724, whilst practising medicine in Venice, he applied mathematics to the design of an hour-glass for use at sea. This won him a prize and a post as Professor of Mathematics at St Petersburg U, where he worked on a number of probability problems. He returned to U Basel in 1734, initially as Professor of Botany, then as Professor of Physiology and finally, in 1750, as Professor of Physics.


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Scientist: Daniel Bernoulli
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[b. Groningen, Holland, February 8, 1700, d. Basel, Switzerland, March 17, 1782]

Daniel, son of Jean (Johann) Bernoulli, contributed to oceanography and astronomy as well as mathematics but is best known for his work in physics. He established Bernoulli's principle: A fluid produces less pressure as its velocity increases, an effect that provides much of the lift for airplanes. He also was the first to use the idea that a gas is made from tiny particles, thus deriving the gas laws, which had previously been discovered experimentally.


Biography: Daniel Bernoulli
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The Swiss mathematician and physicist Daniel Bernoulli (1700-1782) is best known for his work on hydrodynamics, but he also did pioneering work on the kinetic theory of gases.

Daniel Bernoulli was born on Jan. 29, 1700, in Gröningen, Netherlands. He was the second son of Jean Bernoulli, a noted mathematician who began the use of "g" for the acceleration of gravity.

When Daniel was 11, he became the pupil of his 16-year-old brother, Nicholas. He continued his studies in Italy until he was 24 and received a doctorate in medicine. The following year he went to St. Petersburg, Russia, as a professor of mathematics. After 8 years he returned to Switzerland because of his health. He first taught anatomy and botany, then changed to experimental and speculative philosophy (or, in modern terminology, theoretical physics). He has been called the father of mathematical physics.

In 1738 Bernoulli published Hydrodynamica. In this treatise, which was far in advance of his time in many ways, is his famous equation governing the flow of fluids in terms of speed, pressure, and potential energy, upon which much modern technology is based, especially aerodynamics. Being interested in practical application as well as in theory, he devised a number of experiments which demonstrated the effects he predicted.

In this treatise is also found his remarkable treatment of gas pressure. Considering an enclosed gas as a swarm of moving particles in dynamic equilibrium, he derived the correct expression for the resulting pressure, thus anticipating the approach adopted about 100 years later.

Bernoulli won or shared 10 prizes of the Paris Academy of Sciences, a feat equaled by only one other person, his friend and rival Leonhard Euler. Because of a difference of opinion with Euler, Bernoulli became interested in sound phenomena and discovered that a closed organ pipe can produce only odd harmonics and that pressure determines the relative amplitudes of the harmonics. His last work involved the application of probability theory to various practical matters, such as inoculation and relative proportion of male and female births. He died in Basel on March 17, 1782.

Further Reading

Information on Bernoulli in English is scarce. E. T. Bell, Men of Mathematics (1937) and The Development of Mathematics (1940; 2d ed. 1945), are valuable. See also Alfred Hooper, Makers of Mathematics (1948), and David E. Smith, History of Mathematics, vol. 1 (1951).

Wikipedia: Daniel Bernoulli
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Daniel Bernoulli

Daniel Bernoulli
Born 29 February 1700
Groningen, Netherlands
Died 8 March 1782 (aged 82)
Basel, Switzerland
Residence Trizzy
Known for Bernoulli's Principle, early Kinetic theory of gases, Thermodynamics

Daniel Bernoulli (Groningen, 8 February 1700 – Basel, 8 March 1782) was a Dutch-Swiss mathematician and was one of the many prominent mathematicians in the Bernoulli family. He is particularly remembered for his applications of mathematics to mechanics, especially fluid mechanics, and for his pioneering work in probability and statistics. Bernoulli's work is still studied at length by many schools of science throughout the world.

Contents

Early life

Frontpage of Hydrodynamica (1738)

Born in Groningen, in the Netherlands, the son of Johann Bernoulli, nephew of Jus 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 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]

When Daniel was seven, his younger brother Johann II Bernoulli was born. Around schooling age, his father, Johann Bernoulli, encouraged him to study business, there being poor rewards awaiting 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]

He was a contemporary and close friend of Leonhard 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]

Mathematical work

His earliest mathematical work was the Exercitationes (Mathematical Exercises), published in 1724 with the help of Goldbach. 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, 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]

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]

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]

Physics

Boltzmann's-equation.jpg To understand the significance of Bernoulli's work on kinetictheory in the context of the development of thermodynamics, see timeline Edit

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]

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]

References

  1. ^ a b c Rouse Ball (1908)
  2. ^ a b c O'Connor & Robertson (1998)
  3. ^ a b [Anon.] (2001) "Daniel Bernoulli", Encyclopaedia Britannica
  4. ^ English translation in Econometrica 22 (1954) pp23-36
  5. ^ Martin (2004)
  6. ^ reprinted in Blower (2004)
  7. ^ Timoshenko (1983)

Bibliography

Original entry based on the public domain Rouse History of Mathematics

External links

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Bernoulli family tree
 
 
 
 
 
 
 
 
 Nikolaus Bernoulli
(1623–1708)
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Jakob Bernoulli
(1654–1705)
 
 Nicolaus Bernoulli
(1662–1716)
 
 
 
 Johann Bernoulli
(1667–1748)
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Nicolaus I Bernoulli
(1687–1759)
 
 Nicolaus II Bernoulli
(1695–1726)
 
 Daniel Bernoulli
(1700–1782)
 
 Johann II Bernoulli
(1710–1790)
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Johann III Bernoulli
(1744–1807)
 
 Daniel II Bernoulli
(1751–1834)
 
 Nicolaus IIII Bernoulli
(1754–1841)
 
 Jakob II Bernoulli
(1759–1789)
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Nicolaus
(1793–1876)
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Fritz
(1824–1913)
 
 Theodor
(1837–1909)
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Hermann Hesse
(1877–1962)
 
 Maria Bernoulli
(1868–1963)
 
 Hans Benno Bernoulli
(1876–1959)
 
Family tree of the Bernoulli family

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Statistics Dictionary. A Dictionary of Statistics. Second edition revised. Copyright © Oxford University Press, 2008. All rights reserved.  Read more
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