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### Bernoulli's principle

**Bernoulli's equationBernoulli effectBernoulli equation**

His name is commemorated in the Bernoulli's principle, a particular example of the conservation of energy, which describes the mathematics of the mechanism underlying the operation of two important technologies of the 20th century: the carburetor and the airplane wing. Bernoulli's principle is of critical use in aerodynamics.

The principle is named after Daniel Bernoulli who published it in his book Hydrodynamica in 1738.

### Fluid mechanics

**fluid dynamicistfluidfluid physics**

He is particularly remembered for his applications of mathematics to mechanics, especially fluid mechanics, and for his pioneering work in probability and statistics.

Rapid advancement in fluid mechanics began with Leonardo da Vinci (observations and experiments), Evangelista Torricelli (invented the barometer), Isaac Newton (investigated viscosity) and Blaise Pascal (researched hydrostatics, formulated Pascal's law), and was continued by Daniel Bernoulli with the introduction of mathematical fluid dynamics in Hydrodynamica (1739).

### Conservation of energy

**law of conservation of energyenergyenergy conservation law**

His name is commemorated in the Bernoulli's principle, a particular example of the conservation of energy, which describes the mathematics of the mechanism underlying the operation of two important technologies of the 20th century: the carburetor and the airplane wing.

The law of conservation of vis viva was championed by the father and son duo, Johann and Daniel Bernoulli.

### Probability

**probabilisticprobabilitieschance**

He is particularly remembered for his applications of mathematics to mechanics, especially fluid mechanics, and for his pioneering work in probability and statistics.

Daniel Bernoulli (1778) introduced the principle of the maximum product of the probabilities of a system of concurrent errors.

### Bernoulli family

**Bernoullidistinguished familyfamous family of mathematicians**

Daniel Bernoulli FRS (29 January 1700 – 17 March 1782) was a Swiss mathematician and physicist and was one of the many prominent mathematicians in the Bernoulli family.

### Nicolaus II Bernoulli

**Bernoulli, Nicolaus IINicholasNicholas Bernoulli**

He had two brothers, Niklaus and Johann II.

Nicolaus II Bernoulli, a.k.a. Niklaus Bernoulli, Nikolaus Bernoulli, (6 February 1695, Basel, Switzerland – 31 July 1726, St. Petersburg, Russia) was a Swiss mathematician as were his father Johann Bernoulli and one of his brothers, Daniel Bernoulli.

### Leonhard Euler

**EulerLeonard EulerEuler, Leonhard**

He was a contemporary and close friend of Leonhard Euler.

Around this time Johann Bernoulli's two sons, Daniel and Nicolaus, were working at the Imperial Russian Academy of Sciences in Saint Petersburg.

### Hydrodynamica

**theory of corpuscular pressure**

Johann Bernoulli also plagiarized some key ideas from Daniel's book Hydrodynamica in his own book Hydraulica which he backdated to before Hydrodynamica.

Hydrodynamica (Latin for Hydrodynamics) is a book published by Daniel Bernoulli in 1738.

### Johann Bernoulli

**JohannBernoulliBernoulli, Johann**

Daniel was a son of Johann Bernoulli (one of the "early developers" of calculus) and a nephew of Jacob Bernoulli (who "was the first to discover the theory of probability").

After Jacob's death Johann's jealousy shifted toward his own talented son, Daniel.

### University of Basel

**BaselBasel UniversityUniversity of Basle**

Daniel studied medicine at Basel, Heidelberg, and Strasbourg, and earned a PhD in anatomy and botany in 1721.

In its over 500-year history the university has been home to Erasmus of Rotterdam, Paracelsus, Daniel Bernoulli, Leonhard Euler, Jacob Burckhardt, Friedrich Nietzsche, Tadeusz Reichstein, Karl Jaspers, Carl Gustav Jung, Karl Barth and Jeanne Hersch.

### St. Petersburg paradox

**Saint Petersburg ParadoxPetersbergSaint Petersburg problem**

In his 1738 book Specimen theoriae novae de mensura sortis (Exposition of a New Theory on the Measurement of Risk), Bernoulli offered a solution to the St. Petersburg paradox as the basis of the economic theory of risk aversion, risk premium, and utility.

The paradox takes its name from its resolution by Daniel Bernoulli, one-time resident of the eponymous Russian city, who published his arguments in the Commentaries of the Imperial Academy of Science of Saint Petersburg.

### Pierre-Simon Laplace

**LaplacePierre Simon LaplacePierre-Simon de Laplace**

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.

While Newton explained the tides by describing the tide-generating forces and Bernoulli gave a description of the static reaction of the waters on Earth to the tidal potential, the dynamic theory of tides, developed by Laplace in 1775, describes the ocean's real reaction to tidal forces.

### Kinetic theory of gases

**kinetic theorythermal motionkinetic**

In Hydrodynamica (1738) he laid the basis for the kinetic theory of gases, and applied the idea to explain Boyle's law.

In 1738 Daniel Bernoulli published Hydrodynamica, which laid the basis for the kinetic theory of gases.

### Aerodynamics

**aerodynamicaerodynamicistsubsonic**

Bernoulli's principle is of critical use in aerodynamics.

Dutch-Swiss mathematician Daniel Bernoulli followed in 1738 with Hydrodynamica in which he described a fundamental relationship between pressure, density, and flow velocity for incompressible flow known today as Bernoulli's principle, which provides one method for calculating aerodynamic lift.

### Christian Goldbach

**GoldbachGoldbach, ChristianGold'''bach**

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

Goldbach is most noted for his correspondence with Leibniz, Euler, and Bernoulli, especially in his 1742 letter to Euler stating his Goldbach's conjecture.

### Euler–Bernoulli beam theory

**Euler–Bernoulli beam equationbeam theoryEuler-Bernoulli beam equation**

He worked with Euler on elasticity and the development of the Euler–Bernoulli beam equation.

Leonhard Euler and Daniel Bernoulli were the first to put together a useful theory circa 1750.

### Censoring (statistics)

**censoringcensoredcensored data**

One of the earliest attempts to analyze a statistical problem involving censored data was Bernoulli's 1766 analysis of smallpox morbidity and mortality data to demonstrate the efficacy of vaccination.

One of the earliest attempts to analyse a statistical problem involving censored data was Daniel Bernoulli's 1766 analysis of smallpox morbidity and mortality data to demonstrate the efficacy of vaccination.

### Utility

**utility functionutility theoryutilities**

In his 1738 book Specimen theoriae novae de mensura sortis (Exposition of a New Theory on the Measurement of Risk), Bernoulli offered a solution to the St. Petersburg paradox as the basis of the economic theory of risk aversion, risk premium, and utility.

The St. Petersburg paradox was first proposed by Nicholas Bernoulli in 1713 and solved by Daniel Bernoulli in 1738.

### Boyle's law

**compressedBoyleBoyle's Gas Law**

In Hydrodynamica (1738) he laid the basis for the kinetic theory of gases, and applied the idea to explain Boyle's law.

Daniel Bernoulli (in 1737–1738) derived Boyle's law by applying Newton's laws of motion at the molecular level.

### Basel

**Basel, SwitzerlandBasleBâle**

The Bernoulli family, which included important 17th- and 18th-century mathematicians such as Jakob Bernoulli, Johann Bernoulli and Daniel Bernoulli, were from Basel.

### International Air & Space Hall of Fame

**International Aerospace Hall of FameInternational Air and Space Hall of Fame**

In 2002, Bernoulli was inducted into the International Air & Space Hall of Fame at the San Diego Air & Space Museum.

### Superposition principle

**superpositionlinear superpositionsuperpose**

According to Léon Brillouin, the principle 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."

According to Léon Brillouin, the principle 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."

### Swiss people

**SwissSwiss-GermanSwiss-Italian**

Daniel Bernoulli FRS (29 January 1700 – 17 March 1782) was a Swiss mathematician and physicist and was one of the many prominent mathematicians in the Bernoulli family.

### Mathematician

**mathematiciansapplied mathematicianMathematics**

Daniel Bernoulli FRS (29 January 1700 – 17 March 1782) was a Swiss mathematician and physicist and was one of the many prominent mathematicians in the Bernoulli family.

### Physicist

**physicistsresearch physicistengineer and physicist**