Leonhard Euler - SpeedyLook encyclopedia

Biography

It was born in Suisse, with Basle, in 1707, and it studies mathematics there. It accepted the lessons of Jean Bernoulli.

It was called by Catherine I {{Re}} of Russia in Russia in 1727, thereafter it works as a mathematics professor with Saint-Pétersbourg. It comes in 1741 to be fixed at Berlin, and turns over to Saint-Petersbourg where it finishes his days.

He was member of the Academies of St-Pétersbourg, of Berlin, associated French Academy of sciences, and was pensioned by Russia. He made take with mathematical science great steps, especially with differential and integral calculus; he applied the analysis to mechanics, the construction of the vessels, and gave the demonstration of several theorems stated by Pierre de Fermat.

Between his many writings, almost all written in Latin, one must notice:

Mechanical analytically exposed , Saint-Pétersbourg, 1736;
Introduction to the analysis of infinite the , Lausanne, 1748;
naval Science ;
Institutions of differential calculus ;
Institutions of integral calculus , 1768;
Letters with a princess of Germany on various subjects of physics and philosophy (princess of Anhalt-Dessau, niece of the king of Prussia), written in French, of 1761 with 1762, published in Saint-Pétersbourg in 1768, 3 volumes, in-8. This last work, where the author treats at the same time physics, of Métaphysique and Logique, was several times reprinted, in particular with Paris in 1787, by the care of Nicolas de Condorcet, which cut off the passages from them antiphilosophic; by Jean-Baptiste Labey in 1812, by Antoine-Augustin Cournot in 1842, by Emile-Edmond Saisset in 1843.

Euler had thirteen children, of which eights die in low age, which almost all went on its traces:

the groin, Jean Albert, born in 1734 in Saint-Pétersbourg, died in 1810, shared several prices with the Academy of Science with Charles Bossut and Alexis Claude Clairaut, and taught physics with St-Pétersbourg.
Charles, born in 1740, died in 1800, also gained several prices with the Academy of Science; he exerted medicine with Saint-Pétersbourg and was doctor of the emperor.
Christophe, born in 1743 in Berlin, died towards 1805, successfully applied mathematics to military engineering

Euler was deeply pious during all its life. The anecdote saying that it defied Denis Diderot at the Court of Catherine Large the with the affirmation : Dear Sir, $e^ {I \ pi} + 1 = 0$ thus God exists, answer!

Discovered

He is the physicist who, with Daniel Bernoulli, establishes the law according to which, the couple on a mean elastic beam is proportional to a measurement of the elasticity of material and the moment of inertia of a transverse section, around an axis crosses the Center of mass while being perpendicular to the plan of the couples.

He also deduced a unit from laws of movement in dynamics of the fluids starting from the Lois of the movement of Newton which state ainsi :

the force acting on a small element of a fluid is equal to the rate of variation of its Quantité of movement.
the couple acting on a small element of a fluid is equal to the rate of variation of the kinetic Moment.

In mathematics, it contributes important shares to the Théorie of the numbers and also to the theory of the differential equations. Its contribution to the analyzes, for example, is resulting from its synthesis of the differential calculus of Leibniz with the method of Newton of the Fluxion S.

It very early establishes its fame by solving a known problem of long time - to knowing the determination of the sum of the opposite of the squares of entiers :

$\ zeta (2) = \ sum_ {n=1} ^ \ infty \ frac {1} {n^2} = \ frac {1} {1^2} + \ frac {1} {2^2} + \ frac {1} {3^2} + \ frac {1} {4^2} + \ cdots = \ frac {\ pi^2} {6}$

where $\ zeta (S) \,$ is the function ζ of Riemann.

It also showed that for any real number X ,

$e^ {ix} = \ cos x+ I \ sin X \,$

It is the Formule of Euler, which establishes the central role of the exponential function. Essentially, all the functions studied in ultimate analysis are or of simple variations of the exponential function or the polynomial functions.

The Identité of Euler that certain scientists called the “most remarkable formula of the world” in is an immediate consequence.

In Arithmetic, it introduces the function Indicatrice of Euler $\ Phi (N)$ , definite like the number of entireties lower than $n$ and first with $n$ . Generalizing the Small theorem of Fermat, it nowadays shows the theorem of Euler at the base of cryptography RSA.

In 1735, it works on the Constante of useful Euler-Mascheroni in some differential equations :

$\ gamma = \ lim_ {N \ rightarrow \ infty} \ left (1+ \ frac {1} {2} + \ frac {1} {3} + \ frac {1} {4}… + \ frac {1} {N} - \ ln (N) \ right)$

He is a joint author of the formula of Euler-Maclaurin which is an extremely powerful tool for the calculation of the integrals, of the sums and the difficult series.

Euler written Tentamen novae theoriae musicae into 1739 which is an attempt to grant mathematics and the music; a biography comments on that work is intended “for musicians too advanced in their mathematics and for too musical mathematicians”.

In the economic scenes, it proves that if each factor of production is paid with the value of its marginal product, then (under constant outputs on the scale) the total income and the output will be completely exhausted.

In Geometry and algebraic Topology, there is a relation called relation of Euler which connects the number on sides, tops, and faces of a polyhedron of kind 0 (by removing a face one obtains a related surface Simplement), for example of a convex Polyèdre . Being given such a polyhedron, the sum of the number of tops S and faces F are always equal to the number on sides C more two c'est-with-dire :

F - C + S = 2

The theorem also applies to any graph of the plan. The relation of Euler gave rise to the Caractéristique of Euler in algebraic topology and homological Algèbre.

In 1736, Euler solves a problem known under the name of the Problème of the seven bridges of Königsberg, publishing an article Solutio problematis AD geometriam situs pertinentis which could be the oldest application of the Graph theory or Topologie. This publication would be also oldest and thus the first in Operations research.

; Source bibtex: @article {Euler36, author = {L. Euler}, title = {Solutio problematis AD geometriam situs pertinentis}, newspaper = {Opera Omnia}, volume = {7}, pages = {128--140}, year = {1736}

Leonhard Euler, Solutio problematis AD geometriam situs pertinentis , How. Acad. Sci. U. Petrop. 8,128-140, 1736. Reprinted in Opera Omnia Series Preceded, vol. 7. pp. 1-10, 1766.

Work of Euler concerning the design of the optical instruments (microscopes, telescopes) was published in the work in three volumes Dioptrica .

Works

all the work of Leonhard Euler, accessible in the form of images scanerized from the editions of origin

If the bond above does not go, here of the alternatives, but not always so practical to consult:

Euler Leonhard, Letters with a princess of Germany , Bookmine.org
Euler Leonhard here some additional works
Works of Euler, SCD of the University Louis Pasteur of Strasbourg

Partial source

See too

Liste of the subjects named according to Leonhard Euler
Henri Dulac
Problème of the rider
Mathématicien S
Physicien S
Table of constant mathematics
Complex number
Trigonométrie complexes
Problème of the seven bridges of Königsberg
Problème of the officers (graph theory)
Fonction Zeta of Riemann
Petit theorem of Fermat
Prime number of Mersenne
Angles of Euler

External bonds

Official site on the tercentenary one of the birth of Euler (2007)

January 22nd 1747 -->

Simple: Leonhard Euler Zh-classical: 歐拉

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