Témbongkeun sumber pikeun Leonhard Euler

[[Gambar:Leonhard Euler 2.jpg|thumb|225px|Leonhard Euler]]

'''Léonhard Euler''' (dibaca [ˈɔʏlɐ]) ([[Basel, Swiss|Basel]], [[Swiss]], [[15 April]] [[1707]] – [[18 September]], [[1783]] di [[St Petersburg]], [[Rusia]]) nyaéta salah saurang [[mathematician|ahli matématika]] jeung [[physicist|fisika]] [[Ancien Régime of Switzerland|Swiss]]. Euler dianggap salah saurang ahli matématika brilian dina abad ka 18 sarta panggedéna salila ieu; kaasup nu pangproduktifna tur ngumpulkeun hasil karyana dina leuwih ti 70 jilid.

Euler ngawangun sababaraha konsép penting jeung [[mathematical proof|ngabuktikeun]] sababaraha [[theorem|teori]] ahir dina [[mathematics]], ti [[kalkulus]] kana [[number theory|teori wilangan]] kana [[topologi]]. Dina hal ieu, ngawanohkeun watesan matématika modérn, ngartikeun konsép ''[[function (mathematics)|fungsi]]'', tur notasina saperti ''sin'', ''cos'', jeung ''tan'' keur [[trigonometric function|fungsi trigonometri]].

== Riwayat hirup ==
Kolotna Euler nyaéta Paul Euler jeung Marguerite Brucker. Paul Euler nyaéta saurang [[pastor]] [[Kristen Protéstan]] tur hayang anakna jiga manéhna. Sanajan Euler dilahirkeun di [[Basel]], Swiss, tapi salila budak leuwih lila hirup di [[Riehen]], tatangga kota tempat bapana jadi menteri Luther. Euler hirup kumbuh tur mikaresep kana [[mathematics|matématika]] tur dididik ku kulawarga [[Johann Bernoulli]].

Nurut kana paménta ramana, anjeunna diajar [[theology|téologi]], [[Hebrew language|Basa Ibrani]], jeung [[Greek language|Basa Yunani]] di [[Universitas Basel]], sanajan teu manggihan hal saperti nu dipikaresep dina matematika. Euler geus jadi saurang pastur sawaktu Bernoulli ngalarang. Bernoulli ngayakinkeun ramana yén Euler bakal jadi [[mathematician|ahli matématika]] kawentar. Euler tamat ti Universitas Basel dina taun 1726. Di dieu anjeunna diajar tur babarengan nyieun karya babarengan jeung ahli matématika kawentar, kaasup [[Pierre Varignon]], [[René Descartes]], [[Isaac Newton]], [[Galileo]], [[Frans van Schooten]], [[Hermann von Reichenau]], [[Brook Taylor]], [[John Wallis]], [[Jacob Bernoulli]] sarta tangtu kaasup ogé Johann Bernoulli.

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In 1727, he entered the [[Paris Academy Prize Problem]] competition, where the problem that year was to find the best way to place the [[mast]]s on a [[ship]]. He received honorable mention, highly commendable for someone only twenty years old. However, Euler was not satisfied; he would go on to win the contest twelve years in a row.

[[Image:Leonhard Euler.jpg|thumb|Leonhard Euler by [[Emanuel Handmann]].]]
Euler was offered a position teaching applications of mathematics at the [[St. Petersburg Academy]]. In November 1726, he accepted the post, but did not travel to [[Russia]] until the following spring. During this period, Euler applied unsuccessfully for a post at the University of Basel. On [[April 5]], [[1727]], Euler left Basel for St. Petersburg. In 1730, he became a professor of [[physics]]. When Bernoulli returned to Basel in 1733, Euler was promoted to the senior mathematics chair.

On [[January 7]], [[1734]], he married Katharina Gsell, daughter of a painter from the Academy Gymnasium. They had thirteen children, of whom only five survived childhood. He was married twice, his second wife being a half-sister of his first. Several of his children also attained distinction.

Euler began to suffer health problems in 1735. He had a severe [[fever]] that almost killed him. By 1740, he could not see with his right [[eye]]. [[Surgery]] fixed this temporarily, but his eye eventually failed again. New surgery in 1771 caused blindness in the other eye as well.

Concerned about continuing turmoil in Russia, Euler debated whether to stay in St. Petersburg or not.  [[Frederick the Great of Prussia]] offered him a post at the [[Berlin Academy]], which he accepted. He left St. Petersburg on [[June 19]], [[1741]], but would return.  He spent twenty-five years in [[Berlin]], where he wrote over 380 articles. However, he left after Frederick placed [[d'Alembert]] into the mathematics position and made Euler President. Euler could not work with d’Alembert and returned to St. Petersburg, where he spent the rest of his life.

On [[September 18]], [[1783]], he suffered a [[brain hemorrhage]] and died.  His elegy was written for the French Academy by the [[Marquis de Condorcet]], and an account of his life, with a list of his works, by von Fuss, Euler's son-in-law and the secretary of the [[Russian Academy of Sciences|Imperial Academy of St. Petersburg]].  The mathematician and philosopher Marquis de Condorcet commented,
:: '' "...il cessa de calculer et de vivre," '' (he ceased to calculate and to live).

==Interests and output==
Euler worked in almost all areas of mathematics: geometry, calculus, trigonometry, algebra, and number theory. He studied continuum mechanics, the lunar theory, and much more.

Euler's knowledge was more general than might have been expected in one who had pursued mathematics and astronomy with such ardor. He made considerable progress in medicine, botany and chemistry. He was also an excellent historian, and read much literature. He was endowed with an uncommon memory and seemed to retain every idea obtained by reading or meditation. He could repeat the [[Aeneid]] of [[Virgil]] in its entirety without hesitation, and indicate the first and last line of every page of the edition which he used.

Euler's works, if printed, would occupy between 60 and 80 [[Book size|quarto]] volumes. It has been estimated that it would take eight hours of work per day for 50 years to copy it all by hand. A project by the Swiss Academy of Sciences begun in 1907, the 200th anniversary of Euler's birth, to publish a complete collection of his works remains ongoing almost a hundred years later.  To date, all of his published works have been republished, and about a quarter of his correspondence.  Plans are underway to publish his notebooks and personal notes as well, which may take another 20 years. It was reported by [[Legendre]] that often he would write down a complete mathematical proof between the first and the second call for supper though this story must be second hand, if not [[apocryphal]].  Though they corresponded extensively, Euler and Legendre never met.

== Discoveries ==
Euler's work touched upon so many fields that he is often the earliest written reference on a given matter. Physicists and mathematicians often jest that often times a discovery or theorem is named after the "first person after Euler to discover it".  A list of his fundamental discoveries is bound to be incomplete -- he can be said to have founded elementary analysis, [[graph theory]], and many of the physical applications of mathematics now fundamental to civil, mechanical, electrical and aeronautical engineering.  So the following examples are just an incomplete sampling.

Euler was the first to publish formulas with the constant [[E (mathematical constant)|''e'']] (occasionally called ''Euler's number''), and showed the usefulness, consistency, and simplicity of defining the [[exponent]] of an [[imaginary number]] by means of the [[Euler's formula]]
:<math> e^{i \theta} = \cos\theta + i\sin\theta \,.</math>
which establishes the central role of the [[exponential function]] in elementary analysis, where virtually all functions are either variations of the exponential function or  [[polynomial]]s.  This formula was called "the most remarkable formula in mathematics" by [[Richard Feynman]] (''Lectures on Physics'', p.I-22-10). [[Euler's identity]] is a special case of this:
:<math>e^{i \pi} +1 = 0 \,.</math>

(Note: The constant ''e'' is not to be confused with γ, the Euler-Mascheroni constant, which is itself sometimes called Euler's constant.)

Euler discovered [[quadratic reciprocity]] and proved that all even [[perfect numbers]] must be of Euclid's form. He investigated [[primitive root]]s, found new large [[Prime number|prime]]s, and deduced the infinitude of the primes from the divergence of the [[Harmonic series (mathematics)|harmonic series]]. This was the first breakthrough in this area in 2000 years, heralding the birth of the analytic [[number theory]]. His work on factoring whole numbers over the complexes marked the beginning of the algebraic number theory.
[[Amicable numbers]] had been known for 2000 years before Euler, and in all that time only 3 pairs were discovered. Euler found 59 more.

With [[Daniel Bernoulli]], Euler developed the [[Euler-Bernoulli beam equation]] that allows the calculation of [[Stress (physics)|stress]] in [[Beam (structure)|beams]]. Euler also deduced the [[Euler equations]], a set of laws of motion in [[fluid dynamics]], formally identical to the [[Navier-Stokes equations]], explaining, among other phenomena, the propagation of [[shock wave]]s.

Euler:
* Elaborated the theory of higher transcendental functions by introducing the [[gamma function]] and the gamma density functions.
* Introduced a new method for solving 4th degree polynomials.
* Proved [[Newton's identities]], [[Fermat's little theorem]], [[Fermat's theorem on sums of two squares]], and made distinct contributions to the [[Lagrange's four-square theorem]].
* Made contributions to combinatorics, the calculus of variations and difference equations.
* Created the theory of [[hypergeometric series]], [[q-series]] and the analytic theory of [[continued fractions]].
* Solved a multitude of [[diophantine equations]]. Introduced and studied the [[hyperbolic functions|hyperbolic trigonometric functions]].
* Calculated integrals with complex limits, which led (via Cauchy) to [[contour integration]] and [[complex analysis]].
* Discovered the addition theorem for [[elliptic integrals]].
* Invented the [[calculus of variations]], including its most well-known result, the [[Euler-Lagrange equation]].
* Proved the [[binomial theorem]] for binomials with real number exponents.
* Described numerous applications of [[Bernoulli numbers|Bernoulli's numbers]], [[Fourier series]], [[Venn diagrams]], [[Euler numbers]], [[E (mathematical constant)|e]] and [[pi]] constants, continued fractions and integrals.
* Discovered the infinite product and partial fraction representations of the [[trigonometric functions]].
* Explicated logarithms of negative numbers.
* Integrated [[Gottfried Leibniz|Leibniz]]'s [[differential calculus]] with Newton's method of [[fluxion]]s. Pioneered applications of [[calculus]] to [[physics]]. 
* Co-discovered the [[Euler-Maclaurin formula]] which facilitates calculation of integrals, sums, and series.
* Published substantial contributions to the theory of [[differential equations]].
* Defined a series of [[Euler approximations|approximations]] which are used in computational mechanics. The most useful of these approximations is known as the [[Euler's method]].
* Euler is frequently misrepresented as having created the [[Latin square]], which likely inspired Howard Garns' number puzzle [[Sudoku]].  However, Greco-Latin squares are several thousand years old, used frequently on sepulchres and graves as a talisman, and were exhaustively enumerated by Arabic numerologists from orders three through nine in the Jabirean Corpus a thousand years before Euler was born. Euler was simply responsible for a revival in their popularity.
*In [[number theory]], Euler invented the [[Euler's totient function|totient function]].  The totient φ(''n'') of a [[positive integer]] ''n'' is defined to be the number of positive integers less than or equal to ''n'' and [[coprime]] to ''n''. For example, φ(8) = 4 since the four numbers 1, 3, 5 and 7 are coprime to 8. With this function Euler was able to generalize [[Fermat's little theorem]] to [[Euler theorem]].
*1735: Euler reaffirmed his scientific reputation by solving the long-standing [[Basel problem]]:
:<math>\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}</math>,
where <math>\zeta(s)</math> is the [[Riemann zeta function]] and also described how to evaluate the zeta function at any positive even number.

*1735: Euler defined the [[Euler-Mascheroni constant]] useful for solution of [[differential equation]]s:
:<math>\gamma = \lim_{n \rightarrow \infty } \left( 1+ \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \cdots + \frac{1}{n} - \ln(n) \right).</math>
*Euler Proved that [[Proof that the sum of the reciprocals of the primes diverges|the sum of the reciprocals of the primes diverges]].
In [[geometry]] and [[algebraic topology]], there is a relationship (also called the Euler's Formula) which relates the number of edges, vertices, and faces of a [[convex set|convex]] [[polyhedron]].  Given such a polyhedron, the sum of the vertices and the faces is always the number of edges plus two. i.e.: ''F'' + ''V'' = ''E'' + 2.  The theorem also applies to any planar graph.  For nonplanar graphs, there is a generalization:  If the graph can be embedded in a [[manifold]] ''M'', then ''F'' - ''E'' + ''V'' = χ(''M''), where χ is the [[Euler characteristic]] of the manifold, a constant which is invariant under continuous deformations.  The Euler characteristic of a simply-connected manifold such as a sphere or a plane is 2.  A generalization of Euler's formula for arbitrary planar graphs exists: ''F'' - ''E'' + ''V'' - ''C'' = 1, where ''C'' is the number of components in the graph.

*1736: Euler solved, or rather proved insoluble, a problem known as the [[seven bridges of Königsberg]], publishing a paper ''Solutio problematis ad geometriam situs pertinentis'' which was the earliest application of graph theory or topology.
*1739: Euler wrote ''Tentamen novae theoriae musicae,'' which was an attempt to combine mathematics and [[music]]; someone commented upon it that ''"for musicians it was too advanced in its mathematics and for mathematicians it was too musical."''

==Distinctions==
*The [[asteroid]] [[2002 Euler]] is named in his honor.
*Euler was ranked number 77 on [[Michael H. Hart]]'s [[The 100|list of the most influential figures in history]].
*For nearly two decades (1979 to 1996), Euler was featured on a Swiss banknote. http://mypage.bluewin.ch/a-z/jke/CH-Noten/bn01090.htm

== Quotes ==
* ''"Lisez Euler, lisez Euler, c'est notre maitre a tous."'' (Read Euler, read Euler, he is the master of us all). attributed to —[[Pierre-Simon Laplace]] though this is quite probably apocryphal, apparently originating with the 19th century commentator Guido Libri.
-->
== Karya ==
Karya-karyana nu diterbitkeun nyaéta:
* Dissertatio physica de sono (Dissertation on the physics of sound) (Basel, 1727, in quarto)
* Mechanica, sive motus scientia analytice; expasita (St Petersburg, 1736, in 2 vols. quarto)
* Ennleitung in die Arithmetik (ibid., 1738, in 2 vols. octavo), in German and Russian
* Tentamen novae théoriae musicae (ibid. 1739, in quarto)
* Methodus inveniendi linéas curvas, maximi minimive proprietate gaudentes (Lausanne, 1744, in quarto)
* Théoria motuum planetarum et cometarum (Berlin, 1744, in quarto)
* Béantwortung, &c., or Answers to Different Questions respecting Comets (ibid., 1744, in octavo)
* Neue Grundsatze, c., or New Principles of Artillery, translated from the English of Benjamin Robins, with notes and illustrations (ibid., 1745, in octavo)
* Opuscula varii argumenti (ibid., 1746-1751, in 3 vols. quarto)
* Novae et carrectae tabulae ad loco lunae computanda (ibid., 1746, in quarto)
* Tabulae astronomicae solis et lunae (ibid., quarto)
* Gedanken, &c., or Thoughts on the Elements of Bodies (ibid. quarto)
* Rettung der gall-lichen Offenbarung, &c., Defence of Divine Revelation against Free-thinkers (ibid., 1747, in 4t0)
* Introductio in analysin infinitorum (Introduction to the analysis of the infinites)(Lausanne, 1748, in 2 vols. 4t0)
* Scientia navalis, seu tractatus de construendis ac dirigendis navibus (St Petersburg, 1749, in 2 vols. quarto)
* Théoria motus lunae (Berlin, 1753, in quarto)
* Dissertatio de principio mininiae actionis, ' una cum examine objectionum cl. prof. Koenigii (ibid., 1753, in octavo)
* Institutiones calculi differentialis, cum ejus usu in analysi Intuitorum ac doctrina serierum (ibid., 1755, in 410)
* Constructio lentium objectivarum, &c. (St Petersburg, 1762, in quarto)
* Théoria motus corporum solidoruni seu rigidorum (Rostock, 1765, in quarto)
* Institutiones,calculi integralis (St Petersburg, 1768-1770, in 3 vols. quarto)
* Lettres a une Princesse d'Allernagne sur quelques sujets de physique et de philosophie (St Petersburg, 1768-1772, in 3 vols. octavo)
* Anleitung zur Algebra, or [http://web.mat.bham.ac.uk/C.J.Sangwin/euler/index.html Elements of Algebra] {{Webarchive|url=https://web.archive.org/web/20060925132713/http://web.mat.bham.ac.uk/C.J.Sangwin/euler/index.html |date=2006-09-25 }} (ibid., 1770, in octavo); Dioptrica (ibid., 1767-1771, in 3 vols. quarto)
* Théoria motuum lunge nova methodo pertr.arctata (ibid., 1772, in quarto)
* Novae tabulae lunares (ibid., in octavo); La théorie complete de la construction et de la manteuvre des vaisséaux (ibid., .1773, in octavo)
* Eclaircissements svr etablissements en favour taut des veuves que des marts, without a date
* Opuscula analytica (St Petersburg, 1783-1785, in 2 vols. quarto). See Rudio, Léonhard Euler (Basel, 1884).

== Bacaan salajengna ==
* Euler Léonhardt : "Lettres à une Princesse d'Allemagne"; free book at http://www.bookmine.org {{Webarchive|url=https://web.archive.org/web/20200324110259/http://www.bookmine.org/ |date=2020-03-24 }} ;
* Euler, Léonhard (1748). ''Introductio in analysin infinitorum''. English translation ''Introduction to Analysis of the Infinite'' by John Blanton (Book I, ISBN 0-387-96824-5, Springer-Verlag 1988; Book II, ISBN 0-387-97132-7, Springer-Verlag 1989).
* Dunham, William (1999). ''Euler: The Master of Us All'', Washington: Mathematical Association of America. ISBN 0-88385-328-0.
* Heimpell, Hermann, Théodor Heuss, Benno Reifenberg (editors). 1956. ''Die großen Deutschen'', volume 2, Berlin: Ullstein Verlag.
* Krus, D.J. (2001) Is normal distribution due to Karl Gauss? Euler, his family of gamma functions, and place in history of statistics. ''Quality and Quantity: International Journal of Methodology,'' 35, 445-446.[http://www.visualstatistics.net/Statistics/Euler/Euler.htm (Request reprint).]
* Simmons, J. (1996). ''The giant book of scientists: The 100 greatest minds of all time'', Sydney: The Book Company.
* Singh, Simon. (2000). ''Fermats letzter Satz'', Munich: Deutscher Taschenbuch Verlag.
* ''Lexikon der Naturwissenschaftler'', Spektrum Akademischer Verlag Heidelberg, 2000.

== Tempo ogé ==
* [[List of topics named after Leonhard Euler]]
* [[Konstanta matematis]]
* [[Nomer komplék]]
* [[Karakteristik Euler]]
* [[Euler's conjecture]]
* [[Euler's disk]]
* [[Téoréma rotasi Euler]] ''([[:en:Euler's rotation theorem|Euler's rotation theorem]])''
* [[Euler's three-body problem]]
* [[Thirty-six officers problem]]
* [[Euler number]]
* [[Euler's totient function]]
* [[Child prodigy]]
* [[Eulerian path]]
* [[Diagram Euler]]
* [[Euler-Lagrange equation]]
* [[Euler product]]
* [[Juru Euler]] ''(Euler angles)''

== Tumbu luar ==
{{wikisource author|Leonhard Euler}}
{{wikiquote|Leonhard Euler}}
{{commons|Leonhard Euler}}
* {{MacTutor Biography|id=Euler}}
* [http://www.eulerarchive.org/ Euler Archive]
* [http://fermatslasttheorem.blogspot.com/2005/05/leonhard-euler.html Biography of Leonhard Euler]
* {{MathGenealogy|id=38586}}
* {{ScienceWorldBiography | urlname=Euler | title=Euler, Leonhard (1707-1783)}}
{{pondok}}

[[Category:Nu babar taun 1707|Euler, Leonhard]]
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[[Category:Calculating prodigies|Euler, Leonhard]]
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