Editing Leonhard Euler (section)

===Physics, astronomy, and engineering===
{{Classical mechanics|cTopic=Scientists}}
Some of Euler's greatest successes were in solving real-world problems analytically, and in describing numerous applications of the [[Bernoulli numbers]], [[Fourier series]], [[Euler number]]s, the constants {{math|[[E (mathematical constant)|e]]}} and [[pi|{{pi}}]], continued fractions, and integrals. He integrated [[Gottfried Leibniz|Leibniz]]'s [[differential calculus]] with Newton's [[Method of Fluxions]], and developed tools that made it easier to apply calculus to physical problems. He made great strides in improving the [[numerical approximation]] of integrals, inventing what are now known as the [[Euler approximations]]. The most notable of these approximations are [[Euler's method]]<ref name=butcher/> and the [[Euler–Maclaurin formula]].{{sfn|Calinger|2016|pp=96, 137}}{{sfn|Ferraro|2008|loc=Chapter 14: Euler's derivation of the Euler–Maclaurin summation formula|pages=171–180}}<ref name=mills/>

Euler helped develop the [[Euler–Bernoulli beam equation]], which became a cornerstone of engineering.<ref name=ojalvo/> Besides successfully applying his analytic tools to problems in [[classical mechanics]], Euler applied these techniques to celestial problems. His work in astronomy was recognized by multiple [[French Academy of Sciences|Paris Academy]] Prizes over the course of his career. His accomplishments include determining with great accuracy the [[orbit]]s of [[comet]]s and other celestial bodies, understanding the nature of comets, and calculating the [[solar parallax|parallax]] of the Sun. His calculations contributed to the development of accurate [[History of longitude|longitude tables]].<ref name=yousch/>

Euler made important contributions in [[optics]].<ref name=davidson/> He disagreed with Newton's [[corpuscular theory of light]],{{sfn|Calinger|1996|pp=152–153}} which was the prevailing theory of the time. His 1740s papers on optics helped ensure that the [[wave theory of light]] proposed by [[Christiaan Huygens]] would become the dominant mode of thought, at least until the development of the [[wave-particle duality|quantum theory of light]].<ref name="optics"/>

In [[fluid dynamics]], Euler was the first to predict the phenomenon of [[cavitation]], in 1754, long before its first observation in the late 19th century, and the [[Euler number (physics)|Euler number]] used in fluid flow calculations comes from his related work on the efficiency of [[turbine]]s.{{r|li}} In 1757 he published an important set of equations for [[inviscid flow]] in [[fluid dynamics]], that are now known as the [[Euler equations (fluid dynamics)|Euler equations]].<ref name=euler2/>

Euler is well known in [[structural engineering]] for his formula giving [[Euler's critical load]], the critical [[buckling]] load of an ideal strut, which depends only on its length and [[Flexural rigidity|flexural stiffness]].{{sfn|Gautschi|2008|p=22}}