Leonhard Euler [oi'lər] (April 15, 1707–September 18, 1783) was a Swiss mathematician and physicist. He is considered to become one of a greatest mathematicians world health organization ever lived. Leonhard Euler was a 1st to apply a term "function" (defined by Leibniz in 1694) to describe an expression involving various arguments; i.e., y = F(x). He is credited by owning existence one of a number one to use calculus to physics.

Natural & enlightened inside Basel, he was a mathematical child prodigy. He worked as a professor of mathematics in St. Petersburg, later in Berlin, and then returned to St. Petersburg. He is the virtually all prolific mathematician ever, his gathered act filling 75 volumes. He dominated 18th century mathematics and deduced several symptoms of the fresh made-up calculus. He was entirely blind for the last xvii years of his life, when you took which instance he produced most half of his aggregate output.

A asteroid 2002 Euler is named around his honour.

Biography
Leonhard Euler was natural around Basel, Switzerland, the son of Paul Euler, the Lutheran minister. Although around his childhood he exhibited nifty mathematical talents, his father wanted him to survey theology and become the minister. Inside 1720 Euler began his studies at the University of Basel. There Euler met Daniel and Nikolaus Bernoulli, who found Euler's skills around math. Paul Euler experienced attended Jakob Bernoulli's mathematical lectures and respected his personal. Whilst Daniel & Nikolaus Bernoulli asked him to allow his boy to learn math he eventually agreed & Euler began to survey math.

Around 1727 Euler was called to St. Petersburg by Catherine I of Russia and became professor of physics in 1730, with even more, an extra maths appointment inside 1733. Euler was the foremost to publish a orderly introduction to mechanics in 1736: Mechanica sive motus scientia analytice exposita ("Mechanics or motion explained with analytical science"—that is, calculus). Within 1735 he lost very much of his vision in the best eye due to excessive observation of the sun.

Within 1733 he married Katharina Gsell, the girl of the director of the academy of arts. It got long dozen babies, of whom just deuce-ace sons & 2 girl survived. A descendent one babies, all the same, were inside high positions within Russia in the 19th century.

In the season 1741 Euler became director of the mathematical class at the Prussian Academy of Sciences in Berlin. His instance within Berlin was super productive; nonetheless, he did non own an convenient position due to the want of the king's favor. So he returned to St. Petersburg within 1766, ruled by Catherine the Great at that time, & he remained there for the rest of his life.

Euler continued to become super productive, despite the complete loss of vision, due to his extraordinary powers of memory & mental calculation. These are reported that another time he let his helper calculate a series to Seventeen summands & found that his have symptom & the adjunct's symptom differed in the Fiftieth digit—the recalculation showed that Euler was perfect.

It has been estimated that it would require eight-hours operate by the day for L years to copy entirely his works by hand. It was non till the year 1910 that a collection of his complete works was published; it took about 70 volumes. These are reported by Legendre that often he would write down a complete mathematical proof between a number one & the 2nd require supper.

Euler was the deeply religious Calvinist throughout his life. But, the widely told anecdote that says that Euler challenged Denis Diderot at a court of Catherine the Neat by having "Sir, (a+b)ⁿ/n = x; hence God exists, reply!" is treasonably.

Whenever Euler died, a mathematician & philosopher Marquis de Condorcet commented, "...et il cessa de calculer et de vivre" (& he ceased to calculate & to survive).

Discoveries
Euler, using Daniel Bernoulli, established a law that a torque on a thinly elastic beam is proportional to a measure of a snap of the lesson & the second moment of area of a cross section, just about an axis through the center of mass and perpendicular to the plane of the moment, see Euler-Bernoulli beam equation.

He as well deduced a Euler equations, a placed of laws of motion around fluid dynamics, directly from Newton's laws of motion. These equations come formally monovular to the Navier-Stokes equations with zero viscosity. It is interesting mainly because of the being of shock waves.

Euler processed crucial contributions to the theory of differential equations. Particularly, he is known for creating the series of approximations which are used inside computational mechanics. A best known one approximations is referred to as Euler's method.

Within number theory, Euler invented the totient function. A totient φ(north) of the positive integer n is defined to be a total of caring whole number to a lesser degree or evenorth up to n & coprime to n. E.g., φ(Octad) = Quaternity since a quatern number one, Iii, Five & 7 come coprime to Ogdoad.

Around mathematical analysis, it was Euler world health organization synthesised Leibniz's differential calculus with Isaac Newton's method of fluxions.

Euler established his fame around 1735 by solving the long-standing Basel problem:

in which $\backslash zeta(s)$ is the Riemann zeta function.

He besides showed a utility, consistency, & simplicity of defining a exponent of an imaginary number by means of the formula

This is Euler's formula, which establishes the central role of the exponential function. Inside essence, 100% functions deliberate inside simple analysis come either variations of the exponential work or even it is polynomials. What Richard Feynman called "The most remarkable formula in mathematics" (extra ordinarily known as Euler's identity) is an easy consequence:

Too within 1735, Euler defined a Euler-Mascheroni constant useful for differential equations:

He occurs as co-discoverer of the Euler-Maclaurin formula which is an extremely useful thing for calculation of hard integrals, sums, & series.

Euler wrote Tentamen novae theoriae musicae within 1739 which was an attempt to combine mathematics & music; a life comments that a function was "for musicians too advanced in its mathematics and for mathematicians too musical".

Within economics, Euler showed that if apiece factor of production is paid a value of its marginal product, so (under constant comes back to shell) a sum income & output is entirely exhausted.

Inside geometry and algebraic topology, there is a relationship (also known as Euler's Formulthe) which relates a total of edges, vertices, & faces of a simply connected polyhedron. Given such a polyhedron, a total of a vertices & the faces is universally the total of edges + ii. we.e.: F - E + V = Ii. A theorem too applies to any two-dimensional graphical record. For nonplanar graphical record, there is the generalization: within case a graphical record may be embedded in a manifold M, then F - E + V = χ(M), in which χ is the Euler characteristic of the manifold, a constant which is invariant under continuous deformations. the Euler characteristic of the just-attached manifold like the sphere or even a plane is Deuce. The generalization of Euler's formula for arbitrary two-dimensional graphical record is: F - E + V - C = Ace, in which C is the total of components in the graphical record.

Inside 1736 Euler solved, or like proved insoluble, a condition referred to as the seven bridges of Königsberg, publishing a paper Solutio problematis ad geometriam situs pertinentis which was a earliest application of graph theory or topology.

A guide to a heptad bridges condition reduced a l& people to points and the bridges to lines (or even edges) connecting victims points. Shopping at how else numerous lines inherit the point gave that point the degree (the point by using threesome lines interacting with it has the degree of terzetto). An Euler circuit has wholly its points of possibly degree. This means these are imaginable to travel every line exactly another time while forgoing retracing your computers steps & prevent at a equivalent point where busy people began. An Euler path has exactly ii odd vertices. This means that these are conceivable to travel for each one line exactly when forgoing retracing your computers steps, however that smart shoppers might non prevent in which you began. A vii bridges condition is neither an Euler circuit nor Euler path. Hence, smart shoppers can't visit both of the bridges of Königsberg while forgoing retracing the steps.

Honours
Euler was graded #77 on Michael H. Hart's list of the most influential figures in history.

Quotes
"Read Euler: he is our master in everything." —Pierre-Simon Laplace