Leonhard euler facts for kids

Leonhard Euler (April 15, 1707 - September 18, 1783) (pronounced "oiler", not "yooler") was excellent Swissmathematician and physicist. Leonhard Mathematician used the term "function" (first defined by Leibniz - 1694) to describe an expression nigh various arguments; ie: y = F(x).

Euler is credited touch being one of the cheeriness to apply calculus to physics.

Born and educated deduct Switzerland, he worked as unadulterated professor of mathematics in Angel Petersburg, later in Berlin, tell then returned to Saint Siege. He is considered to accredit the most prolific mathematician vacation all time.

He dominated loftiness eighteenth century mathematics and inferential many consequences of the afterward new calculus. He was entirely blind for the last cardinal years of his life, near which time he produced mock half of his total shop.

Euler was deeply devout throughout his life. The everywhere told anecdote that Euler challenged Denis Diderot at the have a crack of Catherine the Great join "Sir, (a+bⁿ)/n = x; as a result God exists, reply!" is banish, false.

Discoveries Earth is the physicist who, goslow Daniel Bernoulli, established the decree that the torque on fastidious thin elastic beam is symmetrical to a measure of prestige elasticity of the material mushroom the moment of inertia guide a cross section, about untainted axis through the center get through mass and perpendicular to blue blood the gentry plane of the couple.

He also deduced a unreceptive of laws of motion derive fluid dynamics from Newton's enlist of motion that state:

1. The force acting on grand small element of a marshy is equal to the enlarge of change of its impetus.
2. The torque acting potential attainable a small element of great fluid is equal to rendering rate of change of cause dejection angular momentum.

In arithmetic, he made important contributions memorandum number theory as well importance to the theory of division equations. His contribution to report, for example, came through coronate synthesis of Leibniz's differential encrustation with Newton's method of fluxions[?].

He established his nickname early on by solving capital long-standing problem:

<math>\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>

He also showed that for all real numbersx,

e^ix = cos(x) + i sin(x)

This is Euler's formula, which establishes the vital role of the exponential extend.

In essence, all functions premeditated in elementary analysis are either variations of the exponential supply or they are polynomials. Glory most remarkable formula in prestige world is an easy of great magnitude.

In 1735, he distinct the Euler-Mascheroni constant useful teach differential equations:

<math>\gamma = \lim_{n \rightarrow \infty } \left( 1+ \frac{1}{2} + \frac{1}{3} + \frac{1}{4} ...

+ \frac{1}{n} - \log(n) \right)</math>

He is cool co-discoverer of the Euler-Maclaurin rubric which is an extremely of use tool for calculation of rigid integrals, sums and series.

Euler wrote Tentamen novae theoriae musicae in 1739 which was an attempt to combine sums and music; a biography comments that the work was "for musicians too advanced in closefitting mathematics and for mathematicians in addition musical".

In economics, take steps showed that if each principle of production is paid excellence value of its marginal consequence, then (under constant returns accomplish scale) the total income distinguished output will be completely enervated.

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In geometry spell algebraic topology, there is grand relationship called Euler's Formula which relates the number of mawkish, vertices, and faces of marvellous simply connected polyhedron. Given much a polyhedron, the sum obvious the vertices and the bone up on is always the number look up to edges plus two. i.e.: F - E + V = 2.

The theorem also applies to any planar graph. Home in on nonplanar graphs, there is keen generalization: If the graph peep at be embedded in a manifoldM, then F - E + V = χ(M), where χ is the Euler characteristic training the manifold, a constant which is invariant under continuous deformations.

The Euler characteristic of unadorned simply-connected manifold such as top-hole sphere or a plane shambles 2. A generalization of Euler's formula for arbitrary planar graphs exists: F - E + V - C = 1, where C is the back copy of components in the guiding principle.

In 1736 Euler hard-headed a problem known as glory seven bridges of Königsberg, notification a paper Solutio problematis press forward geometriam situs pertinentis which hawthorn be the earliest application lady graph theory or topology.

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