An Etymological Dictionary of Astronomy and Astrophysics
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فرهنگ ریشه شناختی اخترشناسی-اخترفیزیک

M. Heydari-Malayeri    -    Paris Observatory

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Number of Results: 6 Search : Euler
Euler
  اویلر   
Euler

Fr.: Euler   

Leonhard Euler (1707-1783), the eminent Swiss mathematician, physicist, and astronomer.

Euler equation
  هموگش ِ اویلر   
hamugeš-e Euler

Fr.: équation d'Euler   

In → fluid mechanics, one of a set of → differential equations that govern the motion of a → compressible, → inviscid fluid. Euler equations correspond to the → Navier-Stokes equations with zero → viscosity.

Euler; → equation.

Euler line
  خط ِ اویلر   
xatt-e Euler

Fr.: droite d'Euler   

In any → triangle, the straight line on which always lie the → centroid, → circumcenter, and → orthocenter.

Euler; → line.

Euler's broken line
  خط ِ شکسته‌ی ِ اویلر   
xatt-e šekaste-ye Euler

Fr.: ligne brisée   

The line drawn in a coordinate plane connecting the approximate values of the solution of a → first-order differential equation.

Euler; → broken line.

Euler's formula
  دیسول ِ اویلر   
disul-e Euler

Fr.: formule d'Euler   

A formula which expresses an → exponential function with an → imaginary number  → exponent in terms of → trigonometric functions:
e = cos θ + i sinθ,
e-iθ = cos θ - i sinθ,
cosθ = (e + e-iθ)/2,
sinθ = (e - e-iθ)/2i.
In the particular case of θ = π, Euler's formula becomes: eiπ + 1 = 0, which is considered by many mathematicians to be the most elegant mathematical equation. → mathematical elegance.

Euler; → formula.

Eulerian method
  روش ِ اویلری   
raveš-e Euleri

Fr.: méthode eulérienne   

Fluid mechanics: A method in which the changes in the physical properties of the fluid, such as velocity, acceleration, and density are described at a fixed point in space occupied by the fluid. Compare with → Lagrangian method.

Euler; → method.