An Etymological Dictionary of Astronomy and Astrophysics
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Leonhard Euler (1707-1783), the eminent Swiss mathematician, physicist, and astronomer.

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.

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

→ Euler; → line.

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

→ Euler; → broken line.

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

→ Euler; → formula.

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.