euler

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Definition of euler in English Turkish dictionary

Related Terms

euler's formula
Euler formülü
euler pole
levha tektoniğinde levha hareketlerinin çalışılmasında kullanılan teorik bir dönme kutbu
euler pole
euler kutbu
English - English
Leonhard Euler, Swiss mathematician and physicist
{i} family name; Leonhard Euler (1707-1783), Swiss mathematician; crater on the moon
Swedish physiologist. He shared a 1970 Nobel Prize for studies of nerve impulse transmission
Swiss mathematician (1707-1783)

Related Terms

Euler characteristic
The sum of even-dimensional Betti numbers minus the sum of odd-dimensional ones

A polygon or polyhedron's Euler characteristic is just the number of corners minus the number of edges plus the number of faces.

Euler characteristics
plural form of Euler characteristic
Euler method
A method for numerically approximating the solution to an ordinary differential equation with a given initial value
Euler's formula
Formula which calculates the normal curvature of an arbitrary direction in the tangent plane in terms of the principal curvatures \kappa_1 and \kappa_2 and the angle \theta which that direction makes with the first principal direction:

\kappa_n(\theta) = \kappa_1 \cos^2 \theta + \kappa_2 \sin^2 \theta.

Euler's formula
Formula which links complex exponentiation with trigonometric functions:

e^{i \theta} = \cos \theta + i \sin \theta.

Euler's identity
The equation e^{i \pi} = -1 \,\! which unifies diverse fields of mathematics
Euler's totient function
A function that counts how many integers below a given integer are coprime to it
Euler's formula
Either of two important mathematical theorems of Leonhard Euler. The first is a topological invariance (see topology) relating the number of faces, vertices, and edges of any polyhedron. It is written F + V = E + 2, where F is the number of faces, V the number of vertices, and E the number of edges. A cube, for example, has 6 faces, 8 vertices, and 12 edges, and satisfies this formula. The second formula, used in trigonometry, says e^ix = cos x + isin x where e is the base of the natural logarithm and i is the square root of -1 (see irrational number). When x is equal to or 2, the formula yields two elegant expressions relating , e, and i: e^i = -1 and e^2i = 1
Leonhard Euler
born April 15, 1707, Basel, Switz. died Sept. 18, 1783, St. Petersburg, Russia Swiss mathematician. In 1733 he succeeded Daniel Bernoulli (see Bernoulli family) at the St. Petersburg Academy of Sciences. There he developed the theory of trigonometric and logarithmic functions and advanced mathematics generally. Under the patronage of Frederick the Great, he worked at the Berlin Academy for many years (1744-66), where he developed the concept of function in mathematical analysis and discovered the imaginary logarithms of negative numbers. Throughout his life he was interested in number theory. In addition to inspiring the use of arithmetic terms in writing mathematics and physics, Euler introduced many symbols that became standard, including for summation; n for the sum of divisors of n; e for the base of the natural logarithm; a, b, and c for the sides of a triangle with A, B, and C for the opposite angles; f(x) for a function; for the ratio of the circumference to the diameter of a circle; and i for SquareRoot(-1). He is considered one of the greatest mathematicians of all time
Leonhard Euler
{i} (1707-1783) Swiss mathematician
Turkish - English
eulerian