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Euler angles
Euler angles, also called Cardan angles, represent any three-dimensional rotation as a sequence of three rotations about specified coordinate axes; conventions include yaw, pitch, and roll used in aircraft dynamics.
Euler characteristic
The Euler characteristic, also called the Euler-Poincaré characteristic, is a topological invariant equaling V − E + F, which is 2 for every convex polyhedron.
Euler deconvolution
Euler deconvolution is a semi-automatic method for interpreting magnetic and gravity survey data, estimating the location and depth of field sources by solving Euler's homogeneity equation over moving data windows.
Euler diagram
An Euler diagram represents sets as labeled closed curves whose spatial arrangement shows containment, intersection, and exclusion. Euler introduced it in 1761, and unlike Venn diagrams it draws only relevant intersections.
Euler equations (fluid dynamics)
The Euler equations, or Euler's equations of inviscid motion, describe the velocity, pressure, and density of a fluid with viscosity neglected, first dated to 1757.
Euler number (sequence)
The Euler numbers, also called up/down or zigzag numbers, are the integer sequence counting alternating permutations of n elements, beginning 1, 1, 1, 2, 5, 16.
Euler numbers
The Euler numbers are a sequence of integers introduced by Leonhard Euler in 1755, defined as the coefficients of the hyperbolic secant, beginning 1, -1, 5, -61, 1385.
Euler product
An Euler product is a representation of a Dirichlet series or L-function as a convergent infinite product, one factor per prime, introduced by Euler in 1737.
Euler–Bernoulli beam theory
Euler–Bernoulli beam theory, also called the engineering beam theory, is a mathematical model for beam bending, developed around 1750 and still standard in structural engineering.
Euler–Lagrange equation
The Euler–Lagrange equation is the fundamental equation of the calculus of variations, converting integral minimization problems into differential equations; in mechanics it reduces to Newton's second law.
Euler–Maclaurin formula
The Euler–Maclaurin formula, also called the Euler–Maclaurin summation formula, expresses a finite sum of a smooth function's values as an integral plus derivative corrections; it was found independently by Euler and Maclaurin in the 1730s.
Euler–Maruyama method
The Euler–Maruyama method, also known as Euler discretization, is the simplest numerical scheme for simulating stochastic differential equations, converging with strong order 0.5 and weak order 1.0.
Euler–Mascheroni constant
The Euler–Mascheroni constant γ is the limiting difference between the harmonic series and the natural logarithm, about 0.57721, introduced by Euler in 1734; it is unknown whether it is rational or irrational.
Euler's equations (rigid body dynamics)
Euler's equations, also known as Euler's rotation equations, are three equations of rigid-body rotational motion in body-fixed principal axes, presented by Leonhard Euler in 1752.
Euler's formula
Euler's formula is the identity e^(iθ) = cos θ + i sin θ, relating the complex exponential to sine and cosine, derived by Leonhard Euler in 1748.
Euler's identity
Euler's identity, also written e^iπ = −1, is the mathematical statement that e to the power i times pi equals negative 1, connecting five fundamental constants.
Euler's rotation theorem
Euler's rotation theorem, stated by Leonhard Euler in 1775, says any displacement of a rigid body with one point fixed is a single rotation about an axis through that point.
Euler's sum of powers conjecture
Euler's sum of powers conjecture, also called the Euler quartic conjecture, is a disproved 1769 conjecture of Leonhard Euler that at least n nth powers are needed to sum to an nth power.
Euler's theorem
Euler's theorem, also called Euler's totient theorem, is a number theory result stating that a to the power phi(n) equals 1 modulo n when a and n are coprime.
Euler's totient function
Euler's totient function, also called Euler's phi function, counts the positive integers up to n coprime to n, and it is central to Euler's theorem and RSA encryption.
Eulerian number
An Eulerian number counts the permutations of {1, 2, …, n} with exactly k descents, and the numbers form a Pascal-like triangle whose rows sum to n!.
Eulerian path
An Eulerian path, or Euler trail, is a trail in a graph that visits every edge exactly once, arising from Euler's 1736 solution of the Königsberg bridge problem.
EUMETNET
EUMETNET, the European Meteorological Network, is a network of the National Meteorological Services of 33 European countries that coordinates cooperative programs in observations, forecasting, and warnings.
EUMETSAT
EUMETSAT, the European Organisation for the Exploitation of Meteorological Satellites, is an intergovernmental organization in Darmstadt, Germany, that operates Europe's weather satellites and serves 30 Member States.
Eun-Ah Kim
Eun-Ah Kim (김은아) is a South Korean-born condensed matter physicist and Hans A. Bethe Professor of Physics at Cornell University who applies machine learning to quantum materials.
Eunice Newton Foote
Eunice Newton Foote (1819–1888) was an American amateur scientist who in 1856 linked carbon dioxide in the atmosphere to a warmer Earth, three years before John Tyndall.
Eunkyoung Kim
Eunkyoung Kim (김은경) is a South Korean materials chemist at Yonsei University who works on polymers that switch properties under electric or optical triggers, including smart windows.
Eunomia family
Eunomia family, an S-type collisional asteroid family at 2.5–2.7 AU in the intermediate main belt, parent body 15 Eunomia (255 km), partially differentiated, olivine-rich, thousands of members.
Euphotic zone
The euphotic zone is the sunlit upper ocean layer where 1 percent of surface light still penetrates, allowing photosynthesis and nearly all marine primary production, typically 40 to 200 meters deep.
EURAMET
EURAMET, the European Association of National Metrology Institutes, is a non-profit association founded in Berlin in 2007 that took over EUROMET's role coordinating Europe's national metrology institutes and runs EU metrology research programs.