All articles starting with E
17,681 articles
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 method
The Euler method (also called the forward Euler method) is the simplest numerical method for solving ordinary differential equations, stepping along tangent lines; it is first order and rarely used in practice.
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 critical load
Euler's critical load, also called Euler buckling load, is the axial compressive load at which an ideal elastic column buckles, derived by Leonhard Euler in 1744.
Euler's Disk
Euler's Disk, invented by Joseph Bendik in the late 1980s, is a spinning steel-disk toy whose precession rate rises as Ω ∝ α^−1/2 until an abrupt, finite-time stop.
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 method (fluid dynamics)
The Eulerian method is a fluid simulation approach that solves the equations of flow on a fixed spatial grid, storing velocity and density at fixed points in space.
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.
Eulimidae
Eulimidae (Philippi, 1853), also historically Eulimoidea, is a family of about 1,500 species of small marine caenogastropod snails that parasitize all five echinoderm classes, now placed in Vanikoroidea.
Eulipotyphla
Eulipotyphla, the true insectivores, is a Laurasiatherian mammal order of hedgehogs, shrews, moles, and solenodons in four extant families plus extinct Nesophontidae, defined by nuclear-gene monophyly, parallel venom, and repeated aquatic and fossorial transitions.
Eulji Mundeok
Eulji Mundeok (을지문덕, 乙支文德) was a Goguryeo military commander who annihilated a Sui army of 305,000 at the Salsu River in 612, contributing to the Sui dynasty's fall in 618.
Eulmash-shakin-shumi
Eulmash-shakin-shumi (Eulmaš-šākin-šumi) was king of Babylon from 1004 to 988 BC and founder of the Bazi dynasty, the tenth dynasty in the Babylonian king lists.
Eulmi Incident
The Eulmi Incident (을미사변) was the murder of Queen Min, consort of King Gojong of Korea, by a Japanese group directed by minister Miura Goro at Gyeongbok Palace in Seoul in October 1895.