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Euclidean group
The Euclidean group E(n), also denoted ISO(n), is the group of all distance-preserving transformations of n-dimensional Euclidean space, made up of rotations, translations, reflections, and their compositions.
Euclidean norm
The Euclidean norm, also called the 2-norm, is the square root of the sum of a vector's squared coordinates, and it measures the vector's length.
Euclidean space
Euclidean space is the mathematical structure formalizing the familiar geometry of the plane and three-dimensional space, using distances and angles measured by an inner product.
Euclidean vector
A Euclidean vector, also called a spatial or geometric vector, is a quantity with magnitude and direction, drawn as an arrow with length and direction but no fixed location.
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 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 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–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 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.
Euro Interbank Offered Rate
The Euro Interbank Offered Rate (EURIBOR, Euribor) is the daily benchmark rate for unsecured euro interbank lending, administered by the European Money Markets Institute since 1999.
Évariste Galois
Évariste Galois (1811–1832) was a French mathematician who founded Galois theory and gave the precise criterion for solving polynomial equations by radicals; he died in a duel at 20.
Even and odd functions
Even and odd functions satisfy f(-x) = f(x) and f(-x) = -f(x), giving y-axis and origin symmetry; examples include x², cos x, x³, and sin x.
Event (probability theory)
In probability theory, an event, also called a random event, is a subset of the sample space of a random experiment, such as rolling an even number on a die.
Event study
An event study is a statistical method measuring how an event, such as an earnings announcement or regulatory change, affects an outcome, typically abnormal security returns.
Evidence lower bound
The evidence lower bound (ELBO), also called the variational lower bound, is a computable lower bound on a model's log evidence, maximized in variational inference.
Evolutionary game theory
Evolutionary game theory applies game theory to evolving populations, treating payoffs as Darwinian fitness. Its central concept, the evolutionarily stable strategy, came from Maynard Smith and Price in 1973.
Evolutionary graph theory
Evolutionary graph theory is a branch of mathematical biology studying how the graph structure of a finite population changes evolutionary dynamics, introduced by Lieberman, Hauert, and Nowak in 2005.
Exact differential equation
An exact differential equation is a first-order equation M dx + N dy = 0 with a potential function F whose solutions are level curves F = C.