Euler's formula, named after Leonhard Euler, is a mathematical formula in complex analysis that establishes the fundamental relationship between the trigonometric...
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been given simple yet ambiguous names such as Euler's function, Euler's equation, and Euler's formula. Euler's work touched upon so many fields that he is...
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mechanics, the Euler–Rodrigues formula describes the rotation of a vector in three dimensions. It is based on Rodrigues' rotation formula, but uses a different...
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circle to its diameter. Euler's identity is named after the Swiss mathematician Leonhard Euler. It is a special case of Euler's formula e i x = cos x + i...
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algebraic topology and polyhedral combinatorics, the Euler characteristic (or Euler number, or Euler–Poincaré characteristic) is a topological invariant...
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Leonhard Euler (/ˈɔɪlər/ OY-lər; 15 April 1707 – 18 September 1783) was a Swiss polymath who was active as a mathematician, physicist, astronomer, logician...
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In number theory, Euler's totient function counts the positive integers up to a given integer n that are relatively prime to n. It is written using the...
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Euler, Olinde Rodrigues, or a combination of the two. A detailed historical analysis in 1989 concluded that the formula should be attributed to Euler...
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Eulerian path (redirect from Euler path)
posthumously in 1873 by Carl Hierholzer. This is known as Euler's Theorem: A connected graph has an Euler cycle if and only if every vertex has an even number...
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dynamics, the Euler equations are a set of partial differential equations governing adiabatic and inviscid flow. They are named after Leonhard Euler. In particular...
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The 18th-century Swiss mathematician Leonhard Euler (1707–1783) is among the most prolific and successful mathematicians in the history of the field....
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Leonhard Euler, titled De Progressionibus harmonicis observationes (Eneström Index 43), where he described it as "worthy of serious consideration". Euler initially...
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Gamma function (redirect from Euler Gamma Function)
variables t = −ln s, this becomes the familiar Euler integral. Euler published his results in the paper "De progressionibus transcendentibus seu quarum termini...
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E (mathematical constant) (redirect from Eulers number)
sometimes called Euler's number, after the Swiss mathematician Leonhard Euler, though this can invite confusion with Euler numbers, or with Euler's constant,...
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the equation by multiplying out the left side. De Moivre's formula is a precursor to Euler's formula e i x = cos x + i sin x , {\displaystyle e^{ix}=\cos...
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Euler's critical load or Euler's buckling load is the compressive load at which a slender column will suddenly bend or buckle. It is given by the formula:...
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Euler Mathematical Toolbox (or EuMathT; formerly Euler) is a free and open-source numerical software package. It contains a matrix language, a graphical...
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an Euler brick, named after Leonhard Euler, is a rectangular cuboid whose edges and face diagonals all have integer lengths. A primitive Euler brick...
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An Euler spiral is a curve whose curvature changes linearly with its curve length (the curvature of a circular curve is equal to the reciprocal of the...
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Euler's Proof That 1 + 2 + 3 + ⋯ = −1/12 – by John Baez John Baez (September 19, 2008). "My Favorite Numbers: 24" (PDF). The Euler-Maclaurin formula,...
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Euler's "lucky" numbers are positive integers n such that for all integers k with 1 ≤ k < n, the polynomial k2 − k + n produces a prime number. When k...
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Riemann zeta function (redirect from Euler product formula)
The Riemann zeta function or Euler–Riemann zeta function, denoted by the Greek letter ζ (zeta), is a mathematical function of a complex variable defined...
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functions, in Faulhaber's formula for the sum of m-th powers of the first n positive integers, in the Euler–Maclaurin formula, and in expressions for certain...
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Binomial transform (redirect from Euler transform)
sequence) that computes its forward differences. It is closely related to the Euler transform, which is the result of applying the binomial transform to the...
14 KB (2,438 words) - 15:02, 19 April 2025
of the half-angle formula from trigonometry leads to a generalized formula, discovered by Leonhard Euler, that has Viète's formula as a special case....
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Pick's theorem (redirect from Pick's formula)
way) as the basis for a proof of Euler's formula. Alternative proofs of Pick's theorem that do not use Euler's formula include the following. One can recursively...
20 KB (2,339 words) - 01:48, 17 December 2024
Gompertz constant (redirect from Euler–Gompertz constant)
In mathematics, the Gompertz constant or Euler–Gompertz constant, denoted by δ {\displaystyle \delta } , appears in integral evaluations and as a value...
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Poincaré–Hopf theorem (redirect from Poincaré-Hopf index formula)
is the Euler characteristic of M {\displaystyle M} . A particularly useful corollary is when there is a non-vanishing vector field implying Euler characteristic...
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In mathematics, particularly number theory, an Euler system is a collection of compatible elements of Galois cohomology groups indexed by fields. They...
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actually observed rotation from a previous placement in space. According to Euler's rotation theorem, the rotation of a rigid body (or three-dimensional coordinate...
56 KB (9,999 words) - 14:41, 9 June 2025