• Thumbnail for Euler's formula
    Euler's formula, named after Leonhard Euler, is a mathematical formula in complex analysis that establishes the fundamental relationship between the trigonometric...
    27 KB (3,950 words) - 08:13, 13 June 2025
  • Thumbnail for List of topics named after Leonhard Euler
    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...
    15 KB (1,744 words) - 11:30, 13 June 2025
  • 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...
    14 KB (2,432 words) - 21:03, 20 May 2025
  • Thumbnail for Euler's identity
    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...
    15 KB (1,947 words) - 12:43, 13 June 2025
  • algebraic topology and polyhedral combinatorics, the Euler characteristic (or Euler number, or Euler–Poincaré characteristic) is a topological invariant...
    29 KB (3,403 words) - 00:15, 24 June 2025
  • Thumbnail for Leonhard Euler
    Leonhard Euler (/ˈɔɪlər/ OY-lər; 15 April 1707 – 18 September 1783) was a Swiss polymath who was active as a mathematician, physicist, astronomer, logician...
    99 KB (10,444 words) - 11:09, 1 July 2025
  • Thumbnail for Euler's totient function
    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...
    44 KB (6,519 words) - 13:19, 27 June 2025
  • Euler, Olinde Rodrigues, or a combination of the two. A detailed historical analysis in 1989 concluded that the formula should be attributed to Euler...
    15 KB (2,167 words) - 00:54, 25 May 2025
  • Thumbnail for Eulerian path
    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...
    29 KB (3,459 words) - 04:25, 9 June 2025
  • Thumbnail for Euler equations (fluid dynamics)
    dynamics, the Euler equations are a set of partial differential equations governing adiabatic and inviscid flow. They are named after Leonhard Euler. In particular...
    79 KB (13,150 words) - 01:53, 26 May 2025
  • The 18th-century Swiss mathematician Leonhard Euler (1707–1783) is among the most prolific and successful mathematicians in the history of the field....
    17 KB (2,212 words) - 23:05, 7 April 2025
  • Thumbnail for Euler's constant
    Leonhard Euler, titled De Progressionibus harmonicis observationes (Eneström Index 43), where he described it as "worthy of serious consideration". Euler initially...
    71 KB (9,611 words) - 12:02, 23 June 2025
  • Thumbnail for 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...
    90 KB (13,547 words) - 17:59, 24 June 2025
  • Thumbnail for E (mathematical constant)
    sometimes called Euler's number, after the Swiss mathematician Leonhard Euler, though this can invite confusion with Euler numbers, or with Euler's constant,...
    54 KB (6,480 words) - 22:41, 26 June 2025
  • 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...
    17 KB (3,260 words) - 21:19, 22 May 2025
  • Thumbnail for Euler's critical load
    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:...
    11 KB (1,732 words) - 08:33, 5 June 2025
  • Thumbnail for Euler Mathematical Toolbox
    Euler Mathematical Toolbox (or EuMathT; formerly Euler) is a free and open-source numerical software package. It contains a matrix language, a graphical...
    6 KB (565 words) - 14:25, 20 February 2025
  • an Euler brick, named after Leonhard Euler, is a rectangular cuboid whose edges and face diagonals all have integer lengths. A primitive Euler brick...
    18 KB (2,171 words) - 10:35, 30 June 2025
  • Thumbnail for Euler spiral
    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...
    22 KB (3,251 words) - 14:30, 25 April 2025
  • Thumbnail for 1 + 2 + 3 + 4 + ⋯
    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,...
    33 KB (4,219 words) - 21:04, 11 June 2025
  • 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...
    3 KB (326 words) - 11:28, 3 January 2025
  • Thumbnail for Riemann zeta function
    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...
    74 KB (10,699 words) - 08:13, 30 June 2025
  • 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...
    93 KB (12,975 words) - 23:57, 28 June 2025
  • 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
  • Thumbnail for Viète's formula
    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....
    20 KB (2,271 words) - 09:06, 7 February 2025
  • Thumbnail for Pick's theorem
    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
  • In mathematics, the Gompertz constant or Euler–Gompertz constant, denoted by δ {\displaystyle \delta } , appears in integral evaluations and as a value...
    5 KB (688 words) - 18:18, 23 June 2025
  • Thumbnail for Poincaré–Hopf theorem
    is the Euler characteristic of M {\displaystyle M} . A particularly useful corollary is when there is a non-vanishing vector field implying Euler characteristic...
    7 KB (926 words) - 22:20, 1 May 2025
  • In mathematics, particularly number theory, an Euler system is a collection of compatible elements of Galois cohomology groups indexed by fields. They...
    9 KB (1,055 words) - 14:04, 28 May 2025
  • 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