Euler's formula, named after Leonhard Euler, is a mathematical formula in complex analysis that establishes the fundamental relationship between the trigonometric...

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...

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...

algebraic topology and polyhedral combinatorics, the Euler characteristic (or Euler number, or Euler–Poincaré characteristic) is a topological invariant...

Euler's identity (also known as Euler's equation) is the equality e i π + 1 = 0 {\displaystyle e^{i\pi }+1=0} where e {\displaystyle e} is Euler's number...

Leonhard Euler (/ˈɔɪlər/ OY-lər; German: [ˈleːɔnhaʁt ˈʔɔʏlɐ] , Swiss Standard German: [ˈleɔnhard ˈɔʏlər]; 15 April 1707 – 18 September 1783) was a Swiss...

The 18th-century Swiss mathematician Leonhard Euler (1707–1783) is among the most prolific and successful mathematicians in the history of the field....

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...

Leonhard Euler, titled De Progressionibus harmonicis observationes (Eneström Index 43), where he described it as "worthy of serious consideration". Euler initially...

Euler, Olinde Rodrigues, or a combination of the two. A detailed historical analysis in 1989 concluded that the formula should be attributed to Euler...

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 even degree....

variables t = −ln s, this becomes the familiar Euler integral. Euler published his results in the paper "De progressionibus transcendentibus seu quarum termini...

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:...

sometimes called Euler's number, after the Swiss mathematician Leonhard Euler, though this can invite confusion with Euler numbers, or with Euler's constant,...

dynamics, the Euler equations are a set of partial differential equations governing adiabatic and inviscid flow. They are named after Leonhard Euler. In particular...

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...

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...

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...

Euler (now Euler Mathematical Toolbox or EuMathT) is a free and open-source numerical software package. It contains a matrix language, a graphical notebook...

an Euler brick, named after Leonhard Euler, is a rectangular cuboid whose edges and face diagonals all have integer lengths. A primitive Euler brick...

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...

Thaine (1988). Euler systems are named after Leonhard Euler because the factors relating different elements of an Euler system resemble the Euler factors of...

The Euclid–Euler theorem is a theorem in number theory that relates perfect numbers to Mersenne primes. It states that an even number is perfect if and...

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...

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,...

is the Euler characteristic of M {\displaystyle M} . A particularly useful corollary is when there is a non-vanishing vector field implying Euler characteristic...

the formula is the Euler function. The equality between the product on the first line and the formulas in the third and fourth lines is Euler's pentagonal...

degree sum formula plays a vital role, allowing the algorithm to connect vertices in pairs in order to construct a graph on which an Euler tour forms...

In mathematics, the Gompertz constant or Euler–Gompertz constant, denoted by δ {\displaystyle \delta } , appears in integral evaluations and as a value...

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...