In measure theory, the Euler measure of a polyhedral set equals the Euler integral of its indicator function. By induction, it is easy to show that independent...
990 bytes (80 words) - 16:19, 21 June 2023
mathematician Leonhard Euler (1707–1783), who made many important discoveries and innovations. Many of these items named after Euler include their own unique...
14 KB (1,603 words) - 04:43, 30 August 2024
Euler's formula, named after Leonhard Euler, is a mathematical formula in complex analysis that establishes the fundamental relationship between the trigonometric...
26 KB (3,832 words) - 03:31, 6 August 2024
The Euler angles are three angles introduced by Leonhard Euler to describe the orientation of a rigid body with respect to a fixed coordinate system. They...
48 KB (5,217 words) - 23:24, 1 September 2024
algebraic topology, the Euler class is a characteristic class of oriented, real vector bundles. Like other characteristic classes, it measures how "twisted" the...
11 KB (2,004 words) - 22:38, 18 March 2024
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,...
53 KB (6,453 words) - 12:41, 30 August 2024
Venn diagram (redirect from Venn-Euler diagram)
as by Christian Weise in 1712 (Nucleus Logicoe Wiesianoe) and Leonhard Euler (Letters to a German Princess) in 1768. The idea was popularised by Venn...
30 KB (3,195 words) - 15:25, 17 August 2024
and so on. So the Euler characteristic of the small power set is 1 − 1 + 1 − · · ·. James Propp defines a regularized Euler measure for polyhedral sets...
12 KB (1,719 words) - 08:53, 7 November 2023
Riemann zeta function (redirect from Euler 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...
68 KB (10,314 words) - 06:07, 4 September 2024
Leonhard Euler Telescope, or the Swiss EULER Telescope, is a national, fully automatic 1.2-metre (47 in) reflecting telescope, built and operated by the...
10 KB (907 words) - 01:53, 19 August 2023
definable functions by integrating with respect to the Euler characteristic as a finitely-additive measure. In the presence of a metric, it can be extended...
3 KB (285 words) - 14:20, 18 March 2024
The volume of an n-ball can be calculated in terms of Euler's gamma function. The Lebesgue measure on Rn has the following properties: If A is a cartesian...
18 KB (2,641 words) - 20:13, 3 May 2024
Gamma function (redirect from Euler Gamma Function)
}t^{z-1}e^{-t}\,dt} converges absolutely, and is known as the Euler integral of the second kind. (Euler's integral of the first kind is the beta function.) Using...
90 KB (13,365 words) - 22:20, 23 August 2024
In physics and astronomy, Euler's three-body problem is to solve for the motion of a particle that is acted upon by the gravitational field of two other...
21 KB (3,125 words) - 15:51, 23 August 2024
In mathematics, Hausdorff measure is a generalization of the traditional notions of area and volume to non-integer dimensions, specifically fractals and...
9 KB (1,547 words) - 00:41, 7 November 2023
114–115. Euler (2022), pp. 78–107 Euler (2022), p. 85 Ringe (2014), p. 115 Ringe (2014), p. 114 Euler (2022), p. 81 Euler (2022), p. 78 Euler (2022), p...
56 KB (4,767 words) - 00:51, 3 September 2024
James (2002). "Euler measure as generalized cardinality". arXiv:math.CO/0203289. Propp, James (October 2003). "Exponentiation and Euler measure". Algebra Universalis...
7 KB (663 words) - 07:11, 6 May 2024
Lebesgue integral (redirect from Integral (measure theory))
integral can be generalized in a straightforward way to more general spaces, measure spaces, such as those that arise in probability theory. The term Lebesgue...
41 KB (5,848 words) - 18:07, 12 July 2024
2002 Euler is a stony background asteroid from the inner regions of the asteroid belt, approximately 17 kilometers (11 miles) in diameter. It was discovered...
9 KB (554 words) - 11:51, 2 September 2024
Euler's flycatcher (Lathrotriccus euleri) is a small passerine bird in the tyrant flycatcher family. It breeds in South America east of the Andes from...
6 KB (722 words) - 08:29, 14 June 2023
Radian (redirect from Radian measure)
naturalness as a unit of angular measure. In 1765, Leonhard Euler implicitly adopted the radian as a unit of angle. Specifically, Euler defined angular velocity...
42 KB (5,556 words) - 22:38, 20 August 2024
In mathematical analysis, the Haar measure assigns an "invariant volume" to subsets of locally compact topological groups, consequently defining an integral...
31 KB (5,360 words) - 23:32, 29 December 2023
Angle (redirect from Angular measure)
The magnitude of an angle is called an angular measure or simply "angle". Angle of rotation is a measure conventionally defined as the ratio of a circular...
54 KB (6,768 words) - 22:35, 30 August 2024
as a change in the second Euler angle. If it is not caused by forces external to the body, it is called free nutation or Euler nutation. A pure nutation...
11 KB (1,490 words) - 19:26, 23 June 2024
Euler's quadrilateral theorem or Euler's law on quadrilaterals, named after Leonhard Euler (1707–1783), describes a relation between the sides of a convex...
5 KB (808 words) - 21:01, 30 June 2021
Pyrometer (category Measuring instruments)
mathematician Euler in 1760. Around 1782 potter Josiah Wedgwood invented a different type of pyrometer (or rather a pyrometric device) to measure the temperature...
15 KB (1,591 words) - 15:59, 2 September 2024
Cauchy stress tensor (redirect from Euler-Cauchy stress principle)
eigenvalues of the stress tensor, which are called the principal stresses. The Euler–Cauchy stress principle states that upon any surface (real or imaginary)...
57 KB (8,314 words) - 09:18, 13 June 2024
(orange), and the circumcenter (green) all lie on a single line, known as Euler's line (red line). The center of the nine-point circle lies at the midpoint...
49 KB (5,964 words) - 19:16, 2 September 2024
Dirac delta function (redirect from Dirac's delta measure)
generally oscillatory integrals. An example, which comes from a solution of the Euler–Tricomi equation of transonic gas dynamics, is the rescaled Airy function...
94 KB (13,997 words) - 19:44, 27 August 2024
and ds is the line element along the boundary of M. Here, χ(M) is the Euler characteristic of M. If the boundary ∂M is piecewise smooth, then we interpret...
13 KB (1,842 words) - 10:54, 1 April 2024