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...

mathematician Leonhard Euler (1707–1783), who made many important discoveries and innovations. Many of these items named after Euler include their own unique...

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

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...

algebraic topology, the Euler class is a characteristic class of oriented, real vector bundles. Like other characteristic classes, it measures how "twisted" the...

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

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...

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...

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...

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...

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...

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...

}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...

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...

In mathematics, Hausdorff measure is a generalization of the traditional notions of area and volume to non-integer dimensions, specifically fractals and...

 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...

James (2002). "Euler measure as generalized cardinality". arXiv:math.CO/0203289. Propp, James (October 2003). "Exponentiation and Euler measure". Algebra Universalis...

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...

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...

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...

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...

In mathematical analysis, the Haar measure assigns an "invariant volume" to subsets of locally compact topological groups, consequently defining an integral...

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...

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...

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...

mathematician Euler in 1760. Around 1782 potter Josiah Wedgwood invented a different type of pyrometer (or rather a pyrometric device) to measure the temperature...

eigenvalues of the stress tensor, which are called the principal stresses. The Euler–Cauchy stress principle states that upon any surface (real or imaginary)...

(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...

generally oscillatory integrals. An example, which comes from a solution of the Euler–Tricomi equation of transonic gas dynamics, is the rescaled Airy function...

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...