Search Results for ""

A weighted graph in which the weights are equal to the Euclidean lengths of the edges in a specified embedding (Skiena 1990, pp. 201 and 252).

A Euclidean motion of R^n is an affine transformation whose linear part is an orthogonal transformation.

A theorem sometimes called "Euclid's first theorem" or Euclid's principle states that if p is a prime and p|ab, then p|a or p|b (where | means divides). A corollary is that ...

The derivative (deltaL)/(deltaq)=(partialL)/(partialq)-d/(dt)((partialL)/(partialq^.)) appearing in the Euler-Lagrange differential equation.

According to Euler's rotation theorem, any rotation may be described using three angles. If the rotations are written in terms of rotation matrices D, C, and B, then a ...

Euler integration was defined by Schanuel and subsequently explored by Rota, Chen, and Klain. The Euler integral of a function f:R->R (assumed to be piecewise-constant with ...

Define the Euler measure of a polyhedral set as the Euler integral of its indicator function. It is easy to show by induction that the Euler measure of a closed bounded ...

The general displacement of a rigid body (or coordinate frame) with one point fixed is a rotation about some axis. Furthermore, a rotation may be described in any basis using ...

For signed distances on a line segment, AB^_·CD^_+AC^_·DB^_+AD^_·BC^_=0, since (b-a)(d-c)+(c-a)(b-d)+(d-a)(c-b)=0.

An event is a certain subset of a probability space. Events are therefore collections of outcomes on which probabilities have been assigned. Events are sometimes assumed to ...