The definition of

Euclidean distance is defined in section 2.

In Section 4, the characterizations and enumerations of

Euclidean and Hermitian self-dual cyclic codes of length [p.

Restricting the problem to

Euclidean graphs (where vertices are points in

Euclidean space and edge weights are the

Euclidean distances between pairs of vertices) gives rise to the

Euclidean BDMST Problem [1], The problem finds application in several domains, ranging from distributed mutual exclusion [2] to wire-based communication network design [3] and data compression for information retrieval [4].

The results can be easily transferred to the

Euclidean and Lorentz-Minkowski spaces.

As witnessed by our own work over the last years, we expect that broadening the scope and incorporating tools from the Riemannian world will lead to significant progress in our understanding of the qualitative and quantitative structure of isoperimetric minimizers in the purely

Euclidean setting.

Considering the complicated surroundings in optical images

Euclidean distance transform (EDT) was adopted in this paper.

While all students have generally been exposed to

Euclidean geometry, most do not know much about non-

Euclidean geometries and are very intrigued, if at times baffled, by this different perspective.

This is not just an academic exercise--large parts of the modern world function on the basis of higher-dimensional

Euclidean spaces.

i]] denotes the

Euclidean distance between the starting and ending positions of the joint [j.

Let M be an n-dimensional submanifold of an (n + m)-dimensional

Euclidean space [E.

As the

Euclidean Distance is the proper distance at the time light was emitted from a source of light, it is equal to the comoving distance times the scale factor at the time of emission.

The

Euclidean metric invokes a special demand geometry that is rotation invariant and thus preserves aspects of one-dimensional analysis, where there is no role for direction independently of distance.