From a local point of view one can take to be Euclidean space.

Typical examples are the real numbers or any Euclidean space.

Another familiar example might be the compact 2-torus or Euclidean space under addition.

The distance between two points in Euclidean space is the length of a straight line from one point to the other.

For Euclidean space, it is point reflection in the origin.

It may be embedded in Euclidean space of dimensions 4 and higher.

In three-dimensional Euclidean space there are 16 such normal forms.

This is, in fact, a sharp contrast with the case of Euclidean spaces.

Usually, the world is perceived as a 3D Euclidean space.

To describe such an orientation in 3-dimensional Euclidean space three parameters are required.

See also fixed points of isometry groups in Euclidean space.

Thus a humanly perceived color may be thought of as a point in 3-dimensional Euclidean space.

From the modern viewpoint, there is essentially only one Euclidean space of each dimension.

These spaces can be viewed as extensions of euclidean space.

No space, such as Euclidean space, is required to contain it.

The graph of this function defines a surface in Euclidean space.

In an -dimensional Euclidean space any point can be specified by real numbers.

Every continuous function from a closed ball of a Euclidean space to itself has a fixed point.

Not all metric spaces may be embedded in Euclidean space.

Let be the unit sphere in three dimensional Euclidean space.

It does this by representing data as points in a low-dimensional Euclidean space.

The universal cover of a complete flat manifold is Euclidean space.

The convolution can be defined for functions on groups other than Euclidean space.

Suppose that is a function from one Euclidean space to another having at least (k+1) derivatives.

Let's consider particles with masses in the regular three-dimensional Euclidean space.