Euclidean Space

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euclidean space

[yü′klid·ē·ən ′spās]
A space consisting of all ordered sets (x1, …, xn ) of n numbers with the distance between (x1, …, xn ) and (y1, …, yn ) being given by the number n is called the dimension of the space.

Euclidean Space


in mathematics, a space whose properties are described by the axioms of Euclidean geometry. In a more general sense, a Euclidean space is an n-dimensional vector space, into which several special Cartesian coordinates can be introduced so that its metric is defined in the following manner: If point M has the coordinates (x1x2, …, xn and point M* has the coordinates (x1*, x2*, …, xn*), then the distance between these points is

References in periodicals archive ?
Yukpa's speakings-of the map often took such narrative form, whereby the map was wrested from its Cartesian space to emerge in Yukpa's geographical imaginary where the material and the symbolic, people and the spirit world, and time and space are intimately intertwined in places and thus give meaning to places.
Instead, through performance, maps are unfolded from the grid of striated, Cartesian space and inserted into profoundly emotional geographies that inform current, urgent debates surrounding social change and territoriality.
In most applications of robot manipulators, a desired path for the end-effector is specified in task space such as visual space or Cartesian space.
For numerical testing of this dynamic model, a given linear trajectory between two points in Cartesian space and a 5th degree polynomial low of movement were used.
In order to pass from Cartesian space to joint space in terms of position, velocity and acceleration the inverse kinematics is required.
We define generalised Cartesian space coordinates p, whose elements are the six variables chosen to describe the position and orientation of the platform, as p = f (x, y, z, [phi], [theta], [psi]).
So, the reference coordinates of linear actuators can be computed with (5) for a position of the end-effector in cartesian space.
the non-linear mapping of the motions in Cartesian space,
A positioning accuracy of [+ or -] 0,1mm for each point in the Cartesian space can be realized.