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.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

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

The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.
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.
I have sought to problematize the binary between exclusion and erasure so common in the discussion surrounding participatory mapping, but in so doing, I have come to question the easy assumption that participatory maps are representational artifacts hopelessly trapped in striated, Cartesian space. 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.
Computed torque control in Cartesian space is shown in Fig.
Figure 2 shows a camera alignment that has been optimized for overall focus in Cartesian space. However, look carefully at the image, especially at the corners.
Performance of Linear Motion in the Cartesian Space. A straight stroke is the result of applying the MOVES command (Figure 5), as detailed during the development of this document.
Most of the local approaches aim at producing motions away from the obstacle for every point or each critical point on the manipulator when they are close to the obstacle in Cartesian space [25-28].
Cartesian space to the points in the log-polar parametric space.
The general representation of slave system dynamics (Fig.2) with respect to Cartesian space is
In the most of robot applications, a desired position for the end-effector is usually specified in task space or Cartesian space. In order to move the robot end-effector to the desired position, the exact knowledge of the kinematics is required to solve the inverse kinematics problem to generate the desired position in joint space [6-8].
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]).
A path generator function is used to generate a parametric curve in the cartesian space. The reference signals of the actuators are computed using relation (5).
* the non-linear mapping of the motions in Cartesian space,