A Euclidean space's motion is the same as its isometry: following the transformation, the distance between any two points remains unaltered.A motion that maintains the origin is equivalent to a linear operator on vectors that maintains the same geometric structure but in terms of vectors.The body is said to rotate onto itself, or spin, if the axis of rotation is within the body, implying relative speed and maybe free movement with angular momentum. ![]() In a Euclidean space, any translation is. A translation can also be interpreted as the addition of a constant vector to every point, or as shifting the origin of the coordinate system. An axis is a line that a three-dimensional object revolves around. In Euclidean geometry, a translation is a geometric transformation that moves every point of a figure, shape or space by the same distance in a given direction.
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