translation

=Translation=

toc This article defines a word and clarifies its application and usefulness in scale studies. It is only the word's use in formal langauges of imaging and mathematics that applies to scale studies.

=Overview= Translation is defined mathematically as a transformation consisting of a constant offset with no rotation or distortion. In n-dimensional Euclidean space, a translation may be specified simply as a vector giving the offset in each of the n coordinates.

Thus translation is another word for additive growth, and might help people understand the nature of exponential functions, where translation is mapped to multiplicative growth. This definition is used in Euclidean geometry, where a translation moves every point a constant distance in a specified direction. It is one of the rigid motions (other rigid motions include rotation and reflection). Such movement is interpreted today as the addition of a constant vector to every point, or as shifting the origin of the coordinate system.

In physics, translation (Translational motion) is movement that changes the position of an object, as opposed to rotation.

Translation is the term preferred in formal mathematical discussion for travel.

=Etymology= From the Latin transferre "bear across, carry over, transfer, translate," from trans- "across".