Translation (geometry) Translation (geometry) In Euclidean geometry, a translation is a geometric transformation that moves every point of a figure or a space by the same distance in a given direction. In Euclidean geometry a transformation is a one-to-one correspondence between two sets of points or a mapping from one plane to another. A translation can be described as a rigid motion: the other rigid motions are rotations, reflections and glide reflections. 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. A translation operator is an
Girth (geometry) Girth (geometry) In three-dimensional geometry, the girth of a geometric object, in a certain direction, is the perimeter of its parallel projection in that direction. For instance, the girth of a unit cube in a direction parallel to one of the three coordinate axes is four: it projects to a unit square, which has four as its perimeter. The girth of a sphere in any direction equals the circumference of its equator, or of any of its great circles. More generally, if "S" is a surface of constant width "w", then every projection of "S" is a curve of constant