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
Surface of constant width of a surface of constant width is a curve of constant width. By Barbier's theorem, it follows that every surface of constant width is also a surface of constant girth, where the girth of a shape is the perimeter of one of its parallel projections. Conversely, Hermann Minkowski proved that every surface of constant girth is also a surface of constant width . Surface of constant width In geometry, a surface of constant width is a convex form whose width, measured by the distance between two opposite parallel planes touching its boundary, is the same regardless of the direction of