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
Whitehead's point-free geometry chpt. 2 of "Process and Reality". For an advanced and detailed discussion of systems related to C, see Roeper (1997). Biacino and Gerla (1991) showed that every model of Clarke's theory is a Boolean algebra, and models of such algebras cannot distinguish connection from overlap. It is doubtful whether either fact is faithful to Whitehead's intent. Whitehead's point-free geometry In mathematics, point-free geometry is a geometry whose primitive ontological notion is "region" rather than point. Two axiomatic systems are set out below, one grounded in mereology, the other in mereotopology and known as "connection theory". A point can mark a