Translation (geometry) of the object. The translation vector formula_8 common to all points of the object describes a particular type of displacement of the object, usually called a "linear" displacement to distinguish it from displacements involving rotation, called "angular" displacements. When considering spacetime, a change of time coordinate is considered to be a translation. For example, the Galilean group and the Poincaré group include translations with respect to time. 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
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