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
Hypercycle (geometry) the hypercycle. The segments of the normal between the "axis", and the hypercycle are called the "radii". Their common length is called the "distance" or "radius" of the hypercycle. The hypercycles through a given point that share a tangent through that point converge towards a horocycle as their distances go towards infinity. Hypercycles in hyperbolic geometry have some properties similar to those of lines in Euclidean geometry: Hypercycles in hyperbolic geometry have some properties similar to those of circles in Euclidean geometry: In the hyperbolic plane of constant curvature −1, the length of an arc of a hypercycle can be