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
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