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
Introduction to systolic geometry an intriguing link has emerged with the Lusternik–Schnirelmann category. The existence of such a link can be thought of as a theorem in systolic topology. In projective geometry, the real projective plane formula_18 is defined as the collection of lines through the origin in formula_19. The distance function on formula_18 is most readily understood from this point of view. Namely, the distance between two lines through the origin is by definition the angle between them (measured in radians), or more precisely the lesser of the two angles. This distance function corresponds to the metric of constant Gaussian curvature +1. Alternatively,