Assertion: isometry | /r/HasProperty | rigid motion
Facets:
value: in the particular case
type: TEMPORAL
value: with the standard euclidean metric
type: OTHER
Source sentences:
text: In a two-dimensional or three-dimensional Euclidean space, two geometric figures are congruent if they are related by an isometry; the isometry that relates them is either a rigid motion (translation or rotation), or a composition of a rigid motion and a reflection.
text: In the particular case where we take our space to be the usual Euclidean plane or Euclidean 3-space ( or with the standard Euclidean metric), the isometries are known as rigid motions and two sets which can be transformed onto each other by an isometry are said to be congruent.
text: An isometry is a distance preserving map from some space it itself: a rigid motion.