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Motion (geometry)
In
geometry
, a
motion
is an
isometry
of a
metric space
. For instance, a
plane
with
Euclidean distance
as
metric
is a metric space in which a mapping associating
congruent
figures is a motion. More generally, the term
motion
is a synonym for
surjective
isometry in metric geometry, including
elliptic geometry
and
hyperbolic geometry
. In the latter case,
hyperbolic motions
provide an approach to the subject for beginners.
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