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Hyperbolic motion
In
geometry
,
hyperbolic motions
are
isometric
automorphisms
of a
hyperbolic space
. Under composition of mappings, the hyperbolic motions form a
continuous group
. This group is said to characterize the hyperbolic space. Such an approach to geometry was cultivated by
Felix Klein
in his
Erlangen program
. The idea of reducing geometry to its characteristic group was developed particularly by
Mario Pieri
in his reduction of the
primitive notions
of geometry to merely
point
and
motion
.
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