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Additional
Lobachevskian geometry
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Hyperbolic geometry
In
mathematics
,
hyperbolic geometry
(also called
Bolyai
–
Lobachevskian
geometry
or
Lobachevskian geometry
) is a
non-Euclidean geometry
. In hyperbolic geometry the
parallel postulate
of
Euclidean geometry
is replaced with:
For any given line
R
and point
P
not on
R
, in the plane containing both line
R
and point
P
there are at least two distinct lines through
P
that do not intersect
R
.
(compare this with
Playfair's axiom
, the modern version of
Euclid
's
parallel postulate
)
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