In hyperbolic geometry, a plane is represented by a hyperboloid surface with more parallels than Euclidean geometry, exhibiting distinct characteristics from elliptic and Euclidean geometries.
In hyperbolic geometry, a plane can be represented by a hyperboloid surface. Unlike elliptic geometry where figures can be modeled on a sphere, hyperbolic geometry involves a hyperboloidal surface that works locally as a model with approximately constant negative curvature.
Hyperbolic geometry is characterized by having more parallels than Euclidean geometry. Lines in hyperbolic space that start off as parallel eventually diverge, in contrast to spherical space where lines that start off as parallel eventually intersect.
Overall, hyperbolic geometry is of significant interest as it describes the spatial dimensions of the universe on a cosmological scale, and its unique properties set it apart from Euclidean and elliptic geometries.
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