Hyperbolic plane geometry is the geometry of pseudospherical surfaces, surfaces with a constant negative Gaussian curvature.
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11 Facts About Hyperbolic plane
2.
Hyperbolic plane geometry is more closely related to Euclidean geometry than it seems: the only axiomatic difference is the parallel postulate.
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3.
Ultraparallel lines, the ultraparallel theorem states that there is a unique line in the hyperbolic plane that is perpendicular to each pair of ultraparallel lines.
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4.
Hyperbolic plane geometry was finally proved consistent and is therefore another valid geometry.
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5.
Hyperbolic plane geometry enters special relativity through rapidity, which stands in for velocity, and is expressed by a hyperbolic angle.
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6.
Hyperbolic plane is a plane where every point is a saddle point.
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7.
However, the entire hyperbolic plane cannot be embedded into Euclidean space in this way, and various other models are more convenient for abstractly exploring hyperbolic geometry.
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8.
Hyperbolic plane lines are half-circles orthogonal to the boundary of the hemisphere.
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9.
The characteristic feature of the hyperbolic plane itself is that it has a constant negative Gaussian curvature, which is indifferent to the coordinate chart used.
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10.
Hyperbolic plane geometry is not limited to 2 dimensions; a hyperbolic geometry exists for every higher number of dimensions.
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11.
Hyperbolic plane space of dimension n is a special case of a Riemannian symmetric space of noncompact type, as it is isomorphic to the quotient.
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