Hyperbolic geometry

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Hyperbolic geometry (a non-Euclidean geometry) is also called Lobachevskian geometry or Bolyai-Lobachevskian geometry.

Hyperbolic geometry has the properties

• negative curvature;
• the parallel postulate is false (in two dimensions, there are at least two distinct lines through a point $P$ not on line $L$ which do not intersect $L$);
• the sum of angles of a triangle is less than 180 degrees.

See also

• Hyperbolic geometry (Lobachevskian geometry, with negative curvature)
• Parabolic geometry (Euclidean geometry, with null curvature)
• Elliptic geometry (Riemannian geometry, with positive curvature)