A point is not on a line. In Euclidean geometry, parallel lines do not meet {parallel axiom}|, and only one line through the point is parallel to the line. In elliptic geometry, parallel great circles meet at two points, and only one line through the point is parallel to the line. Parallel great circles meet at poles of sphere. Parallel lines can make obtuse angles, as on imaginary-radius spheres, or acute angles, as on real-radius spheres. In hyperbolic geometry, parallel great circles do not meet, and many lines through the point are parallel to the line. In projective geometry, parallel lines meet at infinity.
Mathematical Sciences>Geometry>Kinds>Projective Geometry
3-Geometry-Kinds-Projective Geometry
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Date Modified: 2022.0224