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hyperbolic geometry |
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hyperbolic geometryNon-Euclidean geometry, useful in modeling interstellar space, that rejects the parallel postulate, proposing instead that at least two lines through any point not on a given line are parallel to that line. Though many of its theorems are identical to those of Euclidean geometry, others differ. For example, two parallel lines converge in one direction and diverge in the other, and the angles of a triangle add up to less than 180°. |
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In areas where the surface has floppy, hyperbolic geometry, the algorithm will identify many mesh points; where the surface has more tightly curved geometry, the algorithm will identify fewer points. Modern three-dimensional hyperbolic geometry actually owes its origins to computer experiments, Adams says. Among closed surfaces, spherical, flat, and hyperbolic geometry are mutually exclusive. |
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hyperbolic geometry
