Hyperbolic geometry is a non-Euclidean geometry that arises from altering Euclid's fifth postulate, the parallel postulate. In hyperbolic geometry, the essential distinction is that, given a line and a point not on that line, there are infinitely many lines through that point that do not intersect the original line. This contrasts with Euclidean geometry, where there is exactly one parallel line that can be drawn through a point not on a line.
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