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Parallel Lines Divergence
In hyperbolic geometry, through a point P not on line L, there are
infinitely many
parallel lines!
Euclid's 5th Postulate fails here!
Euclidean: exactly 1 parallel through P
Hyperbolic: infinitely many parallels through P
Angle of Parallelism:
--
Distance P to L:
--
Formula: Π(d) = 2 arctan(e
-d
)
Parallels:
9
Sweep:
30
Animate sweep
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Line L (base geodesic)
Limiting parallels
Ultra-parallels (diverging)
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