The area of such hyperbolic sectors has been used to define hyperbolic distance in a geometry textbook.
2.
Conversely, the group " G " acts transitively on the set of pairs of points in the unit disk at a fixed hyperbolic distance.
3.
Since the cross-ratio is invariant under projective transformations, it follows that the hyperbolic distance is invariant under the projective transformations that preserve the conic " C ".
4.
I've been asked to draw the set of points within a fixed hyperbolic distance of a geodesic in the unit disc \ mathbb { D } and unit ball B ^ 3, but the trouble is I haven't the faintest clue what they look like.
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