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 Question about length of hyperbolic line segment in sect 2.4 
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Joined: 07 May 2009, 16:45
Posts: 62
Post Question about length of hyperbolic line segment in sect 2.4
In section 2.4 an expression is given to find the hyperbolic distance between two points A and B on a Poincare disc representation of hyperbolic space.

\log{\frac{QA\cdot PB}{QB\cdot PA}}

Where P and Q are points on the boundary circle of the disc where the hyperbolic line through points A and B terminate, and QA, QB, PA, and PB are the Euclidean distances between points Q and A, Q and B etc.

Is the Euclidean distance mentioned here the Euclidean straight line distance between the various points, or the Euclidean arc length along the circle representing the hyperbolic line?


10 May 2009, 06:38
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Joined: 07 Jun 2008, 08:21
Posts: 235
Post Re: Question about length of hyperbolic line segment in sect 2.4
Since under diagram 2.12 Penrose refers to hyperbolic straight lines as being Euclidean circles or lines, which meet the bounding circle orthogonally, then the hyperbolic distance formula must be using QA etc as the distances along the hyperbolic straight lines (Euclidean circles).


11 May 2009, 22:00
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