I'm currently reading through Roger Penrose's book(adsbygoogle = window.adsbygoogle || []).push({}); The Road to Realityand in his Hyperbolic Geometry discussion he introduces the concept of how to define the distance between two points. He defines a Conformal Representation of a Hyperbolic Space bounded by a circle and then he states there are two points A and B (within the hyperbolic space) and there is a hyperbolic line (an arc/Euclidean Circle) That intersects A and B and meets orthogonally to the bounding circle at points P and Q. Where QA etc are the Euclidean distances. The distance between A and B is thus defined by the formula,

log QA.PB/QB.PA

Where log is the natural logarithm and '.' is multiplication, assumingly.

Firstly, can you please define a Euclidean distance and secondly can you help me understand how to derive this formula?

Thanks

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# Hyperbolic Distance Formula

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