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Distance in hyperbolic geometry

  1. Oct 5, 2004 #1
    When you are dealing with the Beltrami-Poincare half plane model, and you have an h-line that is horiztonal, how can you calculate the distance of two points on the horizontal line? For example, say you have the points (-9, 12) and (9,12). Then to calculate the distance you need a semicircle through those two points. A semicircle has the general form of x^2+y^2+ax=b so you have 9^2+12^2-9a=b and 9^2+12^2+9a=b so it is obvious then that there is no solution to the equations. So is the distance on a horizontal line undefined in Beltrami-Poincare model for hyperbolic geometry?
  2. jcsd
  3. Oct 5, 2004 #2

    matt grime

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    You mean a=0 and b=225 isn't a solution? When did that happen?
  4. Oct 5, 2004 #3
    yeah what the hell was i thinking :biggrin: Arithmetic has always been my weakest subject.
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