Distance in hyperbolic geometry

[gravenewworld]

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?

 

[matt grime]

You mean a=0 and b=225 isn't a solution? When did that happen?

 

[gravenewworld]

yeah what the hell was i thinking Arithmetic has always been my weakest subject.