3.1 Diameters
If A and B are collinear with O, then the
hyperbolic line passing through A and B is a diameter of
γ. Although diameters are simple in theory, there are some complications
when implementing this case in GeoGebra since in the end all three cases
will be combined into a single custom tool. In an ideal world, we could
use the Segment[ <Point>,
<Point> ] command to construct the diameter.
Unfortunately, the If[ <Condition>,
<Then>, <Else> ] command
needed to combine the cases requires that the
<Then> and <Else> objects
be of the same type. Since segments and arcs do not meet this criterion,
the diameter will be approximated using the small arc of a large circle
as shown in Figure 5.