Hyperbolic
arc of circumference
The tool that we
have created allows to construct the hyperbolic arc of a circumference
that goes through three determinated points. The order in which the
points are marked is important since in the construction we will
consider that the first point that the user marks is the origin
of the arc; the second, an intermediate point and the third, the final
point. Like in the case of the circumference that goes through three
points the construction of the arc will not always be possible. It will
be possible if and only if we can construct the circumference.
Given three ordered points we construct the hyperbolic arc by the
following steps:
- Plot the hyperbolic circumference
that goes through the three given points.
- Plot the hyperbolic ray that begins
in
the
center of
the circumference and passes through the second given point.
- Consider the intersection of the ray plotted in the second
step with the hyperbolic circumference.
- Plot the Euclidean arc with origin in the first given point,
which passes through the intersection of the third step and finishes in
the third given point.
We need the third
step to affirm that if the
hyperbolic circumference that passes through the three points does not
exist the tool does not draw the arc, either.
If the circumference exists there will be the intersection and this
will be the second given point.
List of tools
Hyperbolic
geometry
