The parallel tool is used to calculate the
parallel line to a given linear object (line, ray, or segment) through
a point. In the figure below we select the
segment
(1) and the point (2) through which the parallel should pass. When we
click
the parallel tool the parallel to the segment through the point is
constructed.
Multiple parallels can be constructed in this way - just select the
linear
objects and points in successive pairs.
In Hyperbolic Geometry, this tool has a very
different effect, as there is no unique parallel to a given line
through
a point. Thus, when we click on the parallel tool
we get two special parallels called ultraparallels. These are
the
unique parallels that intersect the linear object "at infinity", (in
the case of the Poincare Model, they intersect
on the unit circle).
Finally, note that no
parallels exist in Elliptic Geometry.