The Hausdorff metric
is used to define the distance between two elements of
,
the hyperspace of all nonempty compact subsets of
. The geometry this
metric imposes on
is an interesting one — it is filled with unexpected results and fascinating connections to
number theory and graph theory. Circles and lines are defined in this geometry to make
it an extension of the standard Euclidean geometry. However, the behavior of lines and
segments in this extended geometry is much different from that of lines and segments
in Euclidean geometry. This paper presents surprising results about rays in the geometry
of
,
with a focus on attempting to find well-defined notions of angle and angle measure
in
.