  We have studied the packing of congruent disks on a spherical cap, for caps
of different size and number of disks, $N$. This problem has been considered
before only in the limit cases of circle packing inside a circle and on a
sphere (Tammes problem), whereas all intermediate cases are unexplored. Finding
the preferred packing configurations for a domain with both curvature and
border could be useful in the description of physical and biological systems
(for example, colloidal suspensions or the compound eye of an insect), with
potential applications in engineering and architecture (e.g. geodesic domes).
  We have carried out an extensive search for the densest packing
configurations of congruent disks on spherical caps of selected angular widths
($\theta_{\rm max} = \pi/6$, $\pi/4$, $\pi/2$, $3\pi/4$, $5 \pi/6$) and for
several values of $N$. The numerical results obtained in the present work have
been used to establish (at least qualitatively) some general features for these
configurations, in particular the behavior of the packing fraction as function
of the number of disks and of the angular width of the cap, or the nature of
the topological defects in these configurations (it found that as the curvature
increases the overall topological on the border tends to become more negative).
  Finally we have studied the packing configurations for $N = 19$, $37$, $61$,
$91$ (hexagonal numbers) for caps ranging from the flat disk to the whole
sphere, to observe the evolution (and eventual disappearance) of the curved
hexagonal packing configurations while increasing the curvature.
