[nxbxnnuv] Subdividing some constellations

Given a region and number N, divide the region into N pieces, minimizing the size of the largest piece.  Define the size of a piece to be the size of its circumscribing circle (an unusual definition of size).  After chopping off the largest piece, the region remaining should be divided into N-1 pieces, again minimizing the size of the largest.

Or, given a region and size maximum, find the minimum value of N so that the largest piece is smaller than the size maximum.

The motivation was to name patches of the sky at a finer resolution than existing constellations.  Rather than throw away existing constellations (perhaps replacing it with a regular patchwork of hexagons and pentagons in the style of a geodesic dome), we subdivide existing constellations.  We would like constellations to be compact (not long and skinny) so we use the circumcircle as the size metric.

The subdivision conditions given above only define circumcircle centers and radii.  The actual boundary must be drawn in the overlap between circumcircles.  For astronomy, in keeping with tradition regarding constellation boundaries, the segments that make up the boundary should be along lines of right ascension or declination (in epoch 1875).  But it doesn't seem always possible to draw a boundary satisfying such constraints: we imagine a skinny lens oriented at 45 degrees.

The name of a piece could be some combination of the constellation it is part of and the brightest star in the piece (though star names often include the constellation).

In the past, we did subdivide the very large Argo Navis.  Hydra is currently long and skinny.  Draco is awkwardly nonconvex.

Previously, lots of pieces, enough for everybody.