  This paper views the honeycomb conjecture and the Kepler problem essentially
as extreme value problems and solves them by partitioning 2-space and 3-space
into building blocks and determining those blocks that have the universal
extreme values that one needs. More precisely, we proved two results. First, we
proved that the regular hexagons are the only 2-dim blocks that have unit area
and the least perimeter (or contain a unit circle and have the least area) that
tile the plane. Secondly, we proved that the rhombic dodecahedron and the
rhombus-isosceles trapezoidal dodecahedron are the only two 3-dim blocks that
contain a unit sphere and have the least volume that can fill 3-space without
either overlapping or leaving gaps. Finally, the Kepler conjecture can also be
proved to be true by introducing the concept of the minimum 2-dim and 3-dim
Kepler building blocks.
