Abstract:
We discuss the history of attempts to fill R3 with disjoint circles,
and then
address the question of continuously partitioning a connected open
subset U of R2k+1
into congruent k-spheres. This is possible only for finitely many k,
and in those cases
there is a number Mk such that
volume(U) ≤ Mk
for any such U.
Time permitting, we will show some related computer graphics. |