A pretty mathematical "folklore" problem (solvable easily by induction) states : Given a square and an integer n > 5, it is possible to cut the given square into exactly n squares? (It is not required in general, of course , that the cut squares be equal in size).
Two problems arise naturally:
(i) Is a similar statement true for cutting a cube into a given number of
cubes in dimensions d = 3,4,..., (with the value 5 replaced
possibly by some other number depending on d)?
(ii) Can the procedure be done "asymptotically fairly" in the sense that
for suitable cuttings the ratios the size of the largest square (cube) cut / the
size of the smallest square (cube) cut
will converge to 1, as n approaches infinity?
The talk will provide some answers as well as some details of (or hints
for) proofs.
