Abstract
Let d be a fixed positive integer and let ε > 0. It is shown that for every sufficiently large n ≥ n0(d, ε), the d-dimensional unit cube can be decomposed into exactly n smaller cubes such that the ratio of the side length of the largest cube to the side length of the smallest one is at most 1 + ε. Moreover, for every n ≥ n0, there is a decomposition with the required properties, using cubes of at most d + 2 different side lengths. If we drop the condition that the side lengths of the cubes must be roughly equal, it is sufficient to use cubes of three different sizes.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have