Is zero a cube?
March 2, 2005 5:16 PM Subscribe
mentions, among other things, that "100 is the smallest square which is also the sum of 4 consecutive cubes." Obviously, this refers to the sum of 1^3 (1), 2^3 (8), 3^3 (27) and 4^3 (64). But it seems to me that the sequence can be pushed back to start with 0^3 (0), in which case you can get four consecutive cubes adding up to 36, which is a square. Is zero then not considered a cube?
posted by ubernostrum to Science & Nature (9 answers total)
I've been thinking about this for far too long, and I can see it going either way. For example: zero should not be considered a cube, because the logical implication of this is that it can be divided by its cube root. But its cube root is zero, and division by zero is an undefined operation.
But at the same time, there is a number n such that n^3 = 0, which seems to me to be the very definition of a cube.