It's often claimed that it's possible to wrap gifts in normal 6-sided boxes "perfectly", meaning that the seam on the back side matches the pattern on the paper it overlaps. I'm convinced that it's possible to prove, mathematically, that this is not possible, but my math skills are too deteriorated to actually do so.
It seems to me that, in order to accomplish a "perfect" wrapping job, the length of the diameter of the box to be matched must be a multiple of the length of the pattern and that no amount of folding can overcome this requirement. Can anyone prove that this is true?
This may be a little more trivial than this site usually caters to, but it seems seasonally appropriate...
As a last minute note, it occurred to me this morning that, each time you go around the box, the diameter of the outermost later increases slightly, which means that, given an infinite amount of paper, you could increase the diameter sufficiently to create a match. I seriously doubt that anyone actually wraps gifts in inches of paper though...