The key is that there are three different dimensions being collapsed into two "orientations". With a needle, two dimensions are "horizontal", and one is "vertical". With a disk, two are "vertical", and one is "horizontal". Part of the issue with this problem is that people don't generally have an explicit definition of "vertical" and "horizontal". Ask them whether they know what they mean, and they'll say "sure", but ask them to give a definition, and they'll flounder.