Teeqoz said:
I actually knew the answer to that haha. And also, Mensa can eat shit, because true Klein bottles can only exist in 4D. |
When's the last time you tried embedding a Möbius strip in two-dimensional (Euclidean) space? True Möbius strips can only exist in 3D, or higher.
It is a terrible, terrible question relying on popular misconceptions, but it's not terrible for the reason you claim. The Klein bottle has the same dimension as the Möbius strip: they're both two-dimensional surfaces, so the analogy is very poor. One of them has a boundary (an exposed edge), while the other is closed. One can be realized in R^3 while the other can only be immersed in R^3 and embedded in R^4. That doesn't imbue the Klein bottle with higher dimensionality.
A better answer might have been the solid Klein bottle, which is a 3-dimensional manifold with boundary, just as the Möbius strip is a 2-dimensional manifold with boundary. But that is a distinct object — it's as different from a Klein bottle as the Möbius strip is different from a circle (1-sphere).
