Non-orientable surfaces are geometric shapes that do not have a distinct "inside" and "outside." A classic example is the Möbius strip, which can be created by taking a rectangular strip of paper, giving it a half-twist, and then joining the ends together. If you travel along the surface of a Möbius strip, you can return to your starting point having flipped over without ever crossing an edge. Another well-known non-orientable surface is the Klein bottle. Unlike a Möbius strip, a Klein bottle cannot be constructed in three-dimensional space without intersecting itself. It has no boundary and, like the Möbius strip, challenges our understanding of dimensions and orientation in geometry.