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. When you travel along the surface of a non-orientable shape, you can return to your starting point having flipped upside down, illustrating that there is no consistent way to define left and right. 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 is a closed surface that, like the Möbius strip, has no boundary and challenges our understanding of dimensions and orientation in topology, a branch of mathematics that studies the properties of space.