>[!abstract]
>In mathematics, the Klein bottle (/ˈklaɪn/) is an example of a non-orientable surface; that is, informally, a one-sided surface which, if traveled upon, could be followed back to the point of origin while flipping the traveler upside down. More formally, the surface is a two-dimensional manifold on which one cannot define a consistent direction perpendicular to the surface (normal vector) that varies continuously over the whole shape (Wikipedia, 2025).
>[!related]
>- **North** (upstream): [[Topology]]
>- **West** (similar): [[Möbius strip]]
>- **East** (different): [[Orientable surfaces]]
>- **South** (downstream): [[Non-orientability]]