Möbius Strip and Non‑Orientable Surfaces

A Möbius strip is a surface with only one side. Take a strip of paper, give it a half‑twist, and glue the ends. An ant walking along the centreline returns upside‑down. It is non‑orientable: you cannot consistently define a normal vector. The Möbius strip has Euler characteristic 0 (like a cylinder). It appears in conveyor belts (to wear both sides evenly), in the recycling symbol, and in M.C. Escher’s woodcuts. Cutting a Möbius strip along its centreline yields a single long strip with two full twists – not two separate strips.