Here’s a surprise: The Book of Knowledge of Ingenious Mechanical Devices, a 1206 manuscript by the Turkish author Ismail al-Jazari, depicts a chain pump in the form of a Möbius strip. A rope bearing a chain of cups dips them successively into a water source at the bottom and then pours them into a course at the top. The single, continuous rope makes two passes through this route, describing the edges of a strip with a half twist so that the cups suspended between the loops are turned 180 degrees with each pass. This would permit the cups to last longer, since they’re worn more evenly, and even a broken cup might still convey some water with every second pass.

(Julyan H.E. Cartwright and Diego L. González, “Mobius Strips Before Mobius: Topological Hints in Ancient Representations,” Mathematical Intelligencer 38:2 [June 2016], 69-76.)