A Möbius band or strip is a mathematical form (a tube with a 180-degree twist) with just one edge and one side.
These are guidelines for seamless knitting of a horizontally ribbed Möbius headband or neck warmer in the round to your own measurements. How to cast on in the round and incorporate a 180-degree twist is not immediately obvious, so this pattern includes a TUTORIAL section that will walk your through Colette’s Möbius Cast-On. This is a great project to use up bits of leftover yarn.
I’ve made many of these bands (they are my favourite neck warmers), using sock yarn doubled up and 5.5 mm needles for quick results.