This scarf would have been a great present for M.C. Escher, the Dutch artist who sketched impossible architecture and infinitely repeating systems. Why? Because the scarf is a Mobius strip, a "non-orientable" object with only one side: If an ant were to crawl along the strip, it would traverse both the "inside" and the "outside" without ever crossing an edge.
Sarah-Marie Belcastro specializes in mathematical knitting, and made another non-orientable object, the Klein bottle, into a hat.