The Möbius Strip

August Möbius and Johann Listing both discovered the one-sided surface in 1858 independently. Take a long strip of paper, give it a half-twist, and join the ends. The result has only one side and one edge — an ant walking along the 'outside' finds itself on the 'inside' without ever crossing an edge. Cut it down the middle and it stays in one piece, forming a loop with two full twists. Cut it one-third from the edge and you get two linked loops. The Möbius strip is the simplest non-orientable surface in mathematics, and a recurring symbol of infinity.