Möbius Strip

Take a strip of paper, give it a half-twist, then attach the ends together to form a single band, and you have a Möbius Strip.

Co-discovered in the mid-19th century by the German mathematicians August Ferdinand Möbius and Johann Benedict Listing, the Möbius strip has the curious property of having only one side. A line drawn starting from the seam down the middle will meet back at the seam but at the "other side." If continued the line will meet the starting point and will be double the length of the original strip of paper.

In his 1947 book, One, Two, Three...Infinity, physicist and cosmologist George Gamow muses on the properties of the Möbius Strip, pointing out that a 2-dimensional "being" traveling the surface of the strip would find its left/right orientation reversed upon completing the first circuit of the loop, and then restored upon completing the second circuit. Gamow extends this idea to "what if" our universe itself is shaped like an enormous, multi-dimensional Möbius Strip, in which case an astronaut traveling far enough would eventually find his/her way back to their starting point, finding their left/right orientation reversed.