Sphere has two sides.
A bug may be trapped inside a spherical shape or crawl freely on its visible surface. A thin sheet of paper lying on a desk also has two sides. Pages in a book are usually numbered two per a sheet of paper. The first one-sided surface was discovered by A. F. Möbius (1790-1868) and bears his name: Möbius strip. Sometimes it's alternatively called a Möbius band. (In truth, the surface was described independently and earlier by two months by another German mathematician J. B. Listing.) The strip was immortalized by M. C. Escher (1898-1972).
To obtain a Möbius strip, start with a strip of paper. Twist one end 180o (half turn) and glue the ends together. For comparison, if you glue the ends without twisting the result would look like a cylinder or a ring depending on the width of the strip. Try cutting the strip along the middle line. People unacquainted with Topology seldom guess correctly what would be the result. It's also interesting cutting the strip 1/3 of the way to one edge. Try it.
Now once you know the trick, surely you would like to find other one-sided surfaces. Before gluing the ends together you can twist the strip twice or even three times. Do you get one-sided or two-sided surface?
Acknowledgments:
