Mӧbius band.....

A Mӧbius band    (also called Mӧbius strip) is a one-sided surface that can be obtained by gluing two ends of a half-twisted long rectangular strip. They look cool in M.C. Escher’s drawings and in real life:

Mӧbius bands were independently discovered by German mathematician Johann Listing and German scholar August Ferdinand Mӧbius in the 1850s. Some interesting things about these shapes are as follows:

• If you draw a line down the middle of the strip, you will eventually reach the starting point after drawing on what appears to be both sides of the strip – proving that there really is only one side.
• By tracing one’s finger along the edge of a Mobius band, every possible point on the edge of the object will be touched – proving that the surface has only one edge.
• It is impossible to cut a Mobius band in half. If you cut a Mobius band along the centerline, you will end up with one long strip with two full twists, rather than two separate strips.
• The B.F. Goodrich Company utilized Mӧbius-like shapes to design conveyor belts. Because the “wear and tear” was distributed throughout the entire shape, these belts lasted twice as long as conventional belts.
• Mobius bands have been in the design of electronic resistors, compact resonators and superconductors for complex electrotechnology applications.

After years of searching for examples in natural materials, U.S. Department of Energy scientists have recently discovered Möbius-like shapes occurring in metamaterials – that is, materials engineered from artificial “atoms” and “molecules”. This is big news for scientists who want to create structures with shapes that aren’t naturally occurring in materials or molecules, and up to this point were limited to only mathematical imagination.

aint it cool?????????