Take a look at the object above.
It's made from a single 3x5 index card, no part of which
has been taped or glued. As you examine the object more
closely, do you find it puzzling? Do you wonder how it can exist at all?
Topological puzzles have always fascinated the human mind. We understand shapes and structures on an instinctive level. Thus, when something seems to violate our understanding of three-dimensional shapes, we find it confounding and paradoxical.
An example is the relatively familiar Mobius strip. It's a favorite of math teachers everywhere: You take a long strip of paper, twist one of the ends half a turn, and tape the two ends together. The result is a circular hoop with the intriguing property of having only one surface and only one edge. (Incidentally, the three-arrow symbol commonly used to denote "recyclable" is in the form of a Mobius strip.)
The shape shown above will baffle most people when they see it for the first time. Try showing it to your family or friends and see if they can figure out how you made it. It's best not to let them touch it, or they may discover its secret.
Note: For a more startling effect, you can color the areas on the card
that now consist of the "top." The color difference between this new
top and bottom will help strengthen the illusion by hiding the fact that
part of the card has been inverted.
Click here for instructions on making this impossible shape!