Tuesday, December 14, 2010
Give The Gift of Wonder: Klein Bottles
Today's Gift Idea: Klein Bottles
What is a Klein bottle you ask? Well, have you ever seen a Möbius Loop - a one sided, one edged surface? Grab a strip of paper, give it a half-twist, and tape the ends together. Voila...a Möbius Loop! Now for the really cool part. Take a pencil and trace a line on one side of the loop. Keep drawing until you return to the starting point. Take a look at the line. It appears that you have written on two sides. However, you never lifted your pencil from the paper. That's the fantastic part of the Möbius Loop. It has only one side and one boundary.
In 1882, Felix Klein imagined sewing two Möbius Loops together to create a single sided bottle with no boundary. Its inside would be its outside. It would contains itself. Confused? Don't feel bad. It is the confusing and strange nature of the Klein bottle that makes it so very interesting. It's also what makes it a lovely gift for the scientist/art connoisseur in your life. A ‘true’ Klein bottle can only exist in 4 dimensions because the surface has to pass through itself without a hole. However, some talented glassblowers have figured out how to create 3-dimensional representations of ‘true’ Klein bottles. If dissected into two halves, a Klein Bottle will produce two Möbius Loops.
Looking for that special gift for that special person? Check out a Klein bottle. Hopefully, they'll appreciate the beauty of this hand blown glass sculpture even if they can't understand it. Of course, if glass sculpture isn't your thing, you might want to grab a Klein hat or Klein coffee mug.
Where can I get one?