Theory suggests it is impossible, but geometer George Hart shows that the band's thickness can help you solve this puzzle
From Simons Science News (find original story here).
The mathematics of knot theory says that a simple loop and a trefoil?are fundamentally different knots. But is that all there is to the?question? How can you take a rubber band and turn it into a knot?
Knot theory is the study of knots and their diagrams. It?includes techniques for characterizing how knots can be transformed in three-dimensional?space and tests for determining when two different-looking knots are actually?equivalent. A good introduction is ?The Knot Book? by Colin Adams,?which explains in detail the ?Jones polynomial? mentioned in the?video.
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More videos from the Mathematical Impressions series.
Source: http://rss.sciam.com/click.phdo?i=6f86bfb6cabe23fc7348ada740953dc3
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