Opportunities for the Mathematical Sciences
complicated knot

This is a knot. By following the strand, one can see that it is a single piece of closed string. It is not the un-knot, that is, it is impossible to untangle it into a circle (without cutting and gluing it). Knot theory studies which knots can be transformed into each other; the classification of knots turns out to have a very rich structure, with many links to other fields. Knot theory found very interesting applications in biology, where DNA and proteins fold and knot.

Figure credit: Robert G. Scharein.

URL for this and many other knot pictures: http://www.pims.math.ca/knotplot

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