In deciding friends, I often try to determine if they are knots or tangles.The quintessence of ornamental knots is exemplified by The Book of Kells, an ornately illustrated Gospel Bible, produced by Celtic monks in about A.D. 800. In modern times, the study of knots, such as the trefoil knot with three crossings, is part of a vast bunch of mathematics dealing with closed twisted loops. In 1914, german mathematician Max Dehn (1878-1952) showed that the trefoil knot's mirror images are not equivalent.
For centuries, mathematicians have tried to develop ways to distinguish tangles that look like knots (called unknots) from true knots. Over the years, mathematicians have created seemingly endless tables of distinct knots. So far, more than 1.7 million nonequivalent knots with pictures containing 16 or fewer crossing have been identified.
