How many different types of knot are there?
For millennia people have been tying themselves in knots trying to classify and combine the different types.
Asked by: Richard O'Neill, Glasgow
People have been inventing knots for millennia; the oldest known – used in a fishing net found in Finland in 1913 – dates from around 8000BC. Thousands are now known, but they’re not all unique: some are just combinations of others.
Actually deciding whether two apparently different tangles of string are really just the same knot in disguise or some combination is far from simple. So to bring some order to the chaos, mathematicians have developed ways of classifying knots. This has revealed the existence of truly fundamental ones that can’t be unravelled into collections of simpler ones.
Taking prime numbers as an analogy – which can’t be divided by anything other than themselves and one – these are so-called prime knots. The simplest is the so-called trefoil knot; a combination of two of these form the famous ‘granny knot’. There’s an infinite number of prime knots, and these form an infinite number of composite knots. I wouldn’t go trying to untangle them all!
Robert is a science writer and visiting professor of science at Aston University.