Sometimes a diagram of a knot can be coloured with three colours so that at each crossing either all three colours meet, or there is only one colour.
However much you twist, turn, or pull a diagram of a 3-coloured trefoil, you can still colour it so that it will continue to have either one colour at each crossing, or three.
We say the trefoil is 3-colourable. Some other knots have this property. But if you try to colour the figure eight, or the cinquefoil, then somewhere there will be a crossing with exactly two colours. Therefore 3-colourability would seem to be a way of distinguishing some of our knots.
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© Mathematics and Knots, U.C.N.W.,Bangor, 1996 - 2002
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