Knots crop up all over the place, from tying a shoelace to molecular structure, but they are also elegant mathematical objects. Colin Adams asks when is a molecule knot a molecule? and what happens if you try to build a knot out of sticks?
A question which has been vexing astronomers for a long time is whether the forces of attraction between stars and galaxies will eventually result in the universe collapsing back into a single point, or whether it will expand forever with the distances between stars and galaxies growing ever larger. Toby O'Neil describes how the mathematical theory of dimension gives us a way of
approaching the question.
Suppose you have an infinitely large sheet of paper (mathematicians refer to this hypothetical object as the plane). You also have a number of different colours - pots of paint, perhaps. Your aim is to colour every point on the plane using the colours available. That is, each point must be assigned one colour.