Can you imagine objects that you can't measure? Not ones that don't exist, but real things that have no length or area or volume? It might sound weird, but they're out there. Andrew Davies gives us an introduction to Measure Theory.
As customers will tell you, overcrowding is a problem on trains. Fortunately, mathematical modelling techniques can help to analyse the changing demands on services through the day. Tim Gent explains.
Sometimes a mathematical object can be so big that, however disorderly we make the object, areas of order are bound to emerge. Imre Leader looks at the colourful world of Ramsey Theory.
Bill Casselman writes about the intriguing amateur mathematician Henry Perigal, who took his elegant proof of Pythagoras' Theorem literally to his grave - by having it carved on his tombstone.
This pattern with kite-shaped tiles can be extended to cover any area, but however big we make it, the pattern never repeats itself. Alison Boyle investigates aperiodic tilings, which have had unexpected applications in describing new crystal structures.

This is a game played between a team of 3 people (Ann, Bob and Chris, say), and a TV game show host. The team enters the room, and the host places a hat on each of their heads. Each hat is either red or blue at random (the host tosses a coin for each team-member to decide which colour of hat to give them). The players can see each others' hats, but no-one can see their own hat.