Plus.Maths.org
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Modelling, step by step 
Why can't human beings walk as fast as they run? And why do we prefer to break into a run rather than walk above a certain speed? Using mathematical modelling, R. McNeill Alexander finds some answers.
Rogue trading? 
The dangers of trading derivatives have been well-known ever since they were catapulted into the public eye by the spectacular losses of Nick Leeson and Barings Bank. John Dickson explains what derivatives are, and how they can be both risky, and used to reduce risk.
From quasicrystals to Kleenex 
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.
On the dissecting table 
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.
Friends and strangers 
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.
Model Trains 
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.
Mathematical mysteries: What colour is my hat? 
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.
Measure for measure 
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.