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Fractal photo finish

If you're bored with your holiday snaps, then why not turn them into fractals? A new result by US mathematicians shows that you can turn any reasonable 2D shape into a fractal, and the fractals involved are very special too. They are intimately related to the famous Mandelbrot set.
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Rotation revolution

The laws of symmetry are unforgiving, but a team of researchers from the US have come up with a pattern-producing technique that seems to cheat them. The new technique is called moiré nanolithography and the researchers hope that it will find useful applications in the production of solar panels and many other optical devices.
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Gearing up for gold

Inspired by Sara Storey's phenomenal gold medal we calculate whether we, and our bikes, have what it takes to triumph in our newfound quest for speed!
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Making mathematical tools

This week the International Symposium on Mathematical Programming (ISMP) took place in Berlin. It's the world congress of mathematical optimisation, which drew over 2,000 scientists and members of industry to Germany's capital. But what exactly were they talking about?
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Why the answer to any sum is 10

Learning mathematics involves a progression to higher and higher concepts, building on the foundations of what we have already learnt. But Andrew Irving and Ebrahim Patel explain that no matter how high your mathematical knowledge reaches you must never lose sight of your foundations, no matter how basic they may seem.
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Mixing doubles

Andy Murray and Laura Robson made a good team at London 2012, bringing home silver in the mixed doubles. But how do you make sure that the competing pair is the best you can pick from the team?

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Spinning the perfect serve

A new mathematical analysis of how to hit a winning serve shows that spin is the thing. Perhaps there's still time for Murray's coach to include some maths in his preparations for the match today...
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The logic of drug testing

London 2012 vowed to be the cleanest Olympics ever, with more than 6,000 tests on athletes for performance enhancing drugs. But when an athlete does fail a drug test can we really conclude that they are cheating? John Haigh does the maths.
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Schrödinger's equation — in action

In the previous article we introduced Schrödinger's equation and its solution, the wave function, which contains all the information there is to know about a quantum system. Now it's time to see the equation in action, using a very simple physical system as an example. We'll also look at another weird phenomenon called quantum tunneling.

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Schrödinger's equation — what is it?

In the 1920s the Austrian physicist Erwin Schrödinger came up with what has become the central equation of quantum mechanics. It tells you all there is to know about a quantum physical system and it also predicts famous quantum weirdnesses such as superposition and quantum entanglement. In this, the first article of a three-part series, we introduce Schrödinger's equation and put it in its historical context.

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Mapping the medals

Predicting the final Olympic medal count is a black art. Sport, with all its intricacies and vagaries, is always susceptible to variations in form, weather conditions and simple random events. But we like a challenge! So without further ado, here is our predicted 2012 London Olympic medal count.