Articles

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    Visual curiosities and mathematical paradoxes

    When your eyes see a picture they send an image to your brain, which your brain then has to make sense of. But sometimes your brain gets it wrong. The result is an optical illusion. Similarly in logic, statements or figures can lead to contradictory conclusions, which we call paradoxes. This article looks at examples of geometric optical illusions and paradoxes and gives explanations of what's really going on.
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    Diophantine problems for garden gnomes

    Mr and Mrs Magnus are a happy gnome couple. Unfortunately, foreseeing that they will be unable to keep up with their rising mortgage repayments, they've been forced to move into my back garden, where they've acquired a plot to build a house on. Gnome by-laws state that the total number of bricks used in any construction project must be 177 or planning permission will not be granted. How can they manage to stick to the rules?
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    Magnetic tangles

    What happens when magnetic fields get tangled up in knots? This does happen in the Sun's atmosphere and mathematical models predict that once the magnetic field becomes tangled, it must retain some vestige of this complexity for a long time. This enables the storage of vast quantities of energy. In this article I will outline how the notion of magnetic topology helps us to understand the physical situation and draw such conclusions.

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    Curious dice

    In this article we present a set of unusual dice and a two-player game in which you will always have the advantage. You can even teach your opponent how the game works, yet still win again! We'll also look at a new game for three players in which you can potentially beat both opponents — at the same time!

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    Making a racket: the science of tennis

    As London is heading for the 2012 Olympics, it's not just athletes who are gearing up for action. Engineers, too, are working hard to produce the cutting-edge sporting equipment that guarantees record performances. If you're a tennis player, your most important piece of equipment is your racket. Over recent decades new materials have made tennis rackets ever bigger, lighter and more powerful. So what kind of science goes into designing new rackets?
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    Understanding uncertainty: how psychic was Paul?

    England's performance in the World Cup last summer was thankfully overshadowed by the attention given to Paul the octopus, who was reported as making an unbroken series of correct predictions of match winners. David Spiegelhalter looks at Paul's performance in an attempt to answer the question that (briefly) gripped the world: was Paul psychic?

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    Wiring up brains

    The human brain faces a difficult trade-off. On the one hand it needs to be complex to ensure high performance, and on the other it needs to minimise "wiring cost" — the sum of the length of all the connections — because communication over distance takes a lot of energy. It's a problem well-known to computer scientists. And it seems that market driven human invention and natural selection have come up with similar solutions.
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    Classroom activity: the game of life

    One of the amazing things about life is its sheer complexity. How can a bunch of mindless cells combine to form something as complex as the human brain, or as delicate, beautiful and highly organised as the patterns on a butterfly's wing? Maths has some surprising answers you can explore yourself with this interactive activity.

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    Biology's next microscope, mathematics' next physics

    It is thought that the next great advances in biology and medicine will be discovered with mathematics. As biology stands on the brink of becoming a theoretical science, Thomas Fink asks if there is more to this collaboration than maths acting as biology's newest microscope. Will theoretical biology lead to new and exciting maths, just as theoretical physics did in the last two centuries? And is there a mathematically elegant story behind life?
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    Eat, drink and be merry: making it go down well

    This article is part of a series of two articles exploring two ways in which mathematics comes into food, and especially into food safety and health. In this article we will take a dive into the rather smelly business of digesting food, and how a crazy application of chaos theory shows the best way to digest a medicinal drug.
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    Eat, drink and be merry: making sure it's safe

    This article is part of a two-part series exploring ways in which mathematics comes into food, and especially into food safety and health. In this part we'll look at how maths can tell us the safest way to cook food.
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    Outer space: A question of tactics

    In many sports a particular tactical conundrum arises. The team captain has to choose the best order in which to use a group of players or set-plays in the face of unknown counter choices by the opposition. Do you want to field the strongest players first to raise morale or play them last to produce a late run for victory? John D. Barrow shows that randomness holds the answer.