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Understanding uncertainty: Visualising probabilities

Probabilities and statistics: they are everywhere, but they are hard to understand and can be counter-intuitive. So what's the best way of communicating them to an audience that doesn't have the time, desire, or background to get stuck into the numbers? This article explores modern visualisation techniques and finds that the right picture really can be worth a thousand words.
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Maths behind the rainbow

Keats complained that a mathematical explanation of rainbows robs them of their magic, conquering "all mysteries by rule and line". But rainbow geometry is just as elegant as the rainbows themselves.

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Join the celebration of mind!

It's 21st of October and for puzzle lovers this can only mean one thing: the G4G Celebration of mind. This annual party celebrates the legacy of Martin Gardner, magician, writer and father of recreational maths, with mathemagical events in his honour happening all over the world.
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Shattering crystal symmetries

In 1982 Dan Shechtman discovered a crystal that would revolutionise chemistry. He has just been awarded the 2011 Nobel Prize in Chemistry for his discovery — but has the Nobel committee missed out a chance to honour a mathematician for his role in this revolution as well?
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Mathematics and the nature of reality

How many universes are there? What has made us into who we are? Is there absolute truth? These are difficult questions, but mathematics has something to say about each of them. It can probe the physical reality that surrounds us, shed light on human interaction and psychology, and it answers, as well as raises, many of the philosophical questions our minds have allowed us to dream up. On this page we bring together articles and podcasts that examine what mathematics can say about the nature of the reality we live in.
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A fly walks round a football

What makes a perfect football? Anyone who plays or simply watches the game could quickly list the qualities. The ball must be round, retain its shape, be bouncy but not too lively and, most importantly, be capable of impressive speeds. We find out that this last point is all down to the ball's surface, the most prized research goal in ball design.
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Meet the gyroid

What do butterflies, ketchup, microcellular structures, and plastics have in common? It's a curious minimal surface called the gyroid.

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Teacher package: Game theory

Game theory is a great way of sneaking up on maths. You can start off playing an actual game, then start thinking about strategies, and before you know it you're doing proper maths, either conceptually or using equations and formulae. In this teacher package you'll find all our articles on game theory.
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Outer space: A very peculiar principle

If you manage a large organisation, then people will come and go. There are always decisions to make about promoting people, promising newcomers versus experienced middle managers, all of whom are aspiring to move up the corporate ladder. But is it better to promote the least competent rather than the most competent? Some new research suggests that it may be.
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This is not a carrot: Paraconsistent mathematics

Paraconsistent mathematics is a type of mathematics in which contradictions may be true. In such a system it is perfectly possible for a statement A and its negation not A to both be true. How can this be, and be coherent? What does it all mean?