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December 20, 2010

23 is a prime number. Mathematicians love primes. But why? Find out with this prime collection of prime articles.

Mathematical mysteries: the Goldbach conjecture
There are lots of seemingly easy questions about primes that are nevertheless hard to answer. Here's the Goldbach conjecture.


Elusive twins
Primes tend to come in pairs: 5 and 7, 11 and 13, and so on. But do they really? That's the question posed by the twin prime conjecture.


Primes lie at the heart of one of the hardest open problems in maths. Find out more with The prime number lottery, The music of the primes and A whirlpool of numbers.


Safety in numbers
Primes are also what keeps your credit card details safe when you buy something over the internet. Find out how with Simon Singh.


The prime numbers are the atoms amongst the integers, and while we know that there are infinitely many of them, there's no general formula that generates them all. Here are two ways of sieving out all primes up to a given number: Sundaram's sieve and a geometrical method.


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December 20, 2010

Oh, Christmas is so magical! But of course magic often boils down to being surprised. Find out how mathemagicians trade off the fact that you can usually predict precisely the outcome of doing something in mathematics, but only if you know the secret beforehand. Here's for some maths and magic!

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December 20, 2010

Mathematicians are often good musicians. To prove this, here are some impressive compositions. Enjoy!

I will derive:

The Klein 4 Group with Finite simple group of order two:

And for some physics here's the The large hadron rap by Alpinekat:

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December 19, 2010

It's time to get out those party invitations! Trouble is, your sister doesn't get on with your boyfriend, your boyfriend doesn't like your best mate, and your best mate's just broken up with your cousin. Who do you invite? Find out why the answer could win you a million dollars! And for a slightly easier question, can you make sure that no two people you've invited have the same number of friends?

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December 17, 2010

Oh, those beautiful snowflakes! They've put us in the mood for fractals, so let's celebrate some favourite shapes:

Pandora's 3D box
An amateur fractal programmer has discovered a new 3D version of the Mandelbrot set. The new creation is based on similar mathematics as the original 2D Mandelbrot set, but its infinite intricacy extends into all three dimensions, revealing fractal worlds of amazing complexity and beauty at every level of magnification.


Unveiling the Mandelbrot set
And if you're wondering what the Mandelbrot set is to start with, here's an introduction from one of the world's experts.


Modelling nature with fractals
Computer games and cinema special effects owe much of their realism to the study of fractals. This article takes you on a journey from the motion of a microscopic particle to the creation of imaginary moonscapes.


How big is the milky way?
A question which has been vexing astronomers for a long time is whether the forces of attraction between stars and galaxies will eventually result in the universe collapsing back into a single point, or whether it will expand forever with the distances between stars and galaxies growing ever larger. Learn how fractal dimension gives us a way of approaching the question.


Extracting beauty from chaos
Images based on Lyapunov Exponent fractals are very striking. Find out what Lyapunov Exponents are, what the much misunderstood phenomenon of chaos really is, and how you can iterate functions to produce marvellous images of chaos from simple mathematics.


Non-Euclidean geometry and Indra's pearls
If you've ever redecorated a bathroom, you'll know that there are only so many ways in which you can tile a flat plane. But once you move into the curved world of hyperbolic geometry, possibilities become endless and the most amazing fractal structures ensue.


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December 17, 2010

In case your holiday has already started, here are a couple of christmassy puzzles to cuddle up on the sofa with:

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