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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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:

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?

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.

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

- Mystery Christmas theft: help Santa find the missing pound.
- Deranged Santa: Santa's had a tipple and mixed up all the presents.

As the odds for a white christmas in the UK shorten and we rug up for another snowy weekend, here is the *Plus* weather forecast...

And now, the weather...

Snowstorms, floods and hurricanes remind us yet again that accurate forecasts are necessary not only to protect property, but more importantly to save lives.

Met office in for another roasting?

We all know that weather prediction, though incredibly sophisticated and advanced, is an inexact science. Perhaps if the Met Office published the probabilities underlying its forecasts, it might get a more rational response to disappointing weather.

Career interview: Meteorologist

Read about what it is like to work at the Meteorological Office in this interview with Helen Hewson.

How maths can make you rich and famous: Part II

The weather is described by the famous, and infamously difficult to solve, *Navier-Stokes equations*. And one million dollars is waiting to be won by anyone who can solve this, one of the grand mathematical challenges of the 21st century.

Tsunami

How are these terrible forces of nature unleashed?

The butterfly flap felt across the world

Edward Lorenz, American mathematician and meteorologist, was known as the father of chaos theory. But he is perhaps best known for coining the term butterfly effect.