49
If you are interested in how medieval cathedrals came into being, and the mathematics associated with their architecture and construction, then this book is for you.

Symmetry abounds: the wallpaper, your chair, even your own body. Familiar types of symmetry include reflection in a line and rotation about a point. Creating a repeating pattern by translating a core segment to a new place, common in wallpaper, also counts as a symmetry, as does switching without the use of a mirror from an anticlockwise segment to one otherwise identical but oriented clockwise.

We've all been there. You're in a bar with a group of friends. The night draws in. The empties pile up. The conversation turns to sublime speculation and ridiculous argument. How many golf balls would you need to circle the Earth? What's the risk of being killed by a shark? How efficient is wind power? How far does your average Premiership footballer run in a game? How can we put an end to all these questions and go home?

So basic, yet so tricky: prime numbers are the atoms among natural numbers and lie at the centre of some of the most difficult open problems in maths. This package brings together all material we have on primes, from prime number algorithms to new discoveries. And you will find out what all that's got to do with David Beckham.

This may seem like an odd question — after all, he’s won — but it opens up some deep philosophical issues surrounding probability. David Spiegelhalter investigates how probability can be defined. 
