## Articles

*x*

^{k}? If you're up to speed with your calculus, you can probably rattle the answer off by heart. But can you prove it?

**Chris Sangwin**introduces an ingenious method for deriving the integral from first principles.

*x*

^{k}really the best one?

**Chris Sangwin**makes an interesting case that it is not.

**Colva Roney-Dougal**and

**Vincent Vatter**explain, taking us on a journey from waiters sorting pancakes, via one of the richest men in the world, to the genetic similarities of mice and humans.

**David Spiegelhalter** explains that waiting for an infinite number of monkeys to produce the complete works of Shakespeare is not just a probabilistic certainty, it also gives us an insight into how long we can expect to wait for a rare event to happen.

**Nicholas Mee**discovers, that would be far too simple. In fact, the length of a day varies throughout the year. If you plot the position of the Sun in the sky at the same time every day, you get a strange figure of eight which has provided one artist with a source for inspiration.

**Liz Newton**takes you on a journey of origami, maths and science.