Coming to think of it, is the standard formula for the integral of xk really the best one? Chris Sangwin makes an interesting case that it is not.

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.

What's the integral of xk? 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.
Think drug-induced hallucinations, and the whirly, spirally, tunnel-vision-like patterns of psychedelic imagery immediately spring to mind. But it's not just hallucinogenic drugs that conjure up these geometric structures. People have reported seeing them in near-death experiences, following sensory deprivation, or even just after applying pressure to the eyeballs. So what can these patterns tell us about the structure of our brains?
We've all heard of origami. It's all about making paper birds and pretty boxes, and is really just a game invented by Japanese kids, right? Prepare to be surprised as Liz Newton takes you on a journey of origami, maths and science.
The obvious answer is 24 hours, but, as 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.