Want to impress an audience? Then why not become a lightning calculator by learning Burkard Polster and Marty Ross' method for working out the day on which someone was born from their birthday really fast.

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

Where's the sweet spot?

Genes normally evolve by tiny mutations, but every now and then something more radical occurs and entire genes along a chromosome get flipped. Understanding gene flipping boils down to solving a problem from pure maths. 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.

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?

Hardly six months go by without a natural disaster striking some part of the globe. While it's next to impossible to predict these catastrophes, let alone prevent them, mathematical modelling gives a way to prepare for their impact. Shane Latchman explains.

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.