## convergence

What is 1-1+1-1+1-1+...? How infinite sums challenge our notion of arithmetic.

What do you get when you add up all the natural numbers 1+2+3+4+ ... ? Not -1/12! We explore a strange result that has been making the rounds recently.

The number pi can be expressed beautifully in terms of infinite sums. For practical purposes though, these sums are rather disappointing: they converge slowly, so you need to sum a large number of terms to get accurate estimates of pi. Here's a clever way to make them converge faster.

Usain Bolt, the "fastest man on the planet", aims to get his 100 metre world record of 9.58 seconds down to 9.40 seconds. What has mathematics got to say about this quest?

*A disappearing number*, a work by Complicite, inspired by the mathematical collaboration of Hardy and Ramanujan.

**Rachel Thomas**went to see the play, and explains some of the maths. You can also read her interview with Victoria Gould about how the show was created.

**C. J. Sangwin**shows us how eighteenth-century mathematician Leonhard Euler solved one of the foremost infinite series problems of his day.

The paradoxes of the philosopher Zeno, born approximately 490 BC in southern Italy, have puzzled mathematicians, scientists and philosophers for millennia. Although none of his work survives today, over 40 paradoxes are attributed to him which appeared in a book he wrote as a defense of the philosophies of his teacher Parmenides.

**John Webb**applies some divergent thinking, taking in the weather, traffic flow and card shuffling along the way.

**John D. Barrow**explains.