geometric series

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

When you flip a coin we assume it has equal chance of coming up head or tails, so any coin flipping game should be a fair one. But Yutaka Nishiyama and Steve Humble can give you the winning advantage.
Infinite series occupy a central and important place in mathematics. 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.

The harmonic series is far less widely known than the arithmetic and geometric series. However, it is linked to a good deal of fascinating mathematics, some challenging Olympiad problems, several surprising applications, and even a famous unsolved problem. John Webb applies some divergent thinking, taking in the weather, traffic flow and card shuffling along the way.
Those who understand compound interest are destined to collect it. Those who don't are doomed to pay it - or so says a well-known source of financial advice. But what is compound interest, and why is it so important? John H. Webb explains.
  • Want facts and want them fast? Our Maths in a minute series explores key mathematical concepts in just a few words.

  • As COP28, the 2023 United Nations Climate Change Conference, kicks off we look at how maths can help understand the climate crisis.

  • How do you create dramatic film out of mathematics? We find out with writer and director Timothy Lanzone.

  • Mathematics plays a central role in understanding how infectious diseases spread. This collection of articles looks at some basic concepts in epidemiology to help you understand this fascinating and important field, and set you up for further study.

  • Find out why the formula we use to work out conditional probabilities is true!

  • We talk about a play that explores the fascinating mathematical collaboration between the mathematicians GH Hardy and Srinivasa Ramanujan.