# limit

Can maths help us understand how ants, of such little brains, manage to cooperate so brilliantly?

Find out about the beautifully intuitive concept that lies at the heart of calculus.

Compound interest is the curse of debt and the blessing of saving. Find out how it works and what it has to do with one of the most important numbers in mathematics.

The Fibonacci sequence – 0, 1, 1, 2, 3, 5, 8, 13, ... – is one of the most famous pieces of mathematics. We see how these numbers appear in multiplying rabbits and bees, in the turns of sea shells and sunflower seeds, and how it all stemmed from a simple example in one of the most important books in Western mathematics.

Sequences of numbers can have limits. For example, the sequence 1, 1/2, 1/3, 1/4, ... has the limit 0 and the sequence 0, 1/2, 2/3, 3/4, 4/5, ... has the limit 1. But not all number sequences behave so nicely. Can we still discern some sort of limiting behaviour?

Calculus is a collection of tools, such as differentiation and integration, for solving problems in mathematics which involve "rates of change" and "areas". In the second of two articles aimed specially at students meeting calculus for the first time, Chris Sangwin tells us how to move on from first principles to differentiation as we know and love it!
Calculus is a collection of tools, such as differentiation and integration, for solving problems in mathematics which involve "rates of change" and "areas". In the first of two articles aimed specially at students meeting calculus for the first time, Chris Sangwin tells us about these tools - without doubt, the some of the most important in all of mathematics.
Arguably, the exponential function crops up more than any other when using mathematics to describe the physical world. In the first of two articles on physical phenomena which obey exponential laws, Ian Garbett discusses light attenuation - the way in which light decreases in intensity as it passes through a medium.

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.

• Want facts and want them fast? Our Maths in a minute series explores key mathematical concepts in just a few words.