Articles

Sundaram's SieveThe prime numbers are the atoms amongst the integers, and while we know that there are infinitely many of them, there's no general formula that generates them all. Julian Havil looks at a little-known algorithm that sieves out all primes up to a given number, and which is astonishing in its simplicity.

Restoring profanityIn 1979 decorating work in a house in Vienna revealed a set of medieval frescoes depicting a cycle of songs by a 13th century poet, who was particularly fond of satirising the erotic relationships between knights and peasant maidens. The frescoes are of great historical significance, but they are badly damaged. In this article Carola Schönlieb explores how mathematicians use the heat equation to fill in the gaps.

Understanding uncertainty: The many ways of spinning risk

Would you prefer a game with a 90% chance of winning, or one with a 10% chance of losing? You might scratch your head and say it's the same thing, and you'd be right, but research has shown that people's perception of risk is surprisingly vulnerable to the way it's presented. In this article David Spiegelhalter and Mike Pearson explore how risk can be spun and there's an interactive animation for you to have a go yourself.

EditorialThese are busy times for Plus. Apart from celebrating our 50th issue by putting together a bumper collection of in-depth articles, news and reviews, we're also working on various special projects, some of which have already gone live, and some of which will reach you over the next few weeks and months. Here's a sneak preview of what's in store for 2009...

It's all in the detailThe computer animation used in movies and games is now so lifelike, it is very hard to believe that you are actually watching a surface built from simple shapes of triangles. Phil Dench tells Plus how he uses mathematics to help bring these models to life.

Thomas Harriot: A lost pioneerIt's International Year of Astronomy and all eyes are on Galileo Galilei, whose astronomical observations 400 years ago revolutionised our understanding of the Universe. But few people know that Galileo wasn't the first to build a telescope and turn it on the stars. That honour falls to a little-known mathematician called Thomas Harriot, who excelled in many other ways too. Anna Faherty takes us on a tour of his work.

Sine languageAs an electronic musician Oli Freke has always been fascinated by sine waves, so much so that he's created a song based on them for the Geekpop festival, which is currently taking place on the Web. In this article he explores his song, touching on ancient Greek mythology, strange piano tunings and Johann Sebastian Bach.

Outer space: When errors snowballWhy length matters

Births and deaths in fluid chaosDescribing the motion of fluids is a huge and unsolved mathematical problem. There are equations that seem to describe it well, but their complete solution is way beyond reach. But could there be a simpler method? The physicist Jerry Gollub tells Plus about a new discovery which combines experiment with sophisticated maths.

Understanding uncertainty: What was the probability of Obama winning?

This may seem like an odd question — after all, he’s won — but it opens up some deep philosophical issues surrounding probability. David Spiegelhalter investigates how probability can be defined.

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Common sense

A risky business: how to price derivativesIn the light of recent events, it may appear that attempting to model the behaviour of financial markets is an impossible task. However, there are mathematical models of financial processes that, when applied correctly, have proved remarkably effective. Angus Brown looks at one of these, a simple model for option pricing, and explains how it takes us on the road to the famous Black-Scholes equation of financial mathematics, which won its discoverers the 1997 Nobel Prize in Economics.