Issue 45
December 2007
This issue of Plus is largely a matter of chance. We find an almighty coincidence and try to model it, explore whether statistical media headlines illuminate or mislead, and try to get our head around league tables. On a more certain note, we examine string theory, which many people think explains everything, look back at one of the greatest mathematical works ever written, and try to pin down the number five. 
NHS budgets, third world debt, predictions of global warming, inflation, Iraqi war dead, the decline of fish stocks or hedgehogs, the threat of cancer — there's hardly a subject people care about that comes without measurements, forecasts, rankings, statistics, targets, numbers of every variety. Do they illuminate or mislead? Introducing their new book, Michael Blastland and Andrew
Dilnot take a look at numbers in the media and show that a little maths goes a long way in unravelling dodgy media claims.

In the fourth and final part of our series celebrating 300 years since Leonhard Euler's birth, we let Euler speak for himself. Chris Sangwin takes us through excerpts of Euler's algebra text book and finds that modern teaching could have something to learn from Euler's methods.

Squares do it, triangles do it, even hexagons do it — but pentagons don't. They just won't fit together to tile a flat surface. So are there any tilings based on fiveness? Craig Kaplan takes us through the fivefold tiling problem and uncovers some interesting designs in the process.

Life is full of coincidences, but how do you work out if something is really as unlikely as it seems? In this article Rob Eastaway and John Haigh find chance in church and work out the odds.

Over the last few years the words string theory have nudged their way into public consciousness. It's a theory of everything in which everything's made of strings — or something like that. But why strings? What do they do? Where did the idea come from and why do we need such a theory? David Berman has an equationfree introduction for beginners.


League tables are controversial and for good reason. Few things are simple enough to be measured by a single outcome like, for example, the number of exam passes or successful heart operations. But even if we do accept a single yardstick, we haven't yet reckoned with chance, which by itself can produce apparent patterns to delight any tabloid editor. 

Jet engines, aircraft carriers and telecommunications networks — these are just some of the things that Nira Chamberlain has modelled. And while he's figuring out defence logistics, he's also pursuing a pure mathematical interest in games. Find out what mathematical modelling can do and why it can also make you slim and fluent in French.

Complex numbers — what are they, how do they work and what do they have to do with computergenerated movies, fractals and chaos? This teacher package brings together all Plus articles on complex numbers and gives some handy links to related problems on our sister site NRICH.

Leonhard Euler was one of the greatest and most prolific mathematicians of all time. His work was of vital importance to a bewildering variety of fields, many of which he himself created


I've read several of Paul Nahin's books before (see my review of Dr. Euler's fabulous formula in Plus) and this is no exception to his excellent style. The strategies of pursuit and evasion have fascinated mathematicians for centuries. One of the earliest problems was posed by Frenchman Pierre Bouger in 1732.

Mathematics is the language of science. Clear, simple, fundamental. Perhaps because of this purity, numbers can be the slaves of spindoctors, politicians and an unscrupulous media.

I will tell you all about the book, but first I want to tell you what it felt like to read it. It felt like being back at the beginning of my adventure into mathematics. It felt like the first time the history, culture, and philosophy of maths were unfolded before me.
