# Articles

Arithmetic, bones and countingJohn Napier was a clever man indeed. Besides inventing the logarithm, he developed ingenious calculating devices that fully exploit the power of the positional system. In this article

**Chris Sangwin**tells you how to make your own set of*Napier's bones*and perform mathemagic with an interactive checker board.
Understanding uncertaintyWhat's the risk of passive smoking? Or climate change? How big is the terrorist threat? And should we trust league tables? These issues concern all of us, but it's not always easy to make sense of the barrage of media information.

**David Spiegelhalter**, Winton Professor for the Public Understanding of Risk, gives*Plus*his take on uncertainty.
Evolutionary mathsHow did we evolve our capacity for maths? Does maths piggy-back on our ability for language, or is it a completely separate faculty? Is it dependent on culture?

*Plus*spoke to the cognitive psychologist**Rosemary Varley**to find some answers.
Frugal nature: Euler and the calculus of variations

**Phil Wilson**continues our series on the life and work of Leonhard Euler, who would have turned 300 this year. This article looks at the calculus of variations and a mysterious law of nature that has caused some scientists to reach out for god.
Maths goes public

*Plus*celebrates its tenth birthday this year. Former editor and present executive editor of*Plus*,**Robert Hunt**, explores how maths popularisation in general, and*Plus*in particular, have changed over the last ten years.
What is the Area of a Circle? You might know the famous formula for an area of a circle, but why does this formula work?

**Tom Körner**'s explanation really is a piece of cake, served up with a hefty estimate of pi.
Quantum geometryOne of the many strange ideas from quantum mechanics is that space isn't continuous but consists of tiny chunks. Ordinary geometry is useless when it comes to dealing with such a space, but algebra makes it possible to come up with a model of spacetime that might do the trick. And it can all be tested by a satellite.

**Shahn Majid**met up with*Plus*to explain.
Non-Euclidean geometry and Indra's pearlsIf you've ever redecorated a bathroom, you'll know that there are only so many ways in which you can tile a flat plane. But once you move into the curved world of hyperbolic geometry, possibilities become endless and the most amazing fractal structures ensue.

**Caroline Series**and**David Wright**give a short introduction to the maths behind their beautiful images.
Perfect buildings: the maths of modern architecture

*Plus*went to see members of Norman Foster's group of architects to learn about the maths behind architecture.