# Articles

A postcard from Italy

**Eugen Jost**is a Swiss artist whose work is strongly influenced by mathematics. He sent us this Postcard from Italy, telling us about his work and the important roles that nature and numbers play in it.
Looking out for number oneYou might think that if you collected together a list of naturally-occurring numbers, then as many of them would start with a 1 as with any other digit, but you'd be quite wrong.

**Jon Walthoe**explains why Benford's Law says otherwise, and why tax inspectors are taking an interest.
Extracting beauty from chaosImages based on Lyapunov Exponent fractals are very striking.

**Andy Burbanks**explains what Lyapunov Exponents are, what the much misunderstood phenomenon of chaos*really*is, and how you can iterate functions to produce marvellous images of chaos from simple mathematics.
Computing the Mandelbrot setAlmost everyone reading this article has no doubt encountered pictures from the Mandelbrot Set. Their appeal is not limited to the mathematician, and their breathtaking beauty has found its way onto posters, T-shirts and computers everywhere. Yet what is a fractal?

The origins of proof III: Proof and puzzles through the agesFor millennia, puzzles and paradoxes have forced mathematicians to continually rethink their ideas of what proofs actually are.

**Jon Walthoe**explains the tricks involved and how great thinkers like Pythagoras, Newton and Gödel tackled the problems.Mathematical mysteries: Foucault's pendulum and the eclipse

You may have seen Foucault's pendulum. There's one in the Science Museum in London (part of the National Museum of Science and Industry), and there are many more in various locations around the UK (for instance, in Glasgow) and the world (including one at the United Nations Headquarters and a famous example at Le Panthéon in Paris).

The origins of proof II : Kepler's proofsJohannes Kepler (1571-1630) is now chiefly remembered as a mathematical astronomer who discovered three laws that describe the motion of the planets.

**J.V. Field**continues our series on the origins of proof with an examination of Kepler's astronomy.