## geometry

When your eyes see a picture they send an image to your brain, which your brain then has to make sense of. But sometimes your brain gets it wrong. The result is an optical illusion. Similarly in logic, statements or figures can lead to contradictory conclusions, which we call paradoxes. This article looks at examples of geometric optical illusions and paradoxes and gives explanations of what's really going on.

London, September, 1854. A cholera outbreak has decimated Soho, killing 10% of the population and wiping out entire families in days. Current medical theories assert that the disease is spread by "bad air" emanating from the stinking open sewers. But one physician, John Snow, has a different theory: that cholera is spread through contaminated water. And he is just about to use mathematics to prove that he is right.

*unless*the lines are parallel. This annoying exception is constantly inserting itself into otherwise simple mathematical statements.

**Burkard Polster**and

**Marty Ross**explain how to get around the problem.

**Nicholas Mee**discovers, that would be far too simple. In fact, the length of a day varies throughout the year. If you plot the position of the Sun in the sky at the same time every day, you get a strange figure of eight which has provided one artist with a source for inspiration.

**Liz Newton**takes you on a journey of origami, maths and science.

**Josefina Alvarez**and

**Cesar L. Garcia**investigate.

**Gábor Domokos**, one of their discoverers, reckons that in some sense they barely exists at all. So what are Gömböcs and what makes them special?