Think drug-induced hallucinations, and the whirly, spirally, tunnel-vision-like patterns of psychedelic imagery immediately spring to mind. But it's not just hallucinogenic drugs that conjure up these geometric structures. People have reported seeing them in near-death experiences, following sensory deprivation, or even just after applying pressure to the eyeballs. So what can these patterns tell us about the structure of our brains?
Many mathematicians find the pure and tight patterns of juggling as irresistible as those of mathematics. Burkard Polster explains how to get to grips with the bewildering range of juggling possibilities and invites you to do your own virtual juggling.
Tilings have adorned buildings from ancient Rome to the Islamic world, from Victorian England to colonial Mexico. But while it sometimes seems free from worldly limitations, tiling is a very precise art, where not much can be left to chance. We can push and turn and wiggle, but if the maths is not right, it isn't going to tile. Josefina Alvarez and Cesar L. Garcia investigate.
In 1997 Andy Green was the first to break the sound barrier in his car Thrust SSC, which reached speeds of over 760mph. Now he and his team want to push things even further with a car called Bloodhound, designed to reach the dizzy heights of 1,000mph, about 1.3 times the speed of sound. Ben Evans explains how maths is used to build this car.
Tim Johnson was drawn into financial maths, not through an interest in finance, but because he was interested in making good decisions in the face of uncertainty. Tim explores the development of this interface between abstract mathematics and our everyday lives, and explains why a painting may only be worth its wall space.
A Gömböc is a strange thing. It looks like an egg with sharp edges, and when you put it down it starts wriggling and rolling around as if it were alive. Until quite recently, no-one knew whether Gömböcs even existed. Even now, 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?
With online socialising and alternative realities like Second Life it may seem as if reality has become a whole lot bigger over the last few years. In one branch of theoretical physics, though, things seem to be going the other way. String theorists have been developing the idea that the space and time we inhabit, including ourselves, might be nothing more than an illusion, a hologram conjured up by a reality which lacks a crucial feature of the world as we perceive it: the third dimension. Plus talks to Juan Maldacena to find out more.