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?
The notion of proof lies at the very heart of maths: it's when it comes to proving things that mathematicians let lose their genius and creativity, and in the process often discover unexpected surprises or deep philosophical issues. But proofs can also be daunting. So to help you and your students along, we've brought together a range of Plus articles on proofs.
Sandy Black, Professor of Fashion and Textile Design, has combined her love of art and design with her love of mathematics in her career as a knitwear designer. Sandy talks to Plus about the mathematics in fashion, knitting, and how science and fashion could make the world a better place.
One in nine women will get breast cancer in her lifetime, and it seems sensible to screen women for breast cancer to treat them as early as possible. But, as David Spiegelhalter explains, screening is a controversial issue.
Did you know that church bell ringers have to memorise sequences of several thousand numbers, and that it can take up to 18 hours to translate these sequences into perfect bell ringing? Burkard Polster and Marty Ross explain why, and explore the maths behind bell ringing.