### Did you solve it? Gems from a mathematical wonderland

Earlier today I set you the following three problems. Solution: 64 If we call the ‘size’ of a triangle the number of individual areas it contains, there are 7 triangles of size 1 14 triangles of size 2 10 triangles of size 3 13 triangles of size 4 6 triangles of size 6 6 triangles…

### Can you solve it? Gems from a mathematical wonderland

Today, three puzzles from Mathigon, a remarkable maths website (about which more later). An easy one to start. Count the number of triangles in the image below. all illustrations ©Mathigon Careful though! It’s always easy to miss a few. Talking of (and walking on) triangles…here’s a probability question about random ants. Finally, a very nice…

### Mathematician calculates wave velocity for post-stroke therapy

A RUDN Mathematician Calculated Wave Velocity for Post-Stroke Therapy. Credit: Natalia Deryugina A RUDN mathematician calculated the velocity of wave propagation in the brain in the course of external stimulation. This procedure is used to treat stroke patients. To do so, the scientists generally formulated the task by creating a reaction-diffusion equation and carried out…

### Frog choruses inspire wireless sensor networks

Figure 1. A male Japanese tree frog that produces the type of call examined in this study. Credit: Osaka University If you’ve ever camped by a pond, you know frogs make a racket at night; but what you might not know is how functional and regulated their choruses really are. Frogs communicate with sound, and…

### Unraveling threads of bizarre hagfish's explosive slime

As long as a free end gets stuck on something, and some force from moving water or struggling fish pulls in the opposite direction, tiny skeins of thread produced by hagfish can unspool fast enough to make an enormous amount of protective slime. Credit: Jean-Luc Thiffeault Hundreds of meters deep in the dark of the…

### Sir Michael Atiyah obituary

The last time I met Michael Atiyah, who has died aged 89, was at Tate Modern in London; not the most likely place to run into probably Britain’s greatest mathematician since Isaac Newton, but entirely consistent with his wide-ranging enthusiasm for his subject. It was June 2012, and I joined him and the flamboyant French…

### Did you solve it? Catriona's colourful conundrums

Earlier today I set you the following five geometrical puzzles by Catriona Shearer. I hope you discovered the clever way of solving them, without recourse to pages of algebra. 1. Orange segments If the radius of each semicircle is 5, what’s the total shaded area? all illustrations © Catriona Shearer Solution: 100. If you rearrange…

### Can you solve it? Catriona's colourful conundrums

Today’s puzzles come from Catriona Shearer, a maths teacher at a school in north Essex, whose colourful geometry puzzles have recently gained a following on social media. These brainteasers are certainly pretty, and some are pretty tricky too! Here are five of her best. 1. Orange segments If the radius of each semicircle is 5,…

### Census data could be used to improve city neighbourhoods

Credit: CC0 Public Domain A new analysis of the 2011 census has revealed that social differences among city populations significantly influence how neighbourhoods take shape. Researchers hope that their insights could help councils to make better planning decisions. Dr. Thilo Gross and Dr. Edmund Barter in the Department of Engineering Mathematics at the University of…

### Sir Peter Swinnerton-Dyer obituary

Peter Swinnerton-Dyer, who has died aged 91, is famous among mathematicians as one author of the Birch-Swinnerton-Dyer conjecture in number theory. Published in 1965, this was immediately influential, becoming even more prominent in 1999 as one of the Clay Mathematics Institute’s seven million dollar Millennium Prize Problems, alongside the Riemann hypothesis. Swinnerton-Dyer’s first published paper…