In the first part of this article we let maths set the scene for a free kick. Now we continue the drama, tracing the trajectory of the ball throughout the milliseconds it takes it to reach the goal line.
A team of Australian researchers has delivered dire news for polar ecosystems, predicting that in some regions biodiversity may be reduced by as much as a third within decades. It's the result of a tipping point induced by global warming.
Some things are so familiar to us that they are simply expected, and we may forget to wonder why they should be that way in the first place. Sex ratios are a good example of this: the number of men and women in the world is roughly equal, but why should this be the case? A simple mathematical argument provides an answer.
Tanya Morton has been drawn to three things throughout her career: problem solving, learning new things and educating others. She tells Plus how her role at the mathematical computing software company, MathWorks, combines these three elements perfectly and how mathematical computing has meant her maths makes a real difference in the world.
Last week leading researchers in sports technology met at the Royal Academy of Engineering in London to demonstrate just how far their field has come over recent years. The changes they make to athletes' equipment and clothes may only make a tiny difference to their performance, but once they're added up they can mean the difference between gold and silver.