## Articles

 Asking good questions is an important part of doing maths. But what makes a good question? Sometimes a piece of maths can be so neat and elegant, it makes you want to shout "eureka!" even if you haven't produced it yourself. One of our favourite examples is the art gallery problem. Free kicks will deliver much of the drama in the football world cup this summer. But how should strikers approach them and how does the design on the ball impact on its behaviour in flight? Maths can give us answers... 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. Disputes over property are all too common. It's quite easy to share a cake, but how do you share out indivisible goods, such as houses or cars, without causing resentment? Here are two easy methods. Patterns and structures lie at the heart of mathematics, some even say they are mathematics. But how do they help us do mathematics?