London's Riverbank Arena is hosting Paralympic football. Image: London 2012.

London's Riverbank Arena will see action today with semi-finals kicking off in Paralympic football. Generally, football fans can be a rowdy a lot and that's something you've got to think about when building a football venue. Imagine the 80,000 people that fit into a stadium like Wembley jumping up and down in unison to We will rock you. Any structure, no matter how solid, has its own natural frequency at which it likes to vibrate, and if that happens to be in tune with the people's, you can end up with a dangerous sway and ultimate disaster. And that's just one of the things you need to take into account when building a stadium. Find out more in our interview with the engineer Paul Shepherd, who's been involved in building the Arsenal football stadium, in our podcast Stadium maths (the interview with Shepherd starts at 8 minutes 10 seconds).

Jamie Clarke at the 2006 Winter Olympics in Torino.

One thing that's characterised the London 2012 Games is its great atmosphere — and that's largely down to the tens of thousands of volunteers who've donated their time, effort and enthusiasm to the Games. For most of them this will probably be a once-in-a-lifetime experience. But it's also possible to be part of big sporting events like this one and earn money at the same time. Jamie Clarke is one of the lucky people who has managed to do this and it's maths that has led him there. To find out how to live the sporting dream as a mathlete rather than an athlete, read our career interview with Jamie.

Relay races are exciting to watch, but for coaches and athletes they pose a particular conundrum: in what order should the athletes be deployed? Should the fastest come first, last, or somewhere in the middle? To a large extent this will depend on your strongest opponent's strategy, which in turn depends on yours. So we're into second-guessing, third-guessing, etc. Perhaps a little randomness might help? Find out more in A question of tactics.

Sarah Storey (photo from Paralympics GB)

Today we say a fond farewell to the velodrome after the final track cycling events on the weekend. From Sarah Storey's first gold for Great Britain on Thursday to the cat-and-mouse gold medal game between compatriots Anthony Kappes and Neil Fachie of the Individual B Sprint yesterday, it has been a fabulous show. To celebrate we calculate just how Storey and her fellow cyclists are able to reach such astonishing speeds in Gearing up for gold.

Storey also features in three maths challenges from the BBC Two Learning Zone (developed with input from us, the Millennium Mathematics Project): the Key Stage 1 - Timing and Ranking Challege, the Key Stage 2 - Timing Challenge and the Key Stage 3 - Measuring Challenge.

And though the Paralympic and Olympic races are over for now, we can look forward to many more split second finishes in this outstanding venue in the coming years. Read more about the maths behind the Velodrome's iconic curves Leaning into 2012 and How the Velodrome found its form.