It's the very last medal day for track cycling! If you've been watching, you might have noticed the steep banks of the elegant wooden cycling track. And you may have been impressed by the sweeping curved roof and beautiful cedar clad exterior of the Velodrome, the first of the 2012 London Olympic venues to be completed.

Today's a great day for badminton with gold medals being awarded in the men's singles and doubles. This got us thinking about shuttlecocks. They are not like balls at all and this means that they don't behave like balls either. John D. Barrow, mathematician, cosmologist and prolific popular science writer, explains.

A new mathematical analysis of how to hit a winning serve shows that spin is the thing. Perhaps there's still time for Murray's coach to include some maths in his preparations for the match today...

The men's lightweight fours and the women's eights are going to compete for medals today, but are they sitting in the right place? Usually you expect to find rowers positioned in a symmetrical fashion, alternately right-left, right-left as you go from one end of the boat to the other. However, the regularity of the rower's positions hides a significant asymmetry that affects the way the boat will move through the water.

Usain Bolt is determined to become a legend this weekend, by running the 100m in 9.4 seconds. But what does mathematics have to say about this quest? Is there an ultimate limit which no runner can possibly surpass? If there is one, where would such a limit lie? For instance, is there a sub 9 second record in the offing?

Some very exciting medals are going to be won today, including the women's 200m butterfly and the men's 100m freestyle. But we're unlikely to see the rush of record-breaking performances we saw in Beijing in 2008 — that's because in 2008 many swimmers benefited from controversial performance swim suits, which have now been banned. But how did these suits improve performance?

We're getting very excited about the medals that will be awarded in canoeing and kayaking over the next three days. But here's a question: does having lots of paddlers helps or slow the boat down? The kayak with two paddlers has twice as many "engines" to power it, but it also has twice as much weight to drag through the water. Which is the dominant factor?

The first Olympic weekend is over! Of course it's the taking part, not the winning, that counts, but let's face it: it's the medals, especially the gold ones, we all get most excited about. So while we were sitting glued to the telly watching the joys of weightlifting, archery and judo we started pondering some serious questions....