The beautiful game has been saved for last at London 2012, with the men's gold medal match taking place on Saturday, the penultimate day of the Games. There are some important questions to ponder while we sit tight in anticipation for the final match. What's the best strategy for taking a penalty kick? When is it worth committing a professional foul? And when is a goal not a goal? Find out about all this and more with our collection of football articles.

When is a goal not a goal? — Remember Frank Lampard's disallowed goal in the 2010 World Cup match against Germany? The ball hit the crossbar, landed well behind the line but then bounced out again. And it all happened too quickly for the ref to spot it was a goal. But do how these kind of (non)-goals happen and what can we do about it?

A fly walks round a football — What makes a perfect football? Find out why the ball's surface is the most prized research goal in ball design.

Eye on the ball — Why the 2006 World Cup ball caused controversy.

Blast it like Beckham? — What tactics should a soccer player use when taking a penalty kick? And what can the goalkeeper do to foil his plans? This article uses game theory to find the answers.

Formulaic football — When's the best time to make a substitution in a football match?

Understanding uncertainty: How psychic was Paul — How likely is it that Paul the octopus' accurate predictions for the 2010 World Cup were really due to psychic powers?

Mathematicians rival octopus in World Cup final prediction — Is maths better than Paul the psychic octopus?

The luck of the draw — How a mathematical improbability turned one day's football action into a once-in-a-lifetime quirk of fate.

On the ball — If your team scores first in a football match, how likely is it to win? And when is it worth committing a professional foul? This article shows us how to use probability to answer these and other questions, and explains the implications for the rules of the game.

Understanding uncertainty: Football crazy — Taking up a challenge from a BBC radio programme David Spiegelhalter and Yin-Lam Ng used their statistical finesse to predict the outcome of the last matches of the English Premier League — and they were 90% correct. Find out how they did it.

Power trip — How long do football managers' careers last and does talent matter? Surprisingly the answer may lie in mathematical power laws.

Understanding uncertainty: the Premiere League — Does a club's ranking in the Premiere League table reflect how good it really is? This article discusses the concepts of mean, variance, standard deviation and confidence intervals.

It's a great day for individual dressage today with the Grand Prix freestyle test taking place in Greenwich Park. It's amazing how those horses can perform elegant and complicated movements without getting their legs in a muddle. Coming to think of it, it's amazing that they can even go through their innate gaits without getting their legs in a muddle, given that there's four of them and they are very long. And what about animals who've got even more legs? It turns out that it's all down to symmetry in the brain. To find out more, read Ian Stewart's Plus article Walk, trot, gallop.

One area in which humans definitely have the edge over horses is ball games. Volleyball is a particularly exciting one and we're looking forward to the semi-finals today and tomorrow and the final on the weekend. As in tennis, spin's the thing in this game. But why does putting a spin on a ball make such a difference to its path through the air? John D. Barrow, mathematician, cosmologist and prolific popular science writer, explains:

One of the key skills for volleyball players to master is to serve the ball with a top spin so that it will drop down more quickly than the receiver of the serve might expect. This is possible because a spinning ball will follow a curved trajectory when a non-spinning ball will not. The reason for the swerve can be understood by looking at the air flowing past the ball. When the air flow impinges on the ball the flow lines are pushed together, so the pressure drops and the speed of the air passing the surface of the ball increases.

If the ball is spinning then the flow lines of the air near the surface of the ball are significantly altered. In the picture on the left you can see what happens if the ball has been given a clock-wise spin in addition to its straight line motion at speed V from left to right. The non spinning motion is just as if the ball were stationary with air going past its surface at speed V. What is the effect of the spin? At the top of the surface of the spinning ball the air speed very close to the surface of the ball is in the opposite direction to the on-coming air whereas at the bottom it is in the same direction. This means that the net speed of the air near the top of the ball is less than that round the bottom. So the pressure on the ball is greater at the top than the bottom and there is a net downward force, F. The orientation of the picture shows how a ball served to the right with top-spin will always swerve downwards. This will reduce the time that it spends in the air and give the receiver less time to respond and return the ball.

You can read more about the effect of spin on the trajectory of a ball in our article Spinning the perfect serve.

Today the men's table tennis teams will be battling for gold. Table tennis first became an Olympic sport in 1988, but changed its scoring system in 2001 to make matches more exciting for spectators. But how do the old and new scoring systems compare in terms of favouring skill versus luck? Find out in our article Ping-Pong is coming home.

And while we're on scoring systems, there's a video of a lecture given by John D. Barrow on our sister site Maths and sport: Countdown to the Games, which looks at them in detail.

It's the very last medal day for track cycling! If you've been watching, you'll have noticed just how steeply the elegant wooden cycling track is banked in the turns. Echoing this shape is the sweeping curved roof of the Velodrome (which hit the headlines in its own right during the torrential rain this weekend) topping the beautiful cedar clad exterior. To find out why and how the track and its buildings came to have the shapes they do, read the Plus articles Leaning into 2012 and How the velodrome found its form.