MATHINFINITY

FOOTBALL

Football is one of the most popular team sports and competition. The objective of the game is to score by kicking the ball into the opposing team's goal, thus scoring a goal. At the end of the match, the team with more goals wins. In China, there have long existed games similar to football. Zhan Guo Ce, over 2000 years ago, has record of "Cuju", a kind of military recreational activity. "Cu" means kick, and "Ju" means ball. In addition, ancient Greeks and Romans also played a ball game known as Harpastum.

Mathematics about the Football Pitch

The standards of football pitches are set by FIFA. The longer sides are called Touchlines, while the shorter sides are called Goal Lines. In general, the touchline of a football pitch is between 90m and 120m (100~130 yards) and the goal line between 45m and 90m (50~100 yards). For international matches, the touchline has to be between 100m and 110m (110~120 yards) and the goal line between 64m and 75m (70~80 yards).

The rectangular football pitch is divided into two halves by the half-way line in the middle. The middle point of the half-way line is the centre of the football pitch, called the centre mark. The centre circle is marked at 9.15m (10 yards) from the centre mark. The centre mark is where the ball is placed during kickoff. A flagpost of at least 1.5m (5 feet) tall is inserted at each of the four right-angled corners of the pitch. An arc is marked at a radius of 1m from each of the four corners to indicate the location to place the ball during a corner kick.

Football Surface Structure and Geometric Figures

FIFA specifies that football has to be made of leather or other suitable materials. The circumference of an inflated football should be between 68 and 70cm (27~28 inches). The weight should be between 410 and 450g (14~16 ounces).

The most well known football is the Telstar which was used by FIFA in official matches in 1970 and 1974. Its leather surface consists of twelve black pentagonal and twenty white hexagonal panels. This kind of structure with 32 panels created the roundest sphere of its time.

The official football - Teamgeist, used in the 2006 FIFA World Cup is a revolutionary 14-panel ball construction. The ball is much rounder and has a smoother surface, making it react more reliably and consistently when kicked. The Jabulani used in the 2010 FIFA World Cup is made from eight spherically molded panels. The surface of the ball is textured with grooves to improve the ball's aerodynamics. The Brazuca used in the 2014 FIFA World Cup is made from six symmetrical panels to enhance grip, stability and aerodynamics on the pitch.

Interactive Game

1) Let's count how many pentagons and hexagons are used on the surface of the disassembled football.

2) Try reassembling the football back to its original look!

Did you know?

3) Before 1863, footballs in the United Kingdom were made of inflated pig's bladders.

4) The International Federation of Association Football (FIFA) was established on May 21, 1904. FIFA is responsible for the organization of football's major international tournaments.

5) The commentators of football matches on the television still use the imperial units for the distance of free kicks.