Mathematical concepts are applied in all spheres of life (Davis, 6). For instance, mathematics has been applied in sports for decades. One of the most popular sports in the world is soccer. Soccer is played by two teams of eleven players each. The teams compete to score the maximum number of goals in 90 minutes. In order to maximize the chances of scoring, players follow a number of rules and regulations that are mostly founded on mathematical reasoning. The mathematical rules relate to field dimensions, size and shape of the soccer ball, duration of match time and angles of ball shooting among other things. There are also rules governing the number of players that should be in the field, their ages and other qualifications. All those aspects can be quantified mathematically. This paper seeks to discuss how mathematics has been applied to the field of soccer.
A careful examination of the soccer rules reveals that mathematical concepts are involved in every aspect of the game. For example, the soccer ball is an intersection of two platonic solids: the dodecahedron and the icosahedrons. A dodecahedron has twelve five-sided faces while icosahedrons have twenty six-sided faces. When the two solids are combined, they form a solid spherical object which is the ball. The ball itself is circular with a specific radius measurement. It also has a specific density and weight that are based on the gravity. The speed that the ball can travel is also considered when designing the ball. Soccer also heavily relies on the mathematical concept of probability. Players and goalkeepers need to estimate the probability of opponent teams scoring a goal based on the positioning of the ball kicker, the defender and the goalkeeper. A slight misjudgment can lead to an easy goal for the opponents and defeat for the defending team. This is the reason why soccer players are assigned specific areas of defense within the football pitch (Product Category). Soccer coaches often employ various strategies that are based on game theory to predict the opponent behavior so as to adopt a strategic choice that will ensure that they score the most goals and prevent the opponent from scoring. The opponent strategies are evaluated based on historical data to assess if there any unique patterns in the datasets.
Similarly, there is a great degree of relying on numerals when playing soccer. Players are required to comprehend the role played by geometry, graphs, algebra, area, and chance data in the field when playing. For example, a goalkeeper relies on the properties of angles to know where to stand to maximize chances of successfully defending goals. The goal keeper also has to understand speed. He should estimate the speed at which the ball is travelling as well as the time it will take to reach where he is based on the speed and distance. That way the goalkeeper can dive just in time to defend a goal. The goal keeper also has to understand the degree of deflection. Players often deflect the ball when shooting to confuse the goalkeeper. Similarly, the goalkeeper relies on probability and complex data analysis to save penalties. Perhaps, the greatest area of mathematics involved in soccer is estimation. Estimation is applied in determining the best angle of shot, how much force a player should use to deny the opponent a ball and the speed of the ball that is necessary to score (Product Category).
The design of soccer fields incorporates different mathematical concepts. All soccer fields are rectangular with conspicuously marked lines to show boundaries of game play. The theme of the rectangles is duplicated near the goal posts to indicate the goal area. In designing the soccer field, the mathematical concepts of symmetry and congruence play an important role. Each half of the field must be congruent to the other. Symmetry makes soccer a fair game and gives both teams equal chances of scoring and winning. As Stewart (71) puts it, all mathematicians know how to formalize symmetries and this applies to soccer players. Teams also change goal posts to ensure that there is equality. In case there is an undue advantage of side. There are equal probabilities that each team will be on the side that has undue advantage.
In regulation of soccer games, the ball must be spherical and made of leather or some other soft materials. The circumference of the ball; should be between 27 and 28 inches. Its weight lies between 14 and 16 ounces when deflated. In addition, a soccer field involves other mathematical concepts of shape and area such as corner arc, goal area, penalty area, center circle, half way line and penalty mark. All these shapes and measurements make soccer a leading consumer of mathematics. It appears that without these rigid mathematical rules, soccer would be a dull game and would probably not be the popular game it is in the world today. Not many people would love a game where there no uniform rules and where the chances of winning are hard to predict. Moreover, the global soccer industry would not be as big as it is if these mathematical rules were not involved in soccer.
According to Biggs, knowledge of measurements and angles can benefit soccer players in both the attacking and defending positions. Knowing how to determine the correct attack and defense angles helps players in improving the likelihood of evading opponents and passing the ball successfully. Usually, attackers would use a series of wide passing angles instead of direct routes. This reduces the chances of opponents intercepting the ball before it is passed forward. In other cases, it is essential for the goalkeeper to have adequate knowledge about angles. Sometimes, it is good for the goalkeeper to move back a little bit or closer to the field. Depending on the position of the ball and that of the opposing striker, the goalkeeper may need to move towards the right, centre or left of the goal area so as to effectively defend the territory. At the same time, the goalkeeper must keep an eye on the ball strikers from both teams in order to make optimal decisions when passing the ball forward.
The mathematics of statistics and decision-making are also applied in soccer games. According to Biggs, soccer players should be able to visualize and analyze situations in real time and take appropriate action. To achieve this, they must understand patterns of steps necessary to move from one point to another to either maximize chances of scoring or minimize the chances of the enemy scoring. Players must make quick decisions regarding whether to pass the ball, dodge it or just give way to the opponent. The more experienced players are at analyzing situations, the more they will be able to achieve victory in the field. Statistics is also used to predict probability of a team winning or losing to the opponent. It involves analyzing past data about a team’s performance to guess the most likely level of performance in current or future games. The art of predicting soccer scores is a commonly used in betting.
Works Cited
Biggs Stuart. Why Are Soccer Balls Made of Hexagons? Accessed on 14 March 2016 http://www.livestrong.com/article/402611-why-are-soccer-balls-made-of-hexagons/
Davis Philip. The Prospects for Mathematics in a Multimedia Civilization. International Congress of Mathematicians, Berlin, 1998.
Ian Stewart. Letters to a Young Mathematician. New York. Basic Books, 2006.
Product Category. Essential Instructions on Soccer Field Dimensions. Accessed on 14 March 2016. http://www.tracknfieldgear.com/essential-instructions-on-soccer-field-dimensions.html
