SOCCER HISTORY
Soccer is one of the most popular sports in Europe, Americas and also other parts of the world. It has a vivid and interesting history in the world of sports. Early evidence of soccer being played as a sport finds occurrence in China during the 2nd and 3rd centuries BC. In China, it was during the Han dynasty that people dribbled leather balls by kicking it into a small net. Recorded facts also support the fact that Romans and Greeks used to play ball for fun and frolic. Some facts point to Kyoto in Japan where kicking of ball was a popular sport. It is said that early growth of the modern soccer started in England. Some amusing facts even mention that the first ball used was the head of some Danish brigand. It is said that during medieval times, the old form of soccer used to allow many ill practices like kicking, punching, biting and gouging. The main aim was to carry the ball to a target spot. People grew so fond of the game that they would throng the field all day long. Sometimes the competition grew fierce and masses got so wild that there were frequent incidents of violence during the game. It is also said that soldiers admired the game so much that they missed archery practice to watch it.King Edward III banned soccer in 1365 owing to the growing incidents of violence and military indulgence in the sport. In 1424 King James I of Scotland also proclaimed in the Parliament— "Na man play at the Fute-ball" (No man shall play football) When and where exactly did soccer start is a question that has no precise answer to it. You can easily say that this popular game has been played for more than three thousand years. The nativity of modern-day soccer must be credited to Britain. It was also known as the association football, with Scotland and England being the co-founders of the systematic game of soccer.
Mathematics on the Soccer Field Katie Purdy
Soccer is one of the most popular sports in the world today. There are two teams each consisting of 11 player that aim to score the most goals in 90 minutes while following a certain set of rules. Players can use their entire bodies, except their hands, to move the ball around the playing field. Each team has a goalie who is allowed to use their hands to stop the ball when an opposing team tries to shoot it into the net. Millions of people play soccer every day, but how many of them take the time to calculate the precise angle to shoot before heading to the field? This was investigation of the mathematics of soccer by using Geometry Expressions, a constraint-based geometry system, and Maple, a computer algebra system (CAS), to model situations that take place during an average soccer game. Questions that were explored were: What is the necessary width of the wall of defenders that will block the entire goal within the angle of a straight shot? What is the angle of both a straight and curved kick as a function of the location on the field and what is the “best” location for each of these kicks to score a goal? What is the “best” location for a sideline kick with a straight shot? What is the “best” location for a corner kick? So far, there has been minimal mathematical research on soccer kicks, although there have been numerous studies on the physics of soccer and how the ball curves. Finally, I considered what the optimal location to shoot a goal from the sideline is. A model was created in Geometry Expressions to represent a straight kick from the left sideline of the field. To find the ideal place on that line I constructed a circle that intersected with the two goal posts and was tangent to the sidelines. The point of intersect of the sideline and the circle gave the location where the angle to score a goal would be the greatest. I was then able to use measure the distance from horizontal and the point to find the exact place a player would have of scoring. This was at 37.286056 yards up the left sideline at 41.938401 degrees from vertical to 48.061599 degrees from vertical. Throughout this investigation the biggest problems that I faced were having situations make sense mathematically but not realistically and trying to calculating a radius for the curve on the ball. I had to use arcs of circles to represent a curved path of the soccer ball, when in actuality a player usually does not kick the ball in a perfect arc. I then had to work with situations like the corner kick, where the best possible position to shoot the ball would simply not work. Next, when trying to find a realistic radius for the curves it would have been very helpful to have better video equipment and multiple views for one shot so I would be able to track the ball better. For all of these problems a field with the dimensions of 120 yards by 75 yards, a goal box of 6 yards by 20 yards, and a penalty box is 18 yards by 40 yards, and a goal of 8 yards was used. Therefore, all of the values discussed in this paper apply to that size field although the dimensions and values could easily be changed for any field size within the programs. The values of the radius for the arcs could be changed as well for players that are able to bend the ball more, or less. Many people go throughout their lives without considering the math behind everyday activities. I looked 4 main situations in soccer, and by modeling and calculating them in Geometry Expressions and Maple, I was able to discover what the necessary width of a wall of defenders that it takes to block the entire path within an angle of a straight shot was, what the angle of both a straight and curved kick as a function of the location on the field was and from that, where the “best” locations for each of these kicks would be to score a goal, what the “best” location and radius was for a corner kick, and finally, what the “best” location was for a sideline kick with a straight shot.
