Math and Graph Models Behind the Olympic Paul Vault Jump Essay

Math and Graph Models Behind the Olympic Paul Vault Jump Essay

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Introduction
Every 4 years, the Olympic games is a major event around the world. International athletes come together to represent their own country at a sport. A gold medal is given to the winner of each game. This math internal assessment aims to consider the trends of the wining men gold medalist’s pole vault height from 1932 to 2008, and predicting 1940 and 1944 record, when the Olympic games were not held due to the world war.

Data – Height Record 1932-2008

The table below shows the men pole vault gold medalists at various Olympic games between 1932 and 2008.

Table 1: the winning heights of men’s pole vault in Olympic games for years between 1932 and 2008. (Excluding 1940 and 1944)
Year 1932 1936 1948 1952 1956 1960 1964 1968 1972 1976 1980 1984 1988 1992
Height (m) 4.31 4.35 4.30 4.55 4.56 4.70 5.10 5.40 5.50 5.50 5.78 5.75 5.90 5.80

Year 1996 2000 2004 2008
Height (m) 5.92 5.90 5.96 5.95

A graph has been produced to represent this data visually with using excel.

Graph 1: The winning men pole vault heights record in Olympic games for years between 1932 and 2008. (Excluding 1940 and 1944)



The x-axis represents the year of the Olympic Games held, and it is begins at 1932 and ends at 2008. The y-axis represents the pole vault gold medalists in meters.

However, there is some limitation to this graph. Since there were no Olympic games held in 1940 and 1944 as a result of world war, the data isn’t consistent as 2 years of gold medalist heights record are missing. The graph also only shows the heights of the 1932 to 2008 Olympic games, which is a small section of the overall Olympic game data. The pole vault games begin in 1896.

Linear Model

Graph 2: The winning heights of Olympic games against year between 1932 and 20...


... middle of paper ...


...gainst years between 1932 and 2008, showing natural logarithmic relationship


I made assumption about World War 2’s effect on the logarithm graph and again lead to disregarding the points 1932 and 1936 record. It would result in a logarithm that would have exclude war, and this is shown in next graph.

Graph 7: Graph of winning heights against years since 1932 between 1948 and 1980 showing natural log graph.



This modified graph allows the natural logarithm graph to model the record better than not removing two points, 1932 and 1940. The majority of the points is passed by the graph and is closed to the line.

Graph 8: Graph of winning heights (m) against years since 1932



Since it is hard to make calculations with real years, I created a graph of height against years since 1932. When considering the trends line and possible equation of this graph models.


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