Math and Graph Models Behind the Olympic Paul Vault Jump

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†¦show more content†¦The war, however, stopped the improvement of the heights record. Therefore, we could deduce that the depression between 1936 and 1948 was due to lack of training due to the war. When the games resumed in 1948, the athletes started to progress their record once again. As you can see above, we could refine our model, disregarding the 1932 and 1936 record. Graph 5: Graph of winning heights (m) against years since 1948 This refined model is better representation of data than graph 1 and 2 even if the line does not pass through every point. Passing through point increased from 2 to 3 (4, 52 and 56) and majority of points are very close to the line. It is true that some points, such as point 16 and 20 quite far from the line, but these points can be disregarded in this model, as the line is touching the following point 24. This gives the new linear equation y=0.0264x+4.4338 However, even though refined graph has better equation than those of past one, there are some limitations with using linear equation to determine the graph. Since a linear graph increases infinitely, and as humans have restraints to achieve to record, their winning height can’t keep increasing at this rate. It is not sustainable. Natural Logarithm Model After considering the limitation of linear function and graph, I have discovered applying any model of equation that has an infinite increase range, such as quadratic or exponential, is unrealistic, since theShow MoreRelatedDeveloping Management Skills404131 Words   |  1617 Pages174 Problem Solving, Creativity, and Innovation 174 Steps in Analytical Problem Solving 174 Defining the Problem 174 Generating Alternatives 176 Evaluating Alternatives 176 Implementing the Solution 177 Limitations of the Analytical Problem-Solving Model 178 Impediments to Creative Problem Solving 178 Multiple Approaches to Creativity 179 Conceptual Blocks 183 Percy Spencer’s Magnetron 185 Spence Silver’s Glue 185 The Four Types of Conceptual Blocks 185 Review of Conceptual Blocks 194 Conceptual Blockbusting

The Downfall of Macbeths Character in William...

The Downfall of Macbeths Character in William Shakespeares Play At the start of Macbeth Macbeth is described with words such as noble, worthy and brave this shows him in a positive way. However at the end of the play he is described with words such as Hell-hound, coward and bloodier villain which shows him to be a completly different person.He is now shown in a negative light. Macbeths characteristics are turned around and the witches show this in the opening scene. Fair is foul, and foul is fair. At the end of the play Macbeth is no longer the hero. O valiant cousin, worthy gentleman. Macbeth was not happy with being known as the Kings loyal cousin and wants†¦show more content†¦I am afraid to think of what I have done. Macbeth killing King Duncan is when his personality takes a turn for the worst. This starts his downfall from good to evil and its because of his own dream to be King. Shakespeare uses a lot of soliloquies to show the reader changes in Macbeth. He believe that the only problem that stands in his way of being king is the prince of cumberland. Macbeth cannot become King until he is taken care of. It lets Shakespeare reveal Macbeths inner most thoughts and what he truley feels It lets the audience see the change in the way Macbeth is feeling and what he is planning to do. Ambition is the most important factor that controls the downfall and sudden change of Macbeths character. Macbeths fears and uncertaintys are influencing the way he acts. Shakespeare also uses a variety of unpleasant words such as Murder, Blood and Blade. This tells the audience that Macbeth is considering an evil act. Macbeths fear of other characters influences Macbeths ultimate descent into evil, when it comes to Macduff. Beware Macduff. At this point in the play Macbeth doesnt want anything to affect his title as king. Events which follow are big factors that control macbethss downfall. To the audience it is clear that Lady Macbeth is a huge character that changes Macbeths character from good to bad. When she hears aboutShow MoreRelatedTaylor Travis . Mr. Ortiz. English 12. 27 February 2017.1321 Words   |  6 Pagesgreatly respected warrior and his wife and their eventual downfall after pursuing a higher position of power. Shakespeare’s play, Macbeth, and Akira Kurosawa’s movie, Throne of Blood, share many similar aspects, ranging from plot to characters to setting. However, the two titles differ in the way that certain characters are portrayed. The actions of various characters in Throne of Blood do not always coincide with those of the characters in the original Macbeth. While differences in plot and settingRead MoreDiscrepancies and Similarities between Shakespeares The Tragedy of Macbeth and History816 Words   |  4 Pagessuccession. William Shakespeare, a playwright of the Renaissance, sculpts events from this era into a dramatic sequence of events. 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Nonetheless, as the play unfolds, it clearly depicts how power can corrupt even the most honorableRead MoreMacbeths Downfall Essay677 Words   |  3 PagesIn William Shakespeares Macbeth, the main character, Macbeth, is a brave and loyal subject to the King of Scotland, but as the play progresses, his character begins to change drastically. Evil and unnatural powers, as well as his own passion to become king, take over his better half and eventually lead to his downfall. The three main factors that intertwine with one another that contribute to Macbeths tragic end are the prophecies told by the three witches, Lady Macbeths influence, and finallyRead More Aristotles Tragic Hero in Shakespeares Macbeth Essay examples1044 Words   |  5 PagesAristotles Tragic Hero in Macbeth      Ã‚  Ã‚   Aristotle and Shakespeare lived ages apart, but Aristotle had a great affect on Shakespeares plays. In Shakespeare’s tragic play, Macbeth, the character of Macbeth is consistent with Aristotles definition of the tragic hero.    Aristotles tragic hero is a man who is characterized by good and evil. He is a mixture of good characteristics and bad characteristics. For example, Macbeth was an honorable Thane of Glamis. He was a valiant fighter

Analyse the dramatic techniques Essay Example For Students

Analyse the dramatic techniques Essay Hobsons choice was written in 1914-15 by Harold Brighouse, as a method to raise the morale of troops during the First World War. Many aspects of Brighouses unconventional childhood shows through in a lot of characters Maggie in particular as he explores many issues that would have occurred in the heart of nineteenth century Salford. He examines many real life crisis in this comedy play and he spectacularly shows how bigger deal image and reputation was to people at the time when the play was set. Henry Horatio Hobson was an immensely patriotic, middle class working man, who lived in Salford, Manchester, during the early 1800s. He had an extremely definite idea on he believed the perfect family should entail, and he worked very hard to make sure that his three daughters Maggie, 30; Alice, 23; Vickey, 21 were raised into a respectable family. He very much wanted the people of Salford ( his daughters included ) to believe that he was a hard working business man, who ran his home with a firm hand, but his efforts and money were in vain, as he spent most hours of the day at the Moonrakers Inn Pub, getting unbelievably drunk and falling into neighbours cellars. Hobson became increasingly worried after he fell down Mr Beenstocks cellar around noon one day. He was extremely drunk and was really concerned that his actions would affect the business trade. My good class customers are not going to buy their boots from a man who has stood up in open court says Hobson, after receiving a fake court order for trespassing. During the 1800s, a court order would have been considered very serious and Hobson would have lost a lot of customers if the trespassing fine was real. Nowadays, people are a lot less bothered about the person running the shop and their personal life. Whereas in the 1800s, Hobsons reputation would have been in tatters, these days, it eould take a lot more than a court order, for a shop to lose customers. Hobson was also worried about losing customers, when he saw his two youngest daughters wearing humps. Hobson described his daughters as immodest, un-English and said that they looked like French madams. Humps were actually considered acceptable if you were in a higher class, but if you were middle class, like Hobson and his daughters, then it was totally unheard of to be seen wearing them. Hobson was very concerned that his daughters wearing unacceptable clothes, would give people the wrong image, and would scare away customers. Fellow businessmen have very little respect for Hobson, who very rarely did even half a days honest work, and yet he was their biggest business threat, stealing all the high class customers, with exceptionally made boots. Mrs Hepworth is particular, was a well-respected high class woman, who many shops fought to have her step through their doors. For Hobson however, she was a regular customer, who he treated like a Queen. Mrs Hepworth, was not served in the shop like other middle class customers. She was shown through to Hobsons own living room, where stage directions prove how differently higher-class citizens were treated. Stage directions quote: Hobson kneeling and fondling her foot. This stagecraft shows us that he gives a lot more care to his higher-class customers. This was deemed socially acceptable during the 1800s, as Mrs Hepworth was very much above Hobson on the social ladder. It was also considered okay for her to tell Hobson to Get up. You look ridiculous on the floor because even though man were technically considered above women concerning rights and social status, a woman of a higher-class, such as Mrs Hepworth, was definitely regarded as above man of a lower class, such as Hobson. That is why Maggies marriage to Will, was totally socially unacceptable at the time. Their marriage was extremely unconventional, because not only did the woman propose to the man, but she did so to a man in a lower social class than she was. Not only was this just not done, Maggie was also 30 years old, which, in the 1800s would have been considered too old for marriage. .u1492adfe437bc31681197ef44228941c , .u1492adfe437bc31681197ef44228941c .postImageUrl , .u1492adfe437bc31681197ef44228941c .centered-text-area { min-height: 80px; position: relative; } .u1492adfe437bc31681197ef44228941c , .u1492adfe437bc31681197ef44228941c:hover , .u1492adfe437bc31681197ef44228941c:visited , .u1492adfe437bc31681197ef44228941c:active { border:0!important; } .u1492adfe437bc31681197ef44228941c .clearfix:after { content: ""; display: table; clear: both; } .u1492adfe437bc31681197ef44228941c { display: block; transition: background-color 250ms; webkit-transition: background-color 250ms; width: 100%; opacity: 1; transition: opacity 250ms; webkit-transition: opacity 250ms; background-color: #95A5A6; } .u1492adfe437bc31681197ef44228941c:active , .u1492adfe437bc31681197ef44228941c:hover { opacity: 1; transition: opacity 250ms; webkit-transition: opacity 250ms; background-color: #2C3E50; } .u1492adfe437bc31681197ef44228941c .centered-text-area { width: 100%; position: relative ; } .u1492adfe437bc31681197ef44228941c .ctaText { border-bottom: 0 solid #fff; color: #2980B9; font-size: 16px; font-weight: bold; margin: 0; padding: 0; text-decoration: underline; } .u1492adfe437bc31681197ef44228941c .postTitle { color: #FFFFFF; font-size: 16px; font-weight: 600; margin: 0; padding: 0; width: 100%; } .u1492adfe437bc31681197ef44228941c .ctaButton { background-color: #7F8C8D!important; color: #2980B9; border: none; border-radius: 3px; box-shadow: none; font-size: 14px; font-weight: bold; line-height: 26px; moz-border-radius: 3px; text-align: center; text-decoration: none; text-shadow: none; width: 80px; min-height: 80px; background: url(https://artscolumbia.org/wp-content/plugins/intelly-related-posts/assets/images/simple-arrow.png)no-repeat; position: absolute; right: 0; top: 0; } .u1492adfe437bc31681197ef44228941c:hover .ctaButton { background-color: #34495E!important; } .u1492adfe437bc31681197ef44228941c .centered-text { display: table; height: 80px; padding-left : 18px; top: 0; } .u1492adfe437bc31681197ef44228941c .u1492adfe437bc31681197ef44228941c-content { display: table-cell; margin: 0; padding: 0; padding-right: 108px; position: relative; vertical-align: middle; width: 100%; } .u1492adfe437bc31681197ef44228941c:after { content: ""; display: block; clear: both; } READ: Baz Luhrmann - Romeo and Juliet AnalysisWill Mossop did not protest to the marriage, which just proved that women of a higher-class were always more worthy and correct, than a man of a lower class, even if you were going to marry them. Will felt intimidated by Maggies social superiority, as he was in a lower working class than she was. Hobson was a very proper and nationalistic 55-year old. He worshipped the Queen and her husband, and had pictures of them in his living room. Hobson described himself, as Im a decent-minded man. Im Hobson. Im British middle-class and proud of it. This is slightly ironic, as he spends most days at the pub and doesnt really earn a decent, honest living. Although he is telling his daughters how to behave, he is not exactly the best example and even though he is telling his children that he is a good man, it is like he is also trying to reassure himself of the fact. Throughout the play, Hobsons character becomes weaker and weaker, and he begins to care less about his image. Maggie however has broken all conventions of the time by marrying Will, who, in return, has been taught by Maggie and has increased self-esteem and courage. At the end of the play, image became very important to Will, when choosing shop names. He wanted to make sure that he was in charge and in control of the decision. Mossop and Hobson or its Oldfield Road for us Maggie he says. This shows us that men were very much above their wives, and they made all the decisions in the household. Overall I believe that image and reputation were considered a lot more important in the 1800s than what they are today. Things were very particular in those days, and I for one, are very glad that image has become less of an issue in every day life.

Comparison of Classical China and India free essay sample

The economic and political similarities between classical China and India are that they are both agricultural societies and both empires divided their land into smaller city-states, while the differences are that India focused more on trade than China, and the Chinese government followed Confucius instead of India’s Buddha. Both societies had a strong agricultural base to them. The agricultural way of life is, after all, what led them to become the great empires that they were during that time. This economic similarity meant that the people stayed basically in the same place and farmed the land and domesticated animals. Not to say that there were no nomadic herders in the empires, but they stayed on more of the outskirts and were greatly outnumbered. Both empires also had many city-states within it. Back in the day, there was no technology so news traveled pretty slow, so it was much easier to just have aristocrats under the king’s(or emperor’s) rule make all of the small decisions and be in charge of their allotted land. In China though, this kind of backfired by the aristocrats having too much power. They overturned the king and there was a period of chaos before the Qin Empire was established with harder rule over the new beurocrats. There were also some differences between the empires. For one, India’s economy was more greatly influenced by trade than China. This was partly just because of the geography. China was basically separated from the other side of the Himalayas so the only way that they could get to places like the Mediterranean and Middle East was through India or actually across the Himalayas. Also, China was basically producing everything they needed so the only reason they traded was for revenue. India on the other hand, had access to the Indian Ocean and flat land that connected them to the Mediterranean and Middle East. The Chinese government had Confucius, the powerful founder of the way of thinking that led the people of China to seek Dao (or the way). India, on the other hand, had the religions of Hinduism and Buddhism that taught their people to seek their dharma. The Confucius way of thinking was originally developed as a political system to govern the state but gradually moved to teach not to care about money, possessions and more on your place in reincarnation. The Hindus believed in caste systems and to stay in your place within the system. The Buddhist religion sort of supplemented it by saying that it was good to know your place, and while striving to achieve a better life, remember your place and how to do your part within your place.