Introduction A French mathematician called Edouard Lucas invented the Tower of Hanoi also known as “The End of The World Puzzle”, in 1883. It is thought that Lucas designed it based on the legend of a Hindu Temple. The priests in the temple were apparently given a tower of 64 gold discs, each smaller in size than the disc beneath. The priests were to move the discs from one of the three poles to another, one by one, without placing a bigger disc on a smaller one, as the weight of the bigger one would crush the smaller one. It’s said that when the priests were able to successfully transfer all the discs from one pole to another, the world will crumble and disappear. If this were true, would there then be a way of predicting the end of the world? …show more content…
The game reveals many mathematical concepts even though it is rather simple. My aim for this mathematical exploration is to put the Tower of Hanoi to the test and find out (according to the legend) how long we have until the end of the world. Finding a Pattern Before finding a pattern it would be wise to familiarise oneself with the task at hand. The task is to find out how many moves it would take to move all 64 discs from one pole to another without placing a bigger disc on a smaller one. Then the task is to work out how many years it would take to move the discs non-stop, each move taking no longer than a second. I will do this by looking for patterns in the Tower of Hanoi. However, first I will look at it using a smaller amount of discs, due to solving the puzzle using less discs would be simpler to analyse and …show more content…
It is possible to use the recursive pattern and equation an= 2an-1+1 to find the answer but in order to do this, one needs to know what “a” is. This reveals a weakness in recursive patterns because in order to know what “a” is for 64 discs, one must know “a” for 63 discs, “a” for 62 discs, and so on. This process would be very time consuming and therefore not an efficient way of solving the problem. Graphing the data to compare the # of discs with the Total Moves would also be impossible. This is because “a” is unknown unless the previous terms are known. Therefore it would be impossible to graph a recursive equation simply because their
On the second day of class, the Professor Judit Kerekes developed a short chart of the Xmania system and briefly explained how students would experience a number problem. Professor Kerekes invented letters to name the quantities such as “A” for one box, “B” for two boxes. “C” is for three boxes, “D” is for four boxes and “E” is for five boxes. This chart confused me because I wasn’t too familiar with this system. One thing that generated a lot of excitement for me was when she used huge foam blocks shaped as dice. A student threw two blocks across the room and identified the symbol “0”, “A”, “B”, “C”, “D”, and “E.” To everyone’s amazement, we had fun practicing the Xmania system and learned as each table took turns trying to work out problems.
We need to solve this to express T(n) in terms of n. The solution to the recurrence relation proceeds as follows. Given the relation
The Peace treaty signed by the United States and Hanoi did not mean an end to conflict in Vietnam. The Republic of Vietnam, as Nixon saw it, was still the sole legitimate government in South Vietnam. The president of South Vietnam, Nguyen Van Thieu, even reiterated his four no’s policy soon after the Paris peace agreement. This policy called for “No recognition of the enemy, no coalition government under any disguise, no procommunist of the southern region of Vietnam, and no concession of territory to the communists.” Thus the war did not end in 1973. The war from 1973 was their war, not America’s. It was a war fought between Vietnamese and not Americans, although America still had a hand in this war.
It is understandable that some Americans strongly opposed the United States getting involved in the Vietnam War. It had not been a long time since the end of World War II and simply put, most Americans were tired of fighting. Mark Atwood Lawrence is one of the people who opposed our involvement in the Vietnam War. In his essay, “Vietnam: A Mistake of Western Alliance”, Lawrence argues that the Vietnam War was unnecessary and that it went against our democratic policies, but that there were a lot of things that influenced our involvement.
The Vietnam war started in December of 1956, and lasted until April of 1975. The war was between the U.S., and Vietnam. This war was a very gruesome, and tragic war. In Vietnam their leader Ho Chi Minh came back after a 30 year trip to explore around the world. When he returned his country was occupied by two major countries, Japan and France. Ho Chi Minh had a plan to run them out of his country, but he needed the U.S. for it to work. U.S. was still in the Cold war with Russia and there was fear of communism there. So the U.S. decided not to help Vietnam and send military aid to help the French and Japanese forces, in order to stop communism. Thus begun The vietnam war!
It could be argued that the greatest architectural structure ever created by Canadians is the CN Tower. Construction on the CN Tower first started on February 6, 1973 and finished on June 26, 1976. The CN Tower was considered to be a breakthrough when it was first created because it broke a record set previously. Once the CN Tower was complete it gained the title as the “world’s tallest free-standing structure” at 1815.4 feet. The creation of the CN Tower was a defining moment for Canada and still impacts Canadians today. One reason why the CN Tower was a defining moment is because it solved a communication problem that the city of Toronto was experiencing at that time. Another reason why the CN Tower is important is because it helps our economy by attracting many tourists every year. The most important reason why the CN Tower was a defining moment is because it gives Canadians a sense of inspiration and national pride.
Simon, S. (2005, March 19). Math Guy: The Birthday Problem. In http://www.npr.org. Retrieved March 20, 2014, from http://www.npr.org/templates/story/story.php?storyId=4542341
Pineda, R. G., Tjoeng, T.H., Vavasseur, C., Kidokoro, H., Neil, J.J., & Inder, T. (2013). Patterns
The Vietnam War was a lengthy and fairly costly armed conflict involving the communist North Vietnamese regime known as the Viet Cong, South Vietnam and the United States. The war began in 1954 although the area was in Conflict since the mid-1940s after North Vietnamese leader Ho Chi Minh and his political party; Viet Minh took power during the Cold War. During the escalating standoff between the democratic United States and the communist Soviet Union; and at the end of the Red Scare, the United States attempted to stop the spread of Communism. The Vietnam War was never officially declared a war by Congress, but rather deemed a “conflict.” The “Conflict” began as a “proxy war” under President Eisenhower and Kennedy, but fully escalated under Lyndon B. Johnson and Richard Nixon. Although the American people wanted end the spread of Communism, the Vietnam War received a vast amount of opposition in the States, along with tons of media coverage and journalists reporting on the war. Unfortunately the Vietnam War was perceived as a failure due to many contributing factors such as the numerous unnecessary casualties inflicted on both sides (History.com).
War is a huge event in any country’s history. The United States has been experiencing this since the first major war with the American Revolutionary. The United States has been known to help out our allies when they are fighting, and intervened when countries have been at war to try and end it. The Vietnam War started in December of 1954 and ended on April 30th of 1975. The Vietnam War was a long and costly battle over communism between North and South Vietnam. The Vietnam War was a failed attempt for the United States to bring peace to South and North Vietnam because it affected our country’s history, the way politics can influence a war, an economy downfall, and how affected protest and media can be used.
Pieces of a puzzle slowly fitting together, to reveal a picture. This is an accurate
It is amazing to see how mathematics has such an influence on the world and the evidence it creates. The world is affected by numbers and mathematics all the time and this mysterious number known as the golden number has proven to be the center of everything.
In this essay I will be discussing how Ho Chi Minh sense of nationalism was the driving force in ending French rule in his country. By tracing Ho Chi Minh’s life it becomes rather obvious that his endeavors would result in a strong sense of nationalism for his country that had long been exploited by French rule. Following his travels throughout the world Minh found that the West had no interest in a free a Vietnam, so Minh was forced to turn to the Communist for help. By working with the communist, Minh was ultimately able to free the Vietnamese people from French rule. The paper argues that Ho Chi Minh’s strong sense of nationalism for his home country far outweighed his allegiance to the communist party.
a spiral, like the markers at the Pet Sematary. Later, when Louis is home alone,
The history of math has become an important study, from ancient to modern times it has been fundamental to advances in science, engineering, and philosophy. Mathematics started with counting. In Babylonia mathematics developed from 2000B.C. A place value notation system had evolved over a lengthy time with a number base of 60. Number problems were studied from at least 1700B.C. Systems of linear equations were studied in the context of solving number problems.