Leonardo Fibonacci Essay -- Mathematics Papers

Leonardo Fibonacci Leonardo Fibonacci was one of the great mathematicians of his time. His lifestyle allowed him to travel and study math in various countries, and he ended up combining his cultural knowledge to discover the most effective ways of doing mathematics. He is most famous for his contributions to the European number system and for his sequence of numbers known as the Fibonacci numbers. Starting with 0 and 1 as the first two numbers, each number in the sequence is the sum of the two preceding numbers. He came across these numbers as a solution to a problem that he used as an example in one of his many publications. He was not aware of the importance of his findings at the time. Many uses have been found for these numbers since Leonardo’s death and many mathematicians have used this sequence in their own theories. Leonardo Fibonacci was born in Pisa, Italy in the middle 1170’s. When he was almost twenty, he moved to Bugia, Algeria with his father, Guielmo Bonacci. Bonacci was the secretary of the Republic of Pisa responsible for directing the Pisan trading colony in Bugia. When he brought his son to Algeria, he had Leonardo educated to become a merchant. During his studies in northern Africa, Fibonacci discovered the Hindu-Arabic number system, which he had not been exposed to in Europe. When his father arranged for him to work for the Pisan republic, Leonardo took advantage of his business trips to countries such as Greece, Sicily, Egypt and Provence. He studied the methods of mathematics that were practiced in these various nations. He discovered that the Hindu-Arabic numerals were much more effective and easier to manipulate than the Roman numeral system used in Italy. [i] .. ...997. Newman, James R., The World of Mathematics. Vol. 1, New York: Simon and Schuster, c1956. Peer Reviewed by Melissa Lenzi and Mike Hartman. [i] http://www.lib.virginia.edu/science/parshall/fibonacc.html [ii] Ibid. [iii] http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibBio.html#who [iv] Sanford, p.25 [v] http://www.lib.virginia.edu/science/parshall/fibonacc.html [vi] Ibid [vii] http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibBio.html#who [viii] http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibFormula.html#calcnext [ix] Ibid. [x] Ibid. [xi] Gullberg, p. 287 [xii] http://www.mcs.surrey.ac.uk/Personal/R.Knot/Fibonacci/lucasNbs.htmll#otherstarts [xiii] Gullberg, p. 288 [xiv] Boyer, p. 287 [xv] http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibpi.html#piandfib [xvi] Newman, p.718

Essay --

Introduction Considered to be the greatest playwright to ever have lived, William Shakespeare’s works continue to fascinate and entrance audiences around the world. Imbued with imagery, his comedy A Midsummer Night’s Dream is perhaps one of his more fantastic but none the less intricate plays. Presiding over the proceedings, the moon is the uniting feature of the play. With its multi-layered symbolism it is the thread that connects the different characters and weaves the tale together. 1. The Keeper of Time Upon its first mention the moon is used as a marker for the passage of time. In the opening lines of the play Theseus, the duke of Athens, laments to his fiancà ©e Hippolyta that time is passing too slow and blames this on the moon: THESEUS: Now, fair Hippolyta, our nuptial hour Draws on apace; four happy days bring in Another moon: but, O, methinks, how slow This old moon wanes! She lingers my desires, Like to a step-dame or a dowager Long withering out a young man’s revenue. (1.1.1-4 (Shakespeare and Brooks)) The old moon keeps Theseus waiting for his wedding night with Hippolyta, on the new moon. Theseus compares the old moon to an older woman, which stepmothers or a dowager usually are, and accuses her of keeping from him what is his to have, Hippolyta and their wedding night, like old widows might keep an inheritance from a young man. 2. The Moon Goddess Unlike the impatient Theseus, who mourns the dark moon, Hippolyta sees the moon as a symbol of Cupid and his arrows, which unite lovers: HIPPOLYTA: four nights will quickly steep themselves in night; Four nights will quickly dream away the time; And then the moon, like a silver bow New bent in heaven, shall behold the night Of our solemnity. (1.1.6-11 (Shakespeare and ... ...moon, therefore creating the image of the ‘Man in the Moon’: STARVELING: This lantern doth the horned moon present; Myself the Man i’th’ Moon do seem to be. (5.1.235-236 (Shakespeare and Brooks)) Thus the moon takes on another more comical and amusing role in contrast to the darker, more serious roles it holds towards the other groups. Conclusion Returning to the introduction, the moon is not only ever present, it actively influences the proceedings throughout the play, not only connecting characters, but also giving them agency for their actions. Shakespeare once again displays his dexterity with imagery through his manifold portrayals of the moon; one moment merely the indicator of time, the next a symbol of the goddess Diana, at once a symbol of order and chaos, of happiness and discord, fertility and chastity, it encompasses all that transpires on the stage.

Hamlet Act 3 – the Dumb Show

The Dumb Show As Claudius asks for the ‘light’, he wants actual light. The light also means the act of asking for forgiveness. People who are of the same rank or are comfortable with each other speak to each other is pros. Hamlet speaking to the players, he speaks down to them in verse. For the play within a play, Shakespeare uses rhymed verse to elevate the language. This was done because Claudius was of a higher status and this raises the severity of the crime. Hamlet is using the language to identify the’ criminals’, through the language.Blank verse – an official occasion or speaking to someone older (like poetry), like Hamlet and his Mother. Hamlet tells Horatio that he admires his sense of loyalty, character and sincerity. In the Excerpt: Identify 3 metaphors, how the theme of appearance vs reality is revealed In what ways is Horatio similar to hamlet? In what ways is he a foil? Is Horatio expendable in the plays plot development? Is act 3 the c limax? No, I do believe that this was the climax. I believe iIs it evident that act 3 might be the climax of this play? This is because at this point we discover who Hamlet truly was. He is not the ideal hero we actually perceive him to be. His murder of Polonius was equal to the murder of King Hamlet. In both cases, there are children who lost their lives. Even though Claudius’s murder was pre-meditated, murder is still murder. Even though Hamlet did this without planning, the fact that he was able to take a life so abruptly shows that he is not in essence the ‘hero’ within the play.Anachronism – When something doesn’t fit the context of the play. For example Hamlet’s school didn’t exist in the time in which Shakespeare wrote the play. The recurring motif is son’s avenging their fathers. (Old Norway and Young Hamlet) Now Hamlet kills Polonius who has a son. Laertes After getting evidence that Claudius is actually guilt, he feel s that he can now kill Claudius. That is why he kills Polonius without confirming why it was. (Deduced that it was Claudius hiding)

Health and fitness

Health and fitness, in general seem quite similar but they are not so. They are two different words symbolizing two different meanings. Health is the state of being free from illness or injury whereas fitness is considered a measure of the bodys ability to function efficiently and effectively in work and leisure activities, to resist diseases, and to meet emergency situations. From a young age it is preached that being healthy and fit are critical to having a strong long life, however the amount of people that have the will power to take action in these parts of their lives are getting smaller and smaller, especially in this generation.It's important that everyone, but especially teenagers, be acquainted with the advantages of a healthy life, and also acknowledge the ramifications of ignoring this cardinal part of life. Being active offers benefits beyond an improved physique and a healthy body. Health and fitness are crucial aspects of someone's lifestyle and has the power to alter a person's life in substantial ways. Healthy eating, the benefits of being active, and consequences of a corrupting lifestyle are all things to keep in mind as one makes decisions and goes through life.Many people have the ability to eat whatever they want and not gain a pound, owever what these people may not grasp is that all the bad food they are ingesting will catch up with them in later years of life, and may be setting them up for many health problems down the road. It's important to have a variety of different foods so your body has a healthy balanced diet. There are over forty nutrients that are essential to our life, and we need these nutrients because our bodies cannot produce them in large enough amounts for optimal health. Benefits of healthy eating, healthandliving. com) Different foods contain different nutrients, which is why it is imperative that we have this combination, and avoid overconsumption. Maintaining a healthy diet not only offers your body the energy and n utrition it needs to function but also offers many health benefits that can help one live longer and have a better life. Healthy eating helps to maintain a healthy body weight, makes one feel better about themselves, creates a stronger immune system, helps to sleep and feel more rested and gives mental alertness. Benefits From eating healthy, livestrong. com) Eating fruits and vegetables may reduce risks for a stroke, and other cardiovascular diseases and protects the body against certain types of cancer such as mouth cancer, and stomach cancer. Eating grains help with weight management, and reduce the risk of coronary artery disease. Grains also have large amounts of dietary fiber which helps to reduce blood cholesterol levels, and lowers your risk of heart disease.Each vitamin benefits your body in some way, for example potassium helps retain a healthy blood pressure, vitamin A keeps the skin and eyes healthy and protects against infections, and vitamin C helps heal cuts and wound s, and keeps the teeth and gums healthy. (Benefits of Healthy Diet, healthyforms. com) Eating healthy is something people need to consciously think about, because it does not come aturally. Sustaining a healthy diet is an essential part of leading a longer more vibrant life. (The 5 Key Benefits of eating healthy, ezinearticles. om) Sustaining a healthy diet is not the only thing to keep in mind, being physically active is equally important. Being active may not always be fun, but the benefits will be worth it in the long run. Being active not only improves health and fitness but it also improves posture and balance, boosts the mood, helps one sleep, makes one stronger, reduces stress and controls the risk of heart disease, such as diabetes. It also protects people rom a stroke, some types of cancer, lowers blood pressure and reduces anxiety and depression. (Benefits of Being Active, health. a) Studies have shown that child obesity is rapidly growing and will continue to grow if our generation does not take action of their health, which is why being active along with being healthy are both critical roles in not only developing as a person, but growing up healthy and happy. As mentioned earlier, child obesity rates are rising at a rapid pace. This is due to the fact that unhealthy foods cost significantly less than healthy foods such as fruits and vegetables. Right now 29% of adolescents are overweight, and this percent is growing by the day.Obesity as young kids and the food eating habits that they get into, carry into their adult life, leading to adult obesity. Currently, 59% of adult Canadians are either overweight or obese, and New Brunswick is one of the cities significantly higher in the overweight/obese population. (Statistics, childhoodobesityfoundation. ca) Not only do people get into bad eating habits that lead to obesity, but they also do not make time for exercise in there busy schedules, which only enhances the unhealthy lifestyle.Being overweight c an lead to ardiovascular disease such as a higher blood pressure, more likely to develop diabetes, and are at a greater risk for bone and Joint problems because the body carrying more weight than it is equipped for. Sleep apnea, social and psychological problems, and a low self esteem are also causes of an unhealthy diet. Dental problems are another thing that comes with unhealthy eating. Eating too much candy, or foods with lots of sugar and not enough other nutrients can lead to tooth decay and cavities.Another thing that many people are not aware of is the mood swings that come from unhealthy eating. Diets that do not include enough vitamins nd minerals can lead to people suffering severe mood swings. The body may become overly energetic and easily excitable only to crash later. In addition, a lack of vitamin B can lead to the hormone levels in the brain to be unbalanced, which can induce depression. (What are the Consequences of not Eating Healthy, ehow. com) Not being active ca n have many negative effects on the body. For example muscle atrophy is a cause of a lack of exercise.Muscle atrophy is a medical term that describes the process of your muscles breaking down or wasting away because they are not being exercised to their full capacity. Not only do you lose muscle but you gain fatty tissue and slow down your metabolism, resulting in more weight gain. Lack of exercise can also lead to increased levels of visceral fat, which is a fat that gets trapped inside your abdomen and is toxic because it causes heart disease and gallbladder problems, it also secrets dangerous hormones that can lead to the development of breast cancer.Cardiac decline is when the heart does not get enough exercise, and the heart, which is a muscle, isn't being exercise and so it rapidly declines in its cardiovascular fitness. The heart will not waste away like an rm or leg, however fat will begin to attack it which can lead to the development of heart disease. In 2006, approximatel y 2. 4 million Americans died from heart disease. (The Effects of Lack of Exercise on the Body, livestrong. com) The effects that unhealthy eating and a lack of exercise has on your body can be life changing and detrimental.This is why it is so important to nave a balance between the two so you can avoid all the consequences of an unhealthy lifestyle. It's very important to keep these things in mind as you grow older, and make time for healthy meals and exercise. Balance it key. To have a healthy life one must have a balance between eating healthy, and exercising, however treating oneself ever once in awhile is not a sin. Everything needs to be done in moderation.

How Do Teachers Use the Internet in Education Essay

How Do Teachers Use the Internet in Education - Essay Example Today, teachers have also incorporated internet in their classroom environment. According to a survey by NetDay (a nonprofit education technology organization), approximately 84% of the teachers consider use of computers and internet a vital part of their curriculum. They think that internet enhances the education quality and 75% of them believe that it is an essential tool to bring new resources for the classes. Today, almost all teachers have access to internet in their respective schools and about 80% of all classrooms have online computers. The internet is beneficial to all its users, be it teachers or students. Most teachers find internet as a research device for retrieving new information for their students and then teaching it in class. According to NetDay, 48% of the teachers view internet as a significant tool for teaching and for the past twelve years has been used in almost every school environment. In the past, books were the only source of information for the teachers an d students but in today’s globalized world, internet has become an important source for all types of information and teachers use it daily to teach their students. (Pastore, 2001) Teachers not only use internet for research and academic work in today’s society. ... In developing nations, it is still vulnerable for girls to attend schools on a daily basis or terrorist activities do not permit daily education; in such instances, online education is the ultimate answer. Teachers at Harvard, Stanford, Oxford, New York University and many other higher educational establishments worldwide give online classes to their students. Video conferencing and virtual education have grown to an extent that people use it widely in all demographic regions of the world. Teachers also update their lesson plans and homework for their students on the internet on various websites of their universities. (Pastore, 2001) Teachers not only use internet for research and communicating with their students, but they receive trainings for their courses online as well. With the expansion of internet and information technology, principals of school find it important to train their staff to use the world of internet. Teachers today receive IT trainings via the internet so that th ey are better able to teach their students. Complex courses and advanced technologies’ trainings are given to teachers worldwide. Teachers are trained in information technology so that they can better integrate it in their classrooms. Approximately 34% of all teachers in Hungary, Canada, Japan, and Iceland use external training for advanced courses over the internet. At least 30 percent of primary school teachers in Hungary and New Zealand have received IT trainings. (OECD, 2001) The percentage of teachers making use of internet for educational purposes has immensely increased during the past ten years. Today, the concept of missing a class and missing all class work and homework has long gone. Teachers make sure that the students work on their

Customer Service Justification Assignment Example | Topics and Well Written Essays - 500 words

Customer Service Justification - Assignment Example This report was written to help Crane Worldwide to solve the rising demand for round the clock customer service. The company has been growing at a very fast pace, which is why it is currently overwhelmed by many customer service demands. The report analyzes two alternatives, Telecommute (Alternative A) and Hiring of Personnel in different time zones (Alternative B). The company requires the alternatives to be evaluated based on cost, desirability, implementation, teamwork, and time management. An extensive evaluation of the two methods shows that Crane Worldwide would benefit more if it implements Alternative A. It is cheaper, faster, and better than Alternative B. Overview of Alternatives The following two alternatives considered in this report meets Crane Worldwide criteria: Alternative A – Telecommute: The Company can opt to hire customer service representatives from one country who can telecommute. It is flexible and fast relatively cheaper. Currently, many global companie s are using this approach to meet the extra customer service demand. Alternative B – Hire personnel in different time zones: The Company can decide to hire workers in different time zones, which makes it possible to adopt the â€Å"follow-the-sun† approach to customer care service. It means customers can be served anywhere anytime. The services not interrupted by the time. The creation of different teams in different time zones means that can be divided to meet the needs of all the customers. Criteria

System Analysis and Design course Term Paper Example | Topics and Well Written Essays - 250 words

System Analysis and Design course - Term Paper Example For example, a reader can comprehend words even when each letter of the word is scrambled. This process is referred to as typoglycemia. This demonstrates that as long as the first and last letters are present, people are able to read the words. Therefore, words are often read as whole and not in parts. As such, system analysis looks and focuses on the bigger picture. Moreover, I should recognize myself as complete as a differentiated whole. To model my life professionally as a system analyst, I will employ the waterfall model. This is because the waterfall model is easy to follow and stick to. Primarily, the model is a sequential one. Each stage has to be fully completed before moving to the next stage. Problems have to be tackled at each stage before moving forward. Consequently, there is no progress if the problem at one stage cannot be addressed. Therefore, I will model my life professionally as a system analyst by adopting a sequential analysis method. The model will enhance professionalism as it is unidirectional. Additionally, there is a linear representation of the life cycle. In addition to this, milestones in my personal life are seen and comprehended