Fibonacci Essays - Fibonacci Numbers, Fibonacci, Numerals

Fibonacci Leonardo da Pisa, or more commonly known as Fibonacci , was born in Pisa, Italy in 1175. He was the son of Guilielmo Bonacci, a secretary of the Republic of Pisa. His father was only a secretary, so he was often sent to do work in Pisan trading colonies. He did this for many years until 1192. In 1192, Bonacci got a permanent job as the director of the Pisan trading colony in Bugia, Algeria. Sometime after 1192, Bonacci brought Fibonacci with him to Bugia. Bonnaci expected Fibbonacci to become a merchant and so arranged for him in instruction of calculational techniques. One of the major themes in this involved the Hindu-Arabic numerals which had not yet been introduced into Europe. Eventually, Bonacci enlisted his son's help in carrying out business for the Pisan republic and sent him on trips to Egypt, Syria, Greece, Sicily, and Provence. Fibonacci took this grand opportunity offered by his father, to study and learn the mathematical techniques employed in these various regions. Around 1200, Fibonacci returned to Pisa where, for at least the next twenty-five years, he worked on his own mathematical compositions. The five works produced by him in this period which have survived are: the Liber Abbaci; the Practica geometriae ; an undated letter to Theodorus, the imperial philosopher to the court of the Hohenstaufen emperor Frederick II; Flos , a collection of solutions to problems posed in the presence of Frederick II; and the Liber quadratorum , a number-theoretic book concerned with the simultaneous solution of equations quadratic in two or more variables. The most famous of these works is Liber Abbaci. The Liber Abbaci is Latin for ?The Book of Calculations?. This book was designed for the Latin-speaking-European-world to accept the decimal number system. The first chapter of Part 1 begins: These are the nine figures of the Indians: 9 8 7 6 5 4 3 2 1. With these nine figures, and with this sign 0 which in Arabic is called zephirum, any number can be written, as will be demonstrated. He also introduced a series in Liber Abacci. It is the Fibonacci sequence, named in his honor. The series begins with 0 and 1. After that, he added the last two numbers to get the next (1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987,...) He discovered it as a solution to. In 1225 Fibonacci took part in a tournament at Pisa ordered by the emperor himself, Frederick II. It went as follows: Beginning with a single pair of rabbits, if every month each productive pair bears a new pair, which becomes productive when they are 1 month old, how many rabbits will there be after n months? After 1228, virtually nothing is known of Leonardo's life, except that by decree the Republic of Pisa awarded the 'serious and learned Master Leonardo Bigollo' (discretus et sapiens) a yearly salarium of 'libre XX denariorem' in addition to the usual allowances . This stipend rewarded Fibonacci for his pro bono advising to the Republic on matters involving accounting and related mathematical matters. Fibonacci died some in 1250, presumably in Pisa. Mathematics

The Diligent A Voyage Through the Worlds of the Slave Trade by Robert Harms

The Diligent A Voyage Through the Worlds of the Slave Trade by Robert Harms The issue of the slave trade is one of the most controversial ones because this question is not only associated with the problem of slavery, but it is also based on the problem of morality which is related to the discussion of slaves as objects of trade. In his book The Diligent: A Voyage through the Worlds of the Slave Trade, Robert Harms presents the records of Robert Durand who was the first lieutenant of The Diligent, the French slaving ship.Advertising We will write a custom essay sample on â€Å"The Diligent: A Voyage Through the Worlds of the Slave Trade† by Robert Harms specifically for you for only $16.05 $11/page Learn More The French people joined the Atlantic slave trade later than the other European countries such as Britain and Portugal, but the French successes were significant, and the slave trade became the characteristic feature France’s development in the 18th century. Thus, the historic significance of the book is in the fac t that it provides the discussion of the role of slave trade in France during the 18th century. However, it is more important to concentrate on the aspect of morality to understand the French public’s attitude to the problem of slavery in the 18th century. Robert Durand does not demonstrate any signs of uncertainty in relation to the morality of the slave trade, and his position corresponds with the position of the French people regarding the nature of the slave trade, but it is possible to condemn Durand for his attitude because reflecting the public’s visions, he violates the universe moral norms and supports cruelty and violence. Robert Durand’s accounts show that the lieutenant does not feel any qualms about the idea of the slave trade in spite of its brutal nature. According to Harms, Durand was writing â€Å"about selling people exactly as he would have written about selling barrels of wine or loads of wheat. He gave no indication that he felt any sense o f shame or moral ambivalence about his mission†1. Durand’s â€Å"businesslike† and â€Å"matter-of-fact† tone can surprise not only the author who analyzes the accounts but also the readers because this tone is not appropriate to discuss the important moral issue of the slave trade in France of the 18th century2. Furthermore, the young lieutenant does not demonstrate the unique attitude to the problem. Instead, Durand’s accounts represent the attitudes of the majority in relation to the issue of the slave trade because the French public paid more attention to the problems of war, to the issue of famine, and to the economic questions associated with inflation and taxes than to such moral issues as the slave trade in the 18th century. In his work, Harms intends to explain Durand’s position while stating that â€Å"the talk focused on issues of access, profits, tariffs, and bonuses†3. Thus, Durand’s approach to discussing the quest ion was typical for the period, and it was even the â€Å"part of a general mind-set in the seaports of early eighteenth-century Brittany†4.Advertising Looking for essay on american literature? Let's see if we can help you! Get your first paper with 15% OFF Learn More From this perspective, it is almost impossible to state clearly whether the French public supported or not the idea of the slave trade because the actual public discussion of the problem was not observed within different social classes. However, the reference to the social tendencies cannot be used to justify the approach of Durand to discussing the problem of the slave trade. The fact that Durand focused more on recording the factual details of the trade operations and prices and on counting the profits supports the idea that the aspects of morality were widely violated in the French society. It is possible to condemn Durand for his actions because his activities are significantly associ ated with a lot of moral aspects, and Durand could reject the development of the slave trade as any other person in the French society. Nevertheless, many people chose to ignore the issue of the slave trade, and they discussed it only from the perspective of its profitability rather than morality. Slave traders chose their path consciously because the business was risky and problematic. That is why, Durand made his choice without thinking about the moral implications of his actions. In spite of the fact that Durand was one of many people who did not focus on the slave trade as the social problem, this fact cannot be referred to while discussing the problem of condemning Durand’s actions. The slave trade was the business characterized by a lot of problems and contradictions associated with the concepts of the slaves’ freedom and use of their work in France. The records and accounts written by Robert Durand demonstrate his focus on the slave trade as on the profitable bu siness rather than on the moral issue. This approach or attitude is also reflected in the general public’s visions of the question which were typical for the French society in the 18th century. However, in spite of the fact that the moral aspect of the slave trade was not actively discussed in the society, Durand’s attitudes and actions cannot be justified because the man violated simple moral norms and promoted the brutal practice of trading people. Thus, the book by Robert Harms is the important source to research the problem of the slave trade in France as the moral issue with references to the historic significance of the phenomenon. Bibliography Harms, Robert. The Diligent: A Voyage Through the Worlds of the Slave Trade. USA: Basic Books, 2002.Advertising We will write a custom essay sample on â€Å"The Diligent: A Voyage Through the Worlds of the Slave Trade† by Robert Harms specifically for you for only $16.05 $11/page Learn More Footnotes 1 Robert Harms, The Diligent: A Voyage Through the Worlds of the Slave Trade (USA: Basic Books, 2002), 5. 2 Ibid., 5. 3 Ibid., 5. 4 Ibid., 5.