History of math Research paper & presentation notes:-
-In EARLY GREEK
Infinity sign called the Laminiscate (ribbon-Latin). Invented in 1655 by John Wallis * Blaise Pascal: “If I consider the short period of time in which my life is intertwined with the eternity preceding and following it, and if I consider the small space in which I dwell, and I consider just that which I see, which is list in infinite space, of which I know nothing, and which knows nothing of me, then I am struck with wonder that I live here and not there.” * However, the rational structure of infinity still needs to be clarified. Many philosophers and mathematicians have struggled to give a rational account of infinity. * The most famous quote derives from German Mathematician David Hilbert (1862-1943) : “The infinite has always stirred the emotions of mankind more deeply than any other question; the infinite has stimulated and fertilized reason as few other ideas have” (Hilbert 1925) (infinity a research) * * Perhaps the most interesting-and most important- feature of Greek mathematics is its treatment of infinity. The Greeks laid the foundation for a rigorous treatment of infinite processes in 19th century calculus. * The most original contributors to the theory of infinity in ancient times were the theory of proportions and the method of exhaustion. Both were devised by Eudoxus and expounded in book V of Euclid’s Elements. * Theory of Proportion develops the idea that a “quantity” lambda (what we would now call a real number) can be known by its position among the rational numbers. I.e. Lambda is known if we know rational number less than and greater than lambda. * The method of exhaustion generalizes this idea from “quantities” to regions of the plane or space. A region becomes “known” (in area or volume) when its position among known areas or volumes is known. For example, we know the area of a circle when we know the areas of the polygons inside and outside of it. * Using this method, Euclid found that the volume of a tetrahedron equals 1/3 of its base area times its height and Archimedes found the area of a parabolic segment. Both of them relied on an infinite process that is fundamental to many calculations of area and volume: the summation of an infinite geometric series. * * Lecture : * To ancient Greeks infinity was problematic and its role in mathematics was unclear * E.g sequence 1,2,3……. Was unending but could not be encompassed ( they avoided saying lets look all the natural numbers at once, they avoided it) * -------------------------------------DARTHMOUTH * The Greek word for infinity was apeiron, which literally means unbounded, but can also mean infinite, indefinite, or undefined. Apeiron was a negative, even pejorative, word. The original chaos out of which the world was formed was apeiron. An arbitrary crooked line was apeiron. A dirty crumpled handkerchief was apeiron. Thus, apeiron need not only mean infinitely large, but can also mean totally disordered, infinitely complex, subject to no finite determination. In Aristotle's words, "... being infinite is a privation, not a perfection but the absence of a limit..."3 * ------------------------------------------------------------------------------------------------------------------------------------------------ Infinity article * We should begin our account of infinity with the "fifth-century Eleatic" Zeno. The early Greeks had come across the problem of infinity at an early stage in their development of mathematics and science. In their study of matter they realized the fundamental question: can one continue to divide matter into smaller and smaller pieces or will one reach a tiny piece which cannot be divided further. Pythagoras had argued that "all is number" and his universe was made up of finite natural numbers. Then there were Atomists who believed that matter was composed of an infinite number of
Term Paper: Research Progress Report By now, you should be making good progress in doing the research for your paper. This assignment will start you thinking about the structure of your paper. For this assignment, you will turn in a progress report about how your work on the paper is going. It should tell us what you have done up to the time when you print it. Your progress report must answer the following questions: 1. What will the title of your paper be? 2. What questions to you plan…
Paid Progress As a second grader who was at the top of the class with the most AR points and highest reading level, you would assume that I enjoyed reading. Instead, I actually despised anything literature or book related. The scent of book pages made my head hurt; to me, they smelled like wet cardboard. Looking at a page for too long made me want to tear my eye balls out and sitting in one place, reading a 100 page story bored me to death. I would walk into my classroom everyday dreading the…
Shawn Whitiak Perspectives On Human Progress Although Condorcet and Thoreau were both considered critics of their times, they presented their beliefs from different perspectives, as they were alive during different time periods. Thoreau lived during the 1800s while Condorcet lived in the 1700s like Condorcet, and it appears that morals and opinions are influenced by the age and their living conditions. In Thoreau’s time, technological advancement was one of the main priorities of society, and…
During last class, our group specified our topic and plan of execution, thus we narrowed the targets for our social media research. Our goal is to observe the users of the different social media network accounts, focusing on the different topics users are posting about and seeing whether there are differences and/or similarities between users. Additionally, we will observe how often each user is posting and whether they use a variety of the different social media network platforms. Instead of researching…
ESSAY 1 In the article "The Paradox of Progress" from the text book, emphasizes that we depend on technology, but we also worry about modern technology. This progress is keeping up with paradox at the same time. The article has points and counterpoints. There are three points: save time, increase life choices, and provide us control the world around us. For example, a consumer may choose many brands of cookies in a local supermarket. That means technology improves our life choices, but too many choices…
Civil Rights: Progress in education 1. Source A is a private comment made by President Eisenhower in May 1954. Eisenhower was not a racist and believed that blacks would not become equal by force, as you cannot force people to not be racist, it comes gradually. It shows that he believed it would set back blacks getting equal rights if the supreme court did decide to mix the school, because although it would be the law, the white people will not be as willing to accept this; therefore could potentially…
Master's Prepared Nurse Interview Interview The interview is conducted with a Mater’s prepared nurse name L.M .She is holding a position as a nurse manager of an ICU unit where I am working. The purpose of the interview is to prove how a nurse with advanced education in nursing can effectively train to hold a higher role in the field of nursing practice, teaching or management. The current accomplishment gave the person many open doors for development and professional growth. Aside from knowing that…
Introduction to Sociology “Sociology is the scientific study of human groups and social behaviour, including its origins, development, organisations, and institutions”. (Anon., n.d.) It uses various methods of investigation and analysis to develop knowledge about social order, social disorder and social change. Sociology and psychology are both social sciences, and deal with behaviour. Sociologists focus on groups of people -- societies, including culture, religion and traditions. Sociologists…
goods and services produced within a specific country in a year. Considering this we can see that GDP is a very broad measure of a country’s economic progress and fails to account for the social and ecological costs involved within a country. Given this knowledge we can draw comparisons between GDP and the Genuine Progress Index (GPI). The Genuine Progress Index provides a much more accurate picture of a country’s standard of living by taking into account things like a clean environment, household work…
Progress Summary Cynthia Finch, Patrina Jackson, and Deluvia Payne HCS/430 03-16-2015 Nancy Geedey Progress Summary In Team B we have: Cynthia Finch, Patrina Jackson, and Deluvia Payne. Each team member will choose an assign portion to be completed. A team member has recently dropped this class, so the three of us will research and study the Employee Handbook Nondiscrimination Section. By doing so, we will obtain knowledgeable information in order to answer the seven questions for week three assignment…