A Timeline History of Mathematics

A Timeline History of Mathematics Mathematics is the science of numbers. To  be precise, the Merriam-Webster dictionary defines mathematics as: The science of numbers and their operations, interrelations, combinations, generalizations, abstractions and of space configurations and their structure, measurement, transformations  and generalizations. There  are several different branches of mathematical science, which include algebra, geometry and calculus. Mathematics is not an invention. Discoveries and laws of science are not considered inventions since inventions are material things and processes. However, there is a history of mathematics, a relationship between mathematics and inventions  and mathematical instruments themselves are considered inventions. According to  the book Mathematical Thought from Ancient to Modern Times, mathematics as an organized science did not exist until the classical Greek period from 600 to 300 B.C. There were, however, prior civilizations in which the beginnings or rudiments of mathematics were formed. For example, when civilization began to trade, a need to count was created. When humans traded goods, they needed a way to count the goods and to calculate the cost of those goods. The very first device for counting numbers was, of course, the human hand and fingers represented quantities. And to count beyond ten fingers, mankind used natural markers, rocks or shells. From that point, tools such as counting boards and the abacus were invented.   Heres a quick tally of important developments introduced throughout the ages, beginning from A to Z.   Abacus One of the first tools for counting invented, the abacus was invented around 1200 B.C. in China and was used in many ancient civilizations, including Persia and Egypt. Accounting The innovative Italians of the Renaissance (14th  through 16th century) are widely acknowledged to be the fathers of modern accounting. Algebra The first treatise on algebra was written by Diophantus of Alexandria in the 3rd century B.C. Algebra comes from the Arabic word al-jabr, an ancient medical term meaning the reunion of broken parts. Al-Khawarizmi is another early algebra scholar and was the first to teach the formal discipline. Archimedes Archimedes was a mathematician and inventor from ancient Greece  best known for his discovery of the relationship between the surface and volume of a sphere and its circumscribing cylinder for his formulation of a hydrostatic principle (Archimedes principle) and for inventing the Archimedes screw (a device for raising water). Differential Gottfried Wilhelm Leibniz (1646-1716) was a German philosopher, mathematician and logician who is probably most well known for having invented differential and integral calculus. He did this independently of Sir Isaac Newton. Graph A graph is a pictorial representation of statistical data or of a functional relationship between variables. William Playfair (1759-1823) is generally viewed as the inventor of most graphical forms used to display data, including line plots, the bar chart, and the pie chart. Math Symbol In 1557, the sign was first used by Robert Record. In 1631, came the    sign. Pythagoreanism Pythagoreanism is a school of philosophy and a religious brotherhood believed to have been founded by Pythagoras of Samos, who settled in Croton in southern Italy about 525 B.C. The group had a profound effect on the development of mathematics. Protractor The simple protractor is an ancient device.  As an instrument used to construct and measure plane angles, the simple protractor looks like a semicircular disk marked with degrees, beginning with 0 º to 180 º. The first complex protractor was created for plotting the position of a boat on navigational charts. Called a three-arm protractor or station pointer, it was invented in 1801 by Joseph Huddart, a U.S. naval captain. The center  arm is fixed, while the outer two are rotatable and capable of being set at any angle relative to the center one. Slide Rulers Circular and rectangular slide rules, an instrument used for mathematical calculations, were both invented by mathematician William Oughtred. Zero Zero was invented by the Hindu mathematicians Aryabhata and Varamihara in India around or shortly after the year 520 A.D.

A cross cultural management study on Toyota

A cross cultural management study on Toyota The aim of this paper is to identify what role culture has played in the organizational structure and management technique of Toyota. Toyota is now the world’s leading automobile industry, knocking out rivals car maker; General Motors (Marr, 2009). The Toyota Motor Company was established in 1937 and 30 years later it entered the US market in 1967. By 1980, the company already had about 20% of the US car market as the indigenous car companies started experiencing customer dissatisfaction. The company based its entrant strategy into the US on the following; Fuel efficiency as compared to ‘gas guzzling’ American cars Environmental friendliness Superior build quality The introduction of the luxury-car line The real reason for the company’s success nevertheless was based on the introduction of Japanese style of production, operation and management. According to Liker and Morgan (2006), management principles must extend beyond the shop floor as they do at Toyot a. The ‘Toyota Way’ is a set of standards that harness the Toyota (Japanese) culture. These standards are applied by the Japanese in virtually all their dealings. Although they are moderate by nature hardly showing emotions, they are still very thorough and they apply the successful cultural traits in almost everything they do. The most important aspect of Toyota America is the techniques the company has used to stay successful given the obvious cultural differences between Toyota Japan and its biggest foreign subsidiary. The Japanese and the Americans have distinctly different business cultures however; the company has been able to work in harmony for decades. The major differences are; communication skills, winning attitude, methodology of maintaining strategies etc for both the countries – Japan and United States. Thus, we can say that while establishing a new company in host country culture is highly important. HOME-COUNTRY BUSINESS VALUES (JAPAN) Managerial Autonomy and Long-term Planning Very often, Japanese employees are engaged to the companies for ‘lifetime employment’. It is therefore probable that managers are not pressured to meet requirements financially and employee related. Corporate Rigidity and Hierarchy Japanese companies like Toyota are very hierarchical in nature and as such have distinctive and autonomous power bases. The roles of top managers are defined and incline towards strategic development of the company. The business unit managers are the ones responsible for initiating and supervising new projects. Participatory Decision-making The practice of exploring ideas of employees by senior management is known as Nemawashi in a given project. The idea behind the Nemawashi is to obtain participation of all employees in the decision-making process. The Japanese style of management is a bottom-up approach as compared to the rather autocratic top-down style of management. HOST-COUNTRY BUSINESS VALUES (UNITED ST ATES) Low Context There is more or less an uncongenial nature of communication in American organizations. Expectations of employees are communicated in competency statements or the criteria of their performance. On the other hand however, the Japanese may be more contained in their communication. Individualism Employees and indeed managers in the United States are often defined by their personal achievements and place little importance in group achievements. Americans also do not place much value on trust as they are likely to engage in business with strangers not necessarily friends or family unlike their Japanese collectivist counterparts.

How museums institutions shape the art world and in turn, how art and Research Paper

How museums institutions shape the art world and in turn, how art and artists have critiqued and sometimes transformed these institutions - Research Paper Example t goes back to the early 1866 in Paris when a group of Americans decided to create an institution and gallery of art so that the art and art education could reach to the people of America. The New York State Legislation then incorporated the Metropolitan Museum of Art with the Incorporation Act in 1870. The purpose of this act was to allow the Metropolitan Museum to serve as a Museum and Art Library in the city and further encourage and develop the study of fine arts and the application of arts in advancing the general knowledge. Eastman Johnson was the artist who acted as the co-founder of the museum, and the former Civil War Officer was the first director under the guidance of whom the holdings of the museum consisted of a roman stone sarcophagus and 174 European paintings. Since its formation, Metropolitan Museum of Art had many additions to its outside view and the building. It also had many additions in its collection of Art works, and is now holding some of America’s best art contributions. There are seventeen separate departments for the collections in Metropolitan. Each of the departments has specialised staff and a department of scientific research and conservation. The permanent collection that the museum holds includes paintings and sculptures of almost all the European masters, American and modern art, and also holding of the African, Asian, Oceanic, Islamic and Byzantine Art. Furthermore, the museum also has a collection of musical instruments and weapons from all around the world. The museum holds more than 13,000 artworks currently. Despite the controversies in 2009 related to the book Rogue’s Gallery by the journalist Michael Gross, and the criticisms that the museum faced, they plan to expand their collections and area in the future. The Metropolitan Museum of Art works under the policies of the State and acquires the world-class paintings. They have acquired artworks that hold immense value and have added to the contribution of promoting

Linguistics - The English Language (750words paper) - Cohesion Essay

Linguistics - The English Language (750words paper) - Cohesion Exercise - Essay Example By repeating it the reader must continue to read because they want to understand why the watch is so important. This is also the idea of repetition because the word is repeated over again. They also use synonyms for the missing watch and the watch itself like "bare wristed arm", "unique timepiece", and "threatening to tarnish". This last one indicates that the watch was silver and overtime would tarnish. There are also incidences of exophoric expression. In the first paragraph, "It is standard tourist advice" says that "it" is something the reader should immediately understand, and most tourists and people who live in the city will agree that this is a situation that everyone knows -- that they should look out for pickpockets. The word "pickpocket" immediately sets off in the readers mind a situation that is "seedy" and negative. This first paragraph sets the stage for the later cataphoic reference in that the watch is lifted from the president. The words "standard tourist" seems to imply that although tourists know this informant "the president" may not. The second paragraph starts off with "film" rather than saying something like "there was a security film" so the reader is not given what type of film, but it is another exophoric reference because the reader will know that some type of film could capture this situation. The use of the words "mobbed" and "plunging into an adoring crowd" seem to be juxtaposed to each other. We think of a "mob" as something out of control and at the same time he is "plunging into" the situation which makes it more positive. This creates a contrast between the words "plunging into" and "mob" so that it almost seems like someone being moved along in a crowd at a rock concert. In fact, the writer actually uses the metaphor phrase, "Mr. Bush†¦was received like a rock star†¦" in paragraph five. This was set up previously to make an endophoric connection. The article implies that the

How to Write a Synthesis Essay :: Synthesis Essay

What is a synthesis essay? A synthesis essay draws on two or more sources and combines their ideas into a coherent whole. What do I need to write one? Writing a successful synthesis essay will require you to do four things: read accurately and objectively, see relations among different viewpoints, define a thesis based on these relations, support the thesis effectively. You will not discuss all the points in every essay; but you should use every essay assigned, and you should use points from each that are appropriate for the thesis of your own essay. How do I write it? A synthesis essay may be developed in several ways, including the following: Thesis supported by examples. Develop a thesis based on common points among the works, and Support the thesis with appropriate examples from each work. This strategy works well with essays that approach a subject from highly diverse viewpoints. Comparison and contrast. Discuss the similarities and differences in the writers' viewpoints and draw whatever conclusions are possible from your comparison. Argument. If you have a clearly defined opinion about the subject, support that opinion by incorporating the valid viewpoints of the writers of the essays you have selected, and show the weaknesses of those ideas which you feel are not valid. What steps should I take in writing this essay? Consider using the following procedure for writing your essay: 1. Read carefully. First, skimming through the readings and look for similar issues in each essay. Reflect on those issues, and jot down your ideas. Reread and decide on one topic that will unify your essay. Note each essay's thesis and main points. Finally, take notes. 2. Next, determine your thesis. A thesis is a direct statement of a main issue or idea that you have developed from studying the essays. If you are writing a comparison/contrast essay, your thesis may explain the main points of agreement and disagreement among the writers you are dealing with. If you are writing a thesis-with-examples essay, your thesis may state the main idea you have developed from your readings, which will be supported with examples from the readings in the body of your essay. If you are writing an argument, your thesis will state your opinion about the subject and will indicate that you will be supporting your views through an analysis of the essays. 3. Then, organize your essay with your thesis in mind. The type of organization you use depends on your thesis, but in general you should be able to use either block-by-block or point-by-point organization with any of the essay types.

A Reaction on Aliens’ Ownership Right of Real Property in the Philippines Essay

A Reaction on Aliens’ Ownership Right of Real Property in the Philippines â€Å"Ang Pilipinas ay para sa mga Pilipino.† (â€Å"The Philippines is for the Filipinos†) Does it sound patriotic or nationalistic? Or does it pertain to selfish motives or mercenary actions? It is a fact that many aliens have been invading to the Philippines. Yes, they are aliens the non-Philippine nationals or foreigners. Most of them are fascinated and attracted to the beautiful sceneries around the Philippine archipelago. Others also pursue their business careers in the country, they are the investors, and the business oriented people who wish to put up their capitals and trade whether in a form of sole proprietorship, partnership or corporation. The aliens are granted the right to acquire a land or real property (immovable property) provided that they will consider the provisions under the Philippine Anti-Dummy Law the limitations on certain economic activity including the enjoyment of rights. In line with the Condominium Act of the Philippines, Republic Act 4726, the aliens are given the right to completely own a condominium unit but when it comes to project, the corporation must be composed of only 40%foreign investors. On the other hand, under the Investor’s Lease Act of the Philippines, foreign nationals or corporation may enter into lease agreement with Filipino landowners for an initial period of fifty years and a renewable extension of 25 years. As we try to comprehend to the law, it is really pro-Filipino. We noticed that the there are only 40% foreign investors or the stockholders and the 60% come from Filipinos. It’s also obvious that the aliens are prohibited to completely possess lands which are really in accordance to Article XII, Section 7 of the Philippine Constitution. Talking about the 40% foreign capitalists and investors, the Philippine  government can gain taxes from them which in turn can be used to accommodate common good for the Filipinos. The issue on Priority Development Assistance Fund (PDAF) or prominently called pork barrel barges in. That huge amount of money came from the taxpayers, both the Philippine nationals and non-Philippine nationals. But due to institutionalized corruption, the money which is intended for the people in the society are being stole by some of the national officials. This is another dilemma that the Philippine government should take into consideration and action. Back to the issue on aliens, the mediocre are skeptical whether the foreigners are given the right to fully own resources in the country or not. This is to clarify that they are not given the full authority; they are just given the opportunity to get into the business world which in turn both the aliens the Filipinos can gain something. It does not mean that though they have been advancing to the country, they steal what’s ours. There are laws for them to follow, thus, there’s no way for us to worry. The law has been already promulgated. All we can do is to deal with it, just no racial deviation, just focus for the common good of all Filipinos. The aliens are striving for their benefits, the same way should we act for ourselves. Let’s do our part and adhere to our virtues as we keep burning the Filipino spirit!

Descriptive Essay - Original Writing - 1187 Words

Rainbow Dash glanced down at her saddlebag, letting a monotonous sigh as she looked over the bunch of rolled up maps poking out from the sack. With a look of profound determination, she lifted her hoof and knocked on the door. â€Å"This is a public library, ya know. There’s no need to knock,† Twilight said from inside. â€Å"Aha†¦hehe, right†¦Ã¢â‚¬  Rainbow pushed through the Golden Oak Library’s front door and made her way over toward Twilight’s desk, then placed her saddlebag on it. â€Å"What s this about, Dash?† Twilight asked, placing a hoof to her chin, her curiosity at its peak. â€Å"Why did you bring a whole bunch of maps?† â€Å"I, uh†¦Ã¢â‚¬  Rainbow scratched the back of her mane and looked off to one side. I shoulda prepared for this.... â€Å"You all right there, Rainbow Dash? You seem†¦off and you’re acting weird,† Twilight said. â€Å"Yeah, yeah. I actually just wanted to ask you something.† Rainbow slid the bag out of her reach and grabbed the rolled-up scrolls with her teeth, setting them down. She was unrolling them on the desk, unfurling and ridding their creases. â€Å"What the heck is this?† Twilight looked genuinely confused. â€Å"Uh†¦what exactly do you mean?† Rainbow was aimlessly flailing her hooves around, while hovering lowly in the air. â€Å"Are you blind, woman?† â€Å"Oh, don’t patronize me. What in Celestia’s green Earth are you talking about?† Rainbow clapped. â€Å"Yes! Earth! Why the hell is the Earth flat?† Twilight flinched, and it looked like she was going to have a heart attack or seizure, orShow MoreRelatedDescriptive Essay - Original Writing1110 Words   |  5 PagesI don’t know how I got to where I am, but I’m here now, and I have to win if I want to live. I am in a game, and in order to live, I have to escape. That’s the thing, though: I don’t know how to escape. I was running for my life around this old house that looked like it came straight out of a horror movie. I doubled over and held my head in pain as I saw the static, which meant it was coming. I was being chased by what looked like a person but in no way acted like one. Just as it was about to appearRead MoreDescriptive Essay - Original Writing1102 Words   |  5 PagesIt is on days like this when we stop to think about our life. Small drops of rain begin to dapple the cobblestone pavement as people whip out their umbrellas for cover. I continue sauntering down the busy street, relishing the feeling of a light shower. Moving with the mass of pedestrians, I stop at a crosswalk where I wait for the stoplight to turn green. A flower shop employee across the street scurries to bring in the numerous bouquets and close the doors as rain starts rolling down the displayRead MoreDescriptive Essay - Original Writing914 Words   |  4 PagesDreamy I thought. 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