Archimedes theory of a circle ABCD and a triangle K

Archimedes theory of a circle ABCD and a triangle K Archimedes compared the area enclosed by a circle to a right triangle whose base has the length of the circle’s circumference and whose height equals the circle’s radius. If the area of the circle is not equal to that of the triangle, then it must be either greater or less. He then eliminates each of these by contradiction, leaving equality as the only possibility. Archimedes’ proof consists of constructing a circle ABCD and a triangle K. Archimedes starts by inscribing a square in the circle and bisects the segments of arc AB, BC, CD, DE subtended by the sides of the square. Afterwards he proceeds to inscribe another polygon on the bisected points. He repeats this process until the difference in area between the circle and the inscribed polygon is smaller than the difference between the area of the circle and the area of the triangle. The polygon is then greater than the triangle K. Archimedes then proceeds to explain that a line from the center of the polygon to the bisection of one of its sides is shorter than the radius of the circle, and its circumference is smaller than the circumference of the circle. This disproves the statement that the polygon is greater than the triangle, since the legs of the triangle are made up of the radius and circumference of the circle. The triangle K cannot be both smaller and larger than the polygon, and thus cannot be smaller than the circle. After Archimedes proved that that the triangle cannot be smaller than the circle, he continues to prove that the triangle cannot be larger than the circle, either. This is accomplished by first assuming the triangle K to be larger than the circle ABCD. Then, a square is circumscribed around the circle so that lines drawn from the center of the circle will go through the points A, B, C, and D and bisect the corners of the square, one of which Archimedes labels T. Archimedes then connects the sides of the square with a tangent line and labels the points at which the line meets the square G and F. He goes on to say that because TG GA GH, the triangle formed by FTG is larger than half the area of the difference in area between the square and the circle. Archimedes uses the fact that continual bisecting of the arc of a circle will produce a polygon with this characteristic to assert that continuing this method will ultimately produce a polygon around the circle such that the difference in area between the polygon and the circle is less than the difference in area between the triangle K and the circle. The polygon is thus less in area than the triangle K The length of a line from the center of the circle to a side of the polygon is equal to the radius of the circle. However, the perimeter of the polygon is larger in length than the circumference of the circle, and since the circumference of the circle is equal to the length of the longer leg of the triangle, the polygon must be larger in area than the triangle K. Again, the triangle cannot be both larger and smaller than the polygon, so the triangle cannot be larger than the circle. Archimedes accomplished to prove his theory by using contradiction. After he proved that the triangle with legs equal to the radius and circumference of a given circle is not greater or less in area than that circle he concludes that the two must be equal in area.

The influence of technology on modernist and avant-garde architecture Essay

The influence of technology on modernist and avant-garde architecture - Essay Example After the liberal-national revolutions of 1848, there was the need to expand the economy of the colonial territories and to fill the political, military and economic conditions with the traditional European. This led to the development of cities in its suburbs. In addition, the decrease in mortality because of the improved standards of living in terms of nutrition and medical techniques in urban areas resulted in urbanisation. The increase in population in urban areas led to transformation of old neighbourhoods into slums as well as entry of jerry-built houses that would provide shelter to people working in the factories. However, the Housing of the Working Classes Act of 1890 and the slum clearance Acts of 1868 and 1875 were established to provide quality housing. As the construction of new houses for workers began, several architectural designs developed in order to produce engaging and beautiful buildings and improve the overall appearance of the urban centres. According to Conrad s (25), in organic architecture, the building, its furnishings and its setting and environment are considered as one thing. Furnishings such as tables, chairs, musical instruments and cabinets are said to be part of the buildings, as well. However, the heating, lighting or ventilation can be incorporated together with other features in the building or excluded. Conrads (25) argues that a human dwelling place should be a complete work of art that is closely related to modern life and fit for people to live. It should include harmonious entity, which is beautiful and suitable in providing the needs of the dwellers. An example of such a building is shown below. Winslow House in Chicago (1893) Conrads (95) states it is through the new evolving techniques that people are able to discover new materials and new ways to construct objects; hence, enabling individuals to learn how to design objects and develop a new attitude towards design. This includes the living environment of vehicles and machines, limitation of certain characteristics such as colours and they should be readily accessible to all. Additionally, they should be economical in terms of space used, time, materials and money. This can be seen in Gropius office (1932) as shown below. Bauhaus argues that the necessities of life are the same for most people. Additionally, he states that the home and its furnishings are mass consumer goods and their design is as a result of reason other than a matter of passion. Machines that produce such products use steam and electricity in order to help people from working manually when producing their daily needs as well as to provide them with cheap products that are better than those produced by hand. According to Conrads (96), Bauhaus workshops are laboratories that are suitable for production of mass products, which are well developed and can be improved with time. An illustration of Bauhaus workshop is as shown below. According to Conrads (96), the Bauhaus represents that the contrast between the industry and the crafts is less marked by the difference in tools used than by the division of labor in the industry, as well as the quality of the work in the crafts. The past crafts have changed, and new ones are expected to emerge in a new and productive industry in which they will carry out work for industrial production. The experiments in the laboratory workshops will produce models and prototypes that will be implemented in the factories to produce quality work. Moreover, the products that have been produced in the Bauhaus are also been produced in other firms with are closely related to Bauhaus. Some of the architectural features that describe a new building according to Le Corbusier houses designs include the supports, the roof gardens, the free designing of the plan, the free design of the facade and the horizontal window. For the supports, it is necessary to distinguish between the non-supporting and the supporting elements,

Self Fulfilling and Self Sealing Theory Essay Example | Topics and Well Written Essays - 1250 words

Self Fulfilling and Self Sealing Theory - Essay Example The essay "Self Fulfilling and Self Sealing Theory" discusses the self-fulfilling and self-sealing theory, the concepts of â€Å"Power Visible† and â€Å"Power Invisible†, the spray diagram of virtual classroom support system, the system and subsystem diversion in the banking system and system thinking in the light of self-sealing doctrine.Many a time, what we think or vouch, by coincidence, appears to be true. It is called as ‘Self Fulfilling’ which was coroneted as ‘Prophesy’ in the  earlier era. The myths of yesteryears, defying the geographical boundary, had stood for this theory. The mythology of different civilization bears the testimonies of the self-fulfilling prophecy. In fact, our own action many a time makes this theory come true. For example, an average student, discouraged from every corner, ends up with a firm belief that he can never do well in the examination. Eventually, his grade slides and he keeps on losing faith, resultin g much more decay in his career.On the other hand, â€Å"Self Sealing† as a theory leads to the cherished mental set that clings to a particular belief or taboo. Prevailing in the orthodox religious group or in different cults this theory prevents the believer to act normally as he gets paranoid in respect to the outside world order. The hideous crime done by some Jihad groups in terms of culpable loss of human life and resources shows us how a person under the grip of severe self-sealing doctrine can mow down innocent lives.

PESTEL analysis for Bank Barclays Essay Example | Topics and Well Written Essays - 1000 words

PESTEL analysis for Bank Barclays - Essay Example History of the Barclays Bank The history of the bank can be tracked down to the year 1690 when two persons named John Feame and Thomas Gould commenced trading in Lombard Street of London basically as goldsmith bankers. In the year 1736, James Barclay became a part of the operation and since then the name Barclays has been related with the bank, however, only in the year 1896 the company got its name as Barclays Bank. Barclays expanded it’s tentacles in business by acquiring a number of smaller operations in all these years and expanded its business all over the UK and worldwide (Financial Advice, n.d.). In the year 1925, the international operations of the bank gained acceleration after the mergers with Colonial Bank, National Bank of South Africa and Anglo Egyptian Bank. The year 1961 saw the opening of the bank’s first computer operated branch in London on Drummond Street. In 1966, the UK got its first credit card which was launched by the Barclays Bank. The first ban k to make use of advertising in the television was also the Barclays in 1972. The bank has also tied up with Post Office Ltd. to spread out its services in personal banking, particularly in the sector of unsecured and secured loans. The Barclays Bank is spread over 50 countries and attends to 27 million customers (The Origin of, 2008). PESTEL Analysis of the Banking Industry Political Analysis Banks in the UK are trying to draw on research performed by Pricewaterhouse Coopers and the study shows that rigid rules in the banking industry will drain a sum of ?1tn from the financial system. As a result of which the businesses and the households would be deprived of any form of credit and loans. The regulatory changes that are being made in 2011 would require the banks to keep larger capital cushions (Treanor, 2010). The â€Å"Big Four† banks in the UK that have resisted radical shake-up calls in their business after the announcement of the bank reform report are Royal Bank of Sco tland, Barclays, Lloyds Banking Group and HSBC. The expected subsidiarisation model states that allocation of capital has to be made to different country operations and units by the bank. This would eventually pressurise the top lenders of the UK for new capital requirements (Reuters, 2011). Economic Analysis Banking sectors are the basic providers of financial services. Therefore, the factors such as tax, inflation rate and interest rates have strong influence. According to the latest information it has been discovered that the banks in the UK that deals in loan primarily would be discussing about the prospects of expected investments by the tax payers, with the concerned authorities (Economy Watch, 2011). The UK is within the top 30 rich countries with the UK’s GDP per capita being $37,400. Out of which the contribution of the financial sector remains to be the highest being 76.2% of GDP (Economy Watch, 2011). Social Analysis Demographics influence the banking industry to a great extent. The factors that are having a significant impact in relation to banking sector are mortgage, living standard, total

IMC is Not a Proven Marketing Theory Essay Example | Topics and Well Written Essays - 2500 words

IMC is Not a Proven Marketing Theory - Essay Example Direct Marketing is an approach used to create relationship with customers and delivering information about products to customer, the method is mainly used for selling financial services to customers, direct marketing also helps to close sales cycle within a short time period. Sales Promotion is the process that helps the company to increase brand visibility in point of sales and point of purchases, companies use the technique to increase new product usage ratio among customers, the process also helps to increase customer footfall in the retail stores, companies use loyalty card, discount method, incentive schemes to increase purchase ratio among customers. Public Relation companies can go for organizing public events or news paper editorial about their new product, they use trade shows to increase category visibility among customers, creating good word of mouth about the product is one of the major objectives of public relation (Jones). Many advertising agencies have shifted focus f rom creating unilateral promotional message to making multidimensional promotional message. Main purpose of IMC is to channelize the promotional message in a unified manner though all promotional medium. David Ogilvy has characterized IMC as one stop solution offered by advertising agencies to companies. Keith Reinhard (CEO of DDB Needham) thinks IMC is an effective way to produce creative brand message. Many research scholars think demassifiction played pivotal role in evolution of IMC. After 1970, media industry started to restructure into smaller operational units. They started giving importance to various promotional medium rather than concentrating on age old advertising model. In this way IMC has emerged as a common platform to integrate various promotional medium (Schultz, Tannenbaum and Lauterborn 6). IMC is a process to align communication objectives of a company with corporate goals to achieve business efficiency. Jerome McCarthy used the concept of four P’s (Produc t, price, place and promotion) during 1950’s for the first time (Jerome McCarthy used 4P’s concept in his book â€Å"Basic Marketing† published in 1960 and he used the concept to explain campaign made by JWT). Philip Kotler and other academicians (in 1965, Philip Kotler described 4P’s as various marketing variables in his article) proselytized the concept in coming years. Four P’s can be described in the following manner. Product- the strategy emphasizes on manufacturing products, maintaining the quality standard of product and optimum utilization of resources during production process. Price- deciding the price of the product in accordance with the demand of the product, setting high price or low price for the product is an important part of pricing strategy. Place- designing distribution network for the product, company creates distribution network to expand the reach of the product, appointing c&f agents, stockiest, wholesalers, retailers are pa rt of distribution strategy. Promotion- companies use direct marketing, sales promotion, and advertising activities to

CRIMINAL JUSTICE 1 question drugs Coursework Example | Topics and Well Written Essays - 500 words

CRIMINAL JUSTICE 1 question drugs - Coursework Example In truth, Colombian drug organizations and Mexican drug organizations have traditionally taken different roles in the drug trafficking chain. In the article by Lyman (2011), the relationship started with Mexican drug organizations acting as surrogates and partners of their Colombian counterpart drug organizations – taking advantage of the borders between Mexico and the United States to smuggle in cocaine from Colombia (page 136). However, towards the end of the 1980s the Mexicans were no longer satisfied with being mere conduits and wanted a share both of the drug loot and the U.S. markets. Lyman explained the consequence of this: Eventually, this arrangement with the Colombians not only resulted in dividing the cocaine shipments down the middle but in dividing much of the U.S. markets down the middle. As the arrangement evolved over time, the Colombians retained the wholesale market in the eastern United States as their own, and Mexican drug cartels took over the wholesale market in the Midwestern and Western states. According to Bagley (1988), the expanded role of the Mexicans in the drug trade had created, in his words, â€Å"an unprecedented wave of drug related violence in Mexico that seriously threatened the country’s fledgling process of democratization. (page 71)†. And this begins to answer the question as to whether or not these drug cartels are as much of a threat to the United States as traditional terrorist organizations. In fact, it may even be argued that drug cartels are even more of a threat to the United States than the terrorist networks that people have come to associate with Islamic fundamentalist groups and the like. For one thing, the scale of violence wrought by drug organization can perhaps rival that of traditional terrorist organizations. Colombia’s principal guerrilla organization, the Fuerzas Armadas Revolucion de

The Challenger Address Essay Example for Free

The Challenger Address Essay Ronald Wilson Reagan was the 40th United States President after winning against the Democratic Challenger Jimmy Carter in the 1980 presidential election. Reagan won by attaining 50. 7% of the popular votes in that particular election. It can be said that the beginning of his term was not that pleasing. On his first year of term, he fired 11,345 air traffic controllers who, according to him violated the regulation of the government that prohibits unions from striking. Also, it had been said that unemployment in the United States increases to 10. 8%, which is greater than any time since the great depression during his first year in position. However, this percentage dropped during the rest of his presidency. It can also be said that after his first term, Reagan gained the respect and trust of the American people by being nominated for the second time as the president of the United States on the 1985 presidential election in which he was elected by landslide, having unprecedented number of votes. It was also said that during his years of presidency, restoration of prosperity was viewed by the people as well as global peace. It was also in the year 1986 that the income tax code was revised by Reagan wherein millions of people with low income were exempted. The year 1986 is not just a year of development in terms of social conditions in the United States; it was also a time wherein space exploration was greatly admired. By that time there had been several developments and expeditions that can be considered successful. Thus, the people especially Americans were very enthusiast to explore and to achieve greater heights in terms of space travel and exploration. However, this year was also a tragic time for the space exploration era when the Space Shuttle Challenger explodes a short while after lifting off, leaving none of the seven crews alive on January 28, 1986. The public was shocked at what they witnessed. Also, by that time, President Reagan was planning to deliver a speech to the American people but was compelled by the tragedy of the Challenger. Thus, President Reagan delivered a speech concerning the accident rather than the one that he intended to deliver to the people. This speech was well known as the â€Å"Challenger Address†. The accident had a great impact in the American people. The main reason was stated by the president himself in his â€Å"Challenger Addressed†. There had been a history in space exploration wherein lives were lost, three of them. The accident happened around 19 years before the Challenger tragedy. Although there had been cases of death regarding space exploration, the fact that the tragedy happen in mid air shocked the Americans and the whole world as well. There had never been any accident regarding space exploration that happened a few seconds after the shuttle’s takeoff. Two interpretations can be given why the speech of President Reagan was known as the â€Å"Challenger Addressed†. The first is, it was given that title since the shuttle was named Challenger. However, looking at the contents of the â€Å"Challenger Addressed†, it can be said the word Challenger does not refer to the name of the shuttle but rather to the contents and message of the speech. The president is challenging the nation to continue their search and to never lose heart in space exploration because of the Challenger accident. There had been several components of the speech that makes it effective and appealing to the American people. The very first part of the speech that Reagan used to encourage the people to pursue space explorations was by calling the astronauts heroes, Reagan stated, â€Å"We mourn seven heroes† (Reagan, 1986). He also states that the astronauts were well aware of the dangers that they must face but have overcome it. The president also showed his sympathy with the people especially the family of the astronauts. In order to gain the sympathy and heart of the people, they must know that you are one with them, in spirit and emotions. President Reagan expressed his anguish and mourned not only with the families of the astronauts but with the whole nation as well. At the beginning of his speech, President Reagan sympathized and mourned with the nation in order to appeal to them. However, his tone was developed in the succeeding paragraphs, from appealing to encouraging. He did this by saying, â€Å"The future doesn’t belong to the fainthearted; it belongs to the brave† (Reagan. 1986). These statements surely challenged the people at that time. The impact of the tragedy was reduced in an instant. The president also stated his desire to talk to the people of NASA and to tell and show them that their efforts are well appreciated as well as their sacrifices and bravery and encourage them to pursue their search despite the Challenger accident. Another part of the â€Å"Challenge Address† was the story of Sir Francis Drake, a great explorer who lived by the sea and died on it. President Reagan uses parallelism to connect the present situation into another situation in the past. Thus, those who died in the tragedy are compared to and are paralleled with Drake that creates a good impression for the seven crews of the Challenger. Just as Drake was considered a great man, they too are considered heroes and great explorers. President Reagan ends his speech by saying that the memories of the seven crews will never be forgotten. Thus, showing that they are valued as well as their sacrifices and hard work will never be in vain. This was also important in order to encourage the youth in pursuing to be an astronaut because of the fear that was established by the Challenger accident. It is important to know that your hard work is acknowledge by the society in general in order to be motivated and to pursue a certain career. One of the main factors why the speech was effective was the image, personality and credibility of the speaker. Being the president that time, people will surely listen to what the Reagan has to say. However, in terms of astronomical knowledge and the risk and sacrifices needed on being an astronaut, he cannot be considered a pro. There will surely be different sides of the address; it may either encourage the audience while others may see that the President was in no position to make such address. In every issue, there is always a positive and as well a negative aspect. However, it can be said that President Reagan was able to really challenge the people to search for greater achievements in terms of space exploration and taking the Challenger tragedy as a part of reaching greater knowledge and understanding of the universe, that every quest has its own risk as well as sacrifices that has to be overcome to really success in that particular area. The occasion or the time in which a speech was delivered was also a very important factor for a speech to be effective. The â€Å"Challenger Speech† will not have the same impact if it was delivered without such event, the Challenger tragedy, happening. Thus, the situation or the tragedy is a very big factor why the address made by President Reagan caught the attention of many people by that time and as well as the attention and interest of the people in the contemporary time. There are a lot of things that has to be considered in order to make an effective speech of which four components are primary; the speaker, the audience, the occasion and of course, the speech itself. It can be said that the â€Å"Challenger Address† by former President Reagan is effective because these components had been addressed properly. The speaker is credible enough for the people to listen to what he has to say as well as the occasion needed to gain the attention and interest of the audience. Of course, the audiences were concerned about the situation because of the impact of the tragedy. And of course, the speech itself was well made, something that is expected for a United States President. References Michigan State University Libraries. (No Date). Space exploration. Retrieved January 30, 2008 from http://www. lib. msu. edu/publ_ser/docs/displays/Displaymarch03. html. Reagan, R. (1986). The space shuttle ‘challenger’ tragedy address. Retrieved January 30, 2008 from http://www. americanrhetoric. com/speeches/ronaldreaganchallenger. htm. The White House. (No Date). President Ronald Reagan 1911-2004. Retrieved January 30, 2008 from http://www. whitehouse. gov/history/presidents/rr40. html.