Business Case Model

Table of Contents Suppliers Customer value Pricing References Suppliers Segway HT incorporated four outside partners in the supply and development of components for the wonder product. These partners had specialized expertise on product development impacting on their ability to transform technical inputs in the business model to economic outputs, what Brown (2010) describes as strategic economic advantage over competitors.Advertising We will write a custom essay sample on Business Case Model specifically for you for only $16.05 $11/page Learn More Reputable partners included silicon sensing systems renown for its supply of silicon micro-machined sensors, pacific scientific which is the manufacturer of high performance motors, Delphi Automotive systems a renown supplier of integrated circuits and smart sensors, and Axicon a leading developer and designer of quiet gear systems. This ensured profit maximization by developing a product with a wide market appeal, making the brand name synonymous with short distance human travels, an important concept in marketing. Brown (2010) identifies this as vertical integration. Afuah (2008) has determined that firms which have technological advantages and have established strong working relationship with suppliers have gained a leadership position in the market against competitors which is evident in the above case study. The firm established strong and reliable working relationship with government agencies, corporations, and the University of Stanford. This reputable institutions provided testing grounds for the products, gave the product a name and an image while risk aversions in regulatory circles were mitigated. These were brilliant strategic management and brand image ideas. Brown (2010) sees these ingenuities as placing the product and the firm in terms of strategic partnerships and suppliers far ahead of the firm’s competitors besides gaining a large market share. Customer value To remain competitive in the market, a product must be unique and address the needs of its consumers. This is demonstrated in the above case study. Segway is a two wheeled, self-balancing, electric powered transporter that is of its kind. In addition to the complex integrated software and hardware, Segway HT had the technological ability to mimic the human body’s ability to balance. In addition, it was small in size and unique. Thus creating and capturing value in customers. Customers will always go for those products that address their needs and wants and from which value for their money is assured. Customers are the core determinants of a successful business. According to Afuah (2008), the firm’s products incorporated such elements as efficiency in product characteristics. Segway HT was designed to accommodate an individual with personal weight while occupying a smaller amount of space thus suitable for a wide variety of customers in America, Asian and the European market.Advertising Looking for essay on business economics? Let's see if we can help you! Get your first paper with 15% OFF Learn More Pricing The product was priced according to customer needs. As a marketing strategy three versions were developed and priced using flexible pricing mechanisms as Pindcky (2008) argues. These were e Series that sold at $ 7000-$ 900, i Series that sold at $4950, and the lighter p Series at $ 2000-$3000. Pindcky (2008) asserts that â€Å"profit-maximizing price-cost margin is inversely related to the firm’s price elasticity of demand†. According to Afuah (2003), the firm identified and used excellent pricing techniques, and a joint pricing mechanism since other versions of the product were produced. This product differentiation and unique pricing mechanism incorporating characteristics of the original product placed the product at a competitive edge against its competitors and new entrants. Product diversifications were tail ored for different classes of people. This is a unique marketing mix described by (Brown, 2010). The architect of the product, according to the case study, is a genius innovation blended with a marketing strategy by creating such a brand image that has captured the public mind. References Afuah A. (2003). Business Models: A strategic Management Approach. University of Michigan  ® McGraw-Hill Irwin Boston Burr Ridge. Brown A. (2010). Working to end horse slaughter: Retrieved from http://www1.udel.edu/alex/chapt2.html Pindyck S.R (2008) Microeconomics. 7 ed. prentice hallAdvertising We will write a custom essay sample on Business Case Model specifically for you for only $16.05 $11/page Learn More This essay on Business Case Model was written and submitted by user Kamila L. to help you with your own studies. You are free to use it for research and reference purposes in order to write your own paper; however, you must cite it accordingly. You can donate your paper here.

Free Essays on Ethics Of Globalization

Ethics of the Effects of Globalization Globalization is the process by which a business or company becomes international or starts to operate on an international level. Some economists recognize globalization as being in the best interest of all states. While others believe that increasingly liberated trade and global economic interaction is necessary in many ways. The negative effects of globalization far outweigh and short term gains. It benefits the wealthy, which are but a minority in comparison to the rest of the population, and leaves the impoverished ones out of the loop. The gap between rich and poor is increasing worldwide; almost one-third of the population of developing countries, 1.3 billion live in absolute poverty. Tight budgets, competitive markets, downsized companies are aspects of globalization that are unfolding on a canvas much broader than is generally appreciated. The unsteady flow of invisible money running in and out of countries has our markets operating like roller coasters. Globalization renders our government powerless and leaves them at the mercy of foreign investors. It does not benefit the majority of the world’s population and is slowly growing to increasingly deadly proportions. While globalization marks a move toward a more open world-trading regime, it can also be linked to strains on sovereignty, worker’s rights, and the environment. Globalization is a concept with many differing definitions. Many see it as a process, which entails the free movement of capital, goods, services and labor around the world. On the surface, it seems not as doing any harm but more of a way of doing business in the world today. For many major companies, going global is a matter of survival, and it means radically changing the way they work. Corporations are globalizing not only to reduce production costs, but also to expand markets, evade taxes, acquire knowledge and resources, and protect themselves ... Free Essays on Ethics Of Globalization Free Essays on Ethics Of Globalization Ethics of the Effects of Globalization Globalization is the process by which a business or company becomes international or starts to operate on an international level. Some economists recognize globalization as being in the best interest of all states. While others believe that increasingly liberated trade and global economic interaction is necessary in many ways. The negative effects of globalization far outweigh and short term gains. It benefits the wealthy, which are but a minority in comparison to the rest of the population, and leaves the impoverished ones out of the loop. The gap between rich and poor is increasing worldwide; almost one-third of the population of developing countries, 1.3 billion live in absolute poverty. Tight budgets, competitive markets, downsized companies are aspects of globalization that are unfolding on a canvas much broader than is generally appreciated. The unsteady flow of invisible money running in and out of countries has our markets operating like roller coasters. Globalization renders our government powerless and leaves them at the mercy of foreign investors. It does not benefit the majority of the world’s population and is slowly growing to increasingly deadly proportions. While globalization marks a move toward a more open world-trading regime, it can also be linked to strains on sovereignty, worker’s rights, and the environment. Globalization is a concept with many differing definitions. Many see it as a process, which entails the free movement of capital, goods, services and labor around the world. On the surface, it seems not as doing any harm but more of a way of doing business in the world today. For many major companies, going global is a matter of survival, and it means radically changing the way they work. Corporations are globalizing not only to reduce production costs, but also to expand markets, evade taxes, acquire knowledge and resources, and protect themselves ...

Evidence Burden Essay Example | Topics and Well Written Essays - 2500 words

Evidence Burden - Essay Example A defendant charged with murder could claim diminished responsibility or insanity1 permitting prosecution to adduce other defence and the same applies to unfitness to plead and stand trial. Woolmington ruling places the burden of proving on defendant2 and at times, had been questionable. Effect of Human Rights Act, 1998 on English Law had been extensive and the Courts3 have taken enormous trouble to read down legislations in order to avoid incompatibility with Convention Human Rights. Accused is innocent as long as he is proven otherwise4 and this enables the criminal statutes to transfer the burden of proof to the accused 'without violating the presumption of innocence'5. In the context of drug trafficking, Lord Hutton disagreed with other Law Lords stating that the social threat posed by drugs was sufficient justification for imposing persuasive burden6. Nowhere compatibility question was more relevant than in Sheldrake v DPP A-G's reference No 4 of 2002, where House of Lords unanimously held that Section 5(2) should not be read down. As per Terrorism Act, 2002, regarding the issue of being a member of terrorist organisations, House of Lords opined that 'Section 11(2) of the Act should be read and given effect as imposing on the defendant an evidential burden only7'. The Magistrates Courts Act, 1980 states that it is necessary to decide if the defendant is relying on exception, exemption, proviso, excuse or qualification, and if so, the burden of proof immediately will fall on him8. Environmental Protection Act, 1990 and its open connection with the Human Rights has become another area of legal difficulties and conflict between EU laws and UK laws9. Section 161 (1) of Highways Act 1980 provides the legal burden on the prosecution to prove that a person 'has left something suspicious or dangerous on the highway' and it has been slightly controversial10 where reverse onus of proof is concerned. Misdirection in a criminal trial on burden of proof can lead to a quashing of a conviction on an appeal11. In civil trials the party who asserts an issue also carries the burden of proving it. In a tort action for negligence the claimant does so and in a contract action, discharge of agreement or frustration, falls on the defendant12. If a particular issue is dependent on a substantive law, like lack of precedent, 'prove a positive' of 'prove a negative' might gain significance13. Privy Council had stated that burden of proof in mitigation of damage should be with defendant. Again the Common Law defences like self-defence, duress, provocation and non-insanity automatism come into picture. Instances of prosecution bearing the legal burden 'beyond reasonable doubt' and the degree of probability could wipe out the gingerly admitted evidence. The main question comes as whether the jury is satisfied that the guilt could be inadequate and usually the judge advises the jury beforehand14 and here Canadian justice differs from English law. Choo's argument that sometimes the proof of burden could be difficult to be proved depending on the circumstances and the rigid rule should be more flexible based on situations. I agree with all the above arguments of Andrew Choo. QUESTION 2: Evidence and proof in criminal proceedings and to a lesser extent, in civil proceedings are the

Logistics and Transportation as A Service Category within a Category Research Paper

Logistics and Transportation as A Service Category within a Category Management Program - Research Paper Example The intention of this study is Nexen. It is Canada based energy generation company having a dedicated workforce of about 3800 employees. In addition to this the company also has a strong and visionary management that helps in catapulting the organization to levels of excellence. The company was incepted in the year 1971 in which the Occidental crude oil company merged its subsidiary of energy and gas to create a conglomerate. The company is also engaged in the exploration of oil and gas and also owns gas fields across Canada. The future strategies of the company include investing in exploration in Mexican gulf, West Africa and North Sea. It also includes exploration of oil sands and unconventional gas fields across the nation.The company has a considerable and commendable supply chain management strategy under which the company focuses on using technology to reduce the cost of inventory. The logistics and supply chain aspects of the organization include management of the movement of goods from the source to the final destination. Transportation and its efficient management can help generate a lot of competitive advantage for the organization. The aspect of supply chain management is very closely linked to the aspect of warehouse maintenance, transportation as well as management of materials over distances. Use of global category management would help in generating not only cost advantage but would also help generate sustainable and long term competitive advantage for the organization. ... The logistics and supply chain aspects of the organization include management of the movement of goods from the source to the final destination. Transportation and its efficient management can help generate a lot of competitive advantage for the organization. The aspect of supply chain management is very closely linked to the aspect of warehouse maintenance, transportation as well as management of materials over distances. The present study would try to analyse the aspect of global category management in the supply chain strategies of the company that would help generate greater efficiency for the organization. Use of global category management would help in generating not only cost advantage but would also help generate sustainable and long term competitive advantage for the organization. Concept of Category Management Category Management program objectives are found to bear strong linkages with the product portfolio of a manufacturing or marketing sector company. In this regard, Ch iplunkar (2011) observes that the product portfolio of a company operating in manufacturing or retail segment is mostly decided by product managers. Product managers managing that category are responsible for getting the right amount and quality of raw materials for the production of such items. The responsibility for arranging the production of the product is shared eventually by the product managers with other departments like administrative and manufacturing units. Further the product manager also coordinates with the sales and marketing team for getting the product rightly sold in the market to help achieve business profits. The category management concept earns further depth in regards to

Mentorship in British Nursing Essay Example | Topics and Well Written Essays - 3750 words

Mentorship in British Nursing - Essay Example This research paper describes the field of nursing and the area of mentor contribution to development of clinical skills in nursing graduates. A mentor is cast in the mold of a teacher. In order to assess the impact of the mentor’s role in enhancing learning, it would be useful to explore how learning actually takes place. Book learning or assimilating theoretical principles are not in question here, since theories and knowledge from textbooks can at best, serve as a general guideline to a nurse faced with real life clinical situations. The ability to perform well in a clinical environment can be grasped only dimly from text book theory and cannot substitute for the valuable experience gained in a working situation under the guidance of a mentor, who functions as a teacher and a role model. The issue to consider here is the manner in which learning takes place and several theories have been presented in this regard. The mentor functions in the role of a demonstrator for a nurs ing student, facilitating learning through real life application of medical principles. But in addition, a mentor also functions as a guide for the nursing student, providing valuable feedback on the actual implementation of nursing principles as practiced by the student. On the job performance appraisals are an important learning tool for a nursing student. Feedback provided by a mentor serves as a valuable tool for the student to understand what he or she is doing wrong or right, so that corrections may be made appropriately.

Reception of photography

Reception of photography Using a broad range of critical, satirical, and photographic texts, assess the cultural reception of photography in the mid nineteenth century. The mid nineteenth century was a time of great technological advancement, and a more modern way of living came to be that bought with it significant cultural and social change. The industrial age was in full swing (as a consequence of the recent development of the steam engine), and photography was an exciting (but also intimidating) technology that caused incredible debate surrounds its status as an art form, and also the ethical and social issues its conception invoked. Although Daguerre/Fox Talbots Victorian audience were generally a receptive and willing one ready to embrace new and exciting technology (Goldberg 1991), there is significant evidence that shows a mixed cultural reception in regards to the emergence of early photographic processes. Wells (2004 p.12) states that: hailed as a great technological invention, photography immediately became the subject of debates concerning its aesthetic status and social uses Henisch (1994 pg.2) agrees stating intense controversies raged concerning its status and role in society. Photography had a huge impact on the Victorian society, and in 1839 artist Paul Delaroche is said to have claimed hysterically upon first seeing a daguerreotype photograph, from this day painting is dead. Japanese artist Renjio Shinoke also reportedly snapped his paintbrushes and become a pioneer of early Japanese photography (Eastman 1962). Whilst these examples are clearly overt exaggerations (almost to the point of satire) , they also highlight genuine fears and anxieties felt by artists (especially portrait) and critics alike, which stimulated and engaged the Victorian society in a plethora of debates surrounding the cultural, ethical and social impact the emergence of photography raised . The majority accepted its ability to record mechanically accurate images that are free of discrimination, but photographys status as an art form (or a creative medium) was much less certain , and something that was fiercely contested. Charles Baudelaire (1821-1867), a French Poet artist (and well known and very vocal critic of early photography) wrote: If photography is allowed to deputize for art, it will not be long before it has supplanted or corrupted art altogether (Baudelaire 1859 pg.297) Baudelaire suggests photography simply should not be allowed to supplant more traditional artistic methods, and to allow it do so would not only undermine, or negatively impact art, but corrupt it altogether. Baudelaire was not alone, as Goldberg (1991 pg.10) declares William Wordsworth shared in Baudelaires cynical view of photography, and in the 1840s penned a sonnet which declared the degradation of mans noblest attire', and expressed fears that a dumb art would lead his once-intellectual land back to the caves. Here Wordsworth is stipulating photographys potential to instigate the death of human intellect, and again, whilst such arguments are surely sensationalist, these declarations shows that not only was there an opposition to photographys ability to render art useless, but also a fear that its mechanical nature would dumb down society by removing a large part of the human aspect from the creative process. Both views show people believed (among what we can consider high artist s) that photography was a genuine threat to the fine arts of the time. Perhaps artists felt threatened by the technology? Threatened by its ability to so effortlessly paint reality, and ultimately achieve what they had been trying to do for long? Satirical publications in circulation in the mid nineteenth century, of which Punch magazine was the most popular, produced a number of cartoons highlighting these very issues. One such untitled illustration (1860 pg. 140) portrays a fashionable photographer forbidding smoking in his studio, as he declares himself not a common artist. Clearly an underhanded attack on the attitudes photographers took to their work which wasnt shared by their critics. Another satirical sketch, titled How the Famous Photographer Nadar Elevates Photography to the Level of Art show the French artist and photographer Fà ©lix Nadar taking to the sky in an air balloon, clutching a camera under his arm, physically lifting photography into the realms of high art. Su ch a picture of absurdity is surely meant to openly ridicule photography and its quest to be recognised as fine art. The latter picture serves a secondary purpose though, as Nadar was famous for his unsuccessful attempt to build a gigantic air balloon named Le Gà ©ant (or The Giant) around the same time as his photographic exploits. These are just two examples of many cartoons published around the mid nineteenth century that served to ridicule not only photographys quest for a higher status, but also many criticized the photographic studios and the rising popularity of carte de visite . In the photographic studios defence, famous photographic studio owner Richard Beard ran a series of advertisements for his business that served as much to promote his business as they did to promote photography as an art form. Close scrutiny of one of his earliest advertisements (Beard 1843) circulated in 1843 reveals the words Photography is indeed as grand a step in the fine arts as the steam engi ne was in the mechanical arts. This isnt to say everybody had difficulty accepting photography as true art, as many did indeed lament the skill that was required of a competent photographer, and the innate talent required to turn out a successful exposure. A Victorian periodical titled Once a Week published in 1862 states that To produce a good photograph, it requires a thoroughly artistic hand. Francious Argo (1930), when asked by the French government to assess the daguerreotypes successes concluded that M Daguerres wonderful discovery is an immense service rendered to art. This prompted the French government to subsidise Daguerre a pension of 6,000 francs for life, and his son 4,000 on the understanding they could use and adapt it for their own need (Goldberg 1991). Newell states that Argos memorandum mustnt be taken as a reflection of the attitudes of all artists to the new discovery. It appears that it was mainly established artists that held the biggest contempt for photograph y, and I believe not only suggests a fear for their livelihoods, but also a fear that the status of artist, usually reserved for a chosen few, would know be available to anyone with enough money to purchase a camera. It is difficult to truly gauge just how profoundly photography affected art in these early days, but it can be certain it was definitely believed at least possible by many that photography could be a form of artistic expression. as Goldberg (1981 pg.20) states photography and art have always been tangled, are tangled still. Millions of daguerreotype portrait photographs were taken in the 1840s and 1850s (to the dismay of photographys critics) as it began to supersede the more traditional painted portraitures. As Goldberg (1991 pg.12) states: After 1839 people who were not wealthy enough to commission portraits by a painter like Jean-Augusta-Dominique Ingres were no longer had to do with silhouettes and stiff pink renditions of their faces turned out by itinerant painters Portrait painters simply couldnt supply the demand necessary, and the affordability and fast turnaround of mainly studio based daguerreotype photographers (there were also the travelling carts) could offer was simply impossible to match. Photographic studios were the staple of early photography, the most famous of which were the Beard chain of studios (aptly ran by Richard Beard) which began opening in London in 1943. His studios were incredibly successful and lucrative business opportunity at the time, as the deal he made with Daguerre (who held the patent to his process) ensured his studios were the only ones in the UK throughout the early years of photography. Punch magazine (18 ran numerous satirical cartoons that highlighted what appears to be a clear distaste for the photographic studio. One cartoon named Step in, and be done sir! features a cat trying to lure a mouse into a photographic studio. More an echo of the society in which photography was operating, this piece could be looked at in a number of different ways. Perhaps the photographer being the cat (fat cat) and the enchanted lower/middle classes being the mice, echoing how the sitters are led into the studios under what could be considered false pretences in order to have their money relieved of them. Julia F Munro (2009 pg.167) states: George Dodd personified the by-then popular process of photography as the optical stranger, and as [s]trange, scientific, mournful, all at once. Such a figuration typifies the Victoria reaction to the uncanny qualities of the new technology. This statement was retrieved from an article entitled Busy with the photograph, published on April 29th 1854, and encapsulates the mixed reactions of the Victorian public towards early photography and more importantly the photographic studio. The idea of the optical stranger was one that was re-enforced by La Gazette de France in 1839, as they declared the invention of photography upsets all scientific theories of light and optics. The whole act of having ones picture taken was seen by many as a mysterious and bizarre concept, and the resulting exposures were often cited as too-real images (Munro 2009 p.168) and encouraged diverse reaction, ranging from that of excitement, to anxiety and fear, often leading to suggestions of magic (the transfiguration of the common photographer to the role of a magician or illusionist). Literature from the mid nineteenth century is rife with personal accounts of visits to local daguerreotype photographers studios and the wonders of photography. A le tter, published in the Times newspaper in 1852, where-by a middle aged man talks of his recent visit to a photography studio discusses how with a fluttering heart he approaches the mysterious apartment. He is of course simply referring to a typical early photographic studio setup, but these anxieties were very real for the everyday person. Another letter, written by a women this time, was published in the Times newspaper in 1854 describes the photographer disappearing into a mysterious closet and alludes to some hocus pocus being indulged in before he returns with the exposed plate. The photos were perceived as taking on a life of their own to a naive Victorian subject. The tone and lack of colour often provoked reactions of dismay, and many linked what were known as the dark mysterious chambers to execution houses (Munro 2009). The small stiff chairs (encouraging the sitter to sit upright), complete with leg clamps. Further controversy was sown by the nature of daguerreotype. Many referred the way a photograph could only be viewed in certain light, and as Munro (2009 pg.172) puts it seemingly wasnt to be seen one moment, only to burst into view the next. Being photographed and indeed even seeing a photograph were completely new and exotic experiences. For many Victorians, photography was too-real, and a large part of the fear was simply a natural reaction to the newness of the communicative medium, and novelty of a strange new and exotic process (Munro 2009 pg.169). The quoted realness of the photos could suggest a sense of fear relating to just how life like the photos were to a first time viewer, or suggest a much more deep routed fear related to magic and the unknown. It wasnt only the daguerreotype that achieved large scale success among the Victorian public. A large trade in what was known as carte de visite photographs soon came about after their circulation became widespread, as highlighted in the Victorian periodical Once a Week. Carte de visite photo graphs were small paper portrait photographs which usually originated from the albumen process (which allowed for paper based prints to be made from the negative, meaning it was a simple process to produce copies). Once a Week (1862 pg 135) states Literary men have a constant sale and their carte de visites were bought for every album. It becomes clear that collecting these small portrait photographs of the rich and famous was a popular pastime among the middle classes. It became so popular among the middle classes that it was often referred to as Cardomania (Once a Week 1862). We can clearly see that there was a need for photography, but these needs arose after its introduction and were not in place before its conception. There was certainly something about early photography which caused an anxiety in the general public, but also fascinated them enough to endure it (even embrace it). It is now widely accepted that photography wasnt truly discovered until 1839, as it was then that Daguerre and Fox Talbot made their discoveries of early photographic processes, the daguerreotype and calotype respectively, and shared them with the world. Goldberg (1991) agrees that it was much earlier when people began to realise a need and take interest in using light as a way of recording images, the need to preserve a moment accurately and without discrimination. Goldberg (1991 pg.10) goes on to state that desire was abroad to catch nature in a net, and that photography came to serve a much needed purpose, one that had been recognised much earlier that its first conception. Indeed as early as the late eighteenth century, devices such as the camera obscura (optical device used mainly to aid drawing) and camera lucida (a piece of technology which allowed artists the ability to precisely record contours of landscape) were rife, and captured the eye of professional and amateur artists alike. Henry Fox Talbot (1800-1877), sometimes referred to as the Grandfather of Photography, was one of many people searching for an answer to the void that existed before the conception of photography, and was most interested in its ability to record nature accurately. Talbot states is his manual The Pencil of Nature (1844) that his photography should be thought of as photogenic drawing. Talbot (1844) goes on to say he pursued his development of the calotype photographic process mainly as a result of his poor ability as an artist. Lewis (1996 pg.16) states: The canon of images to which we are so attached reveals as much and perhaps more about the intervening century Talbots photography, The Open Door for instance, appears to serve very little artistic purpose, and could merely be interpreted as a mechanically accurate recording, something he was simply incapable of doing by hand. On the other it could be seen as an example of how photography could supplant the more traditional arts, an early example of the photographers ability to shape, to frame, and to manipulate reality how he saw fit. We may never know, as whilst we are able to appreciate early photographs, it is impossible to know the original context, how they were read, and indeed, what made them meaningful to the society of which they were a product. It is even more difficult to gauge the early intentions of photographic pioneers. Many widely believed that photography was going to bring a truth to society that had never been seen, its potential as a truth bearer, and an accurate recorder of history. Ernst Mach, an Austrian empiricist (ironically) stated How tranquil politics will be!, an d even the notorious critic Baudelaire (1859 pg. 297) stated photography could be considered a handmade of the arts and sciences although he goes on to say a very humble handmaid. Society became increasingly aware of its benefits as a scientific tool and embraced the possibilities this afforded with open arms: A new found purpose perhaps, a commitment to relating to truth? As Goldberg (1981 pg. 16) states: The engine was an extension of the muscle, the telegraph a superhuman voice, and the photograph an unblinking eye with a new outlook on history and knowledge Baudelaire (1859) also suggests photography was merely a sign of the times, showing that links were made between the mechanical nature of photography and societies rising industrial prowess and reliance on machines. The unstoppable rise of industry so to speak. Wells (2004) states a society will also invest and put time into developing new technologies in order to help satisfy previously unseen social needs, and goes on to summarise (2004 pg. 12) that photography was a consequence, and not a cause of culture. I believe that photography was not a cause of change, but an answer to an unforeseen social need brought about by the emerging modern metropolitan lifestyle. It has become clear to me that there certainly was a need for photography, and the Victorians were fascinated with it, whether they loved it or hated it. As Bede (1855) begins is his satirical book Photographic Pleasure with a metaphor comparing men and womens intrigue with photography to the same intrigue they hold for a h uman child: The ladies are enamoured of him: The gentlemen evince their affection by suggestions for his improvement, and by general attention to his welfare.All are fond of him: everyone is declaring that he is the most beautiful baby yet born to Science. It is entirely feasible that the reason it raised such widespread controversy, why it was so widely debated, and ultimately why it was so popular as an amateur hobby or leisure pursuit was simply because the technology was still in its infancy. It was still new, and fresh. Artists were fearful of photography , not only because their jobs were endangered, but also their status as artists. A profession usually only available to a truly gifted few now had the potential to be available to anyone. These critics only served to fuel the anxieties that were common place among the general public, but, despite this, the public did allow photography room to grow (albeit carefully, and with great caution and concern). It was a new technology which people needed time to come to terms with, time to understand, and time to flourish and co-exist peacefully with other more established art forms in the new, fast paced, and modern Victorian metropolitan lifestyle. Bibliography WELLZ, L. 2004. Photography: A critical introduction. Oxford: Routledge. CLARKE, G. 1997. The Photograph. Oxford: Oxford University Press. BAUDELAIRE, C. 1859. The Salon of 1859. Unknown. BRIGGS, A. 1998. A Victorian Portrait. London: Cassell Publishers Limited. GOLDBERG, V. 1991. The Power of Photography: How photographs changed our lives. New York: Abbeville Publishing Group. BEARD, R. 1843. Advertisement [Accessed 2rd December 2009]. Available from: http://www.gettyimages.com/detail/73604552/Hulton-Archive GOLDBERG, V. 1981. Photography in Print: Writings from 1816 to the present. New York: University of New Mexico Press GREEN-LEWIS, J. 1996. Framing the Victorians. New York: Cornell University Press. HEINZ, K. 1994. The Photographic Experience 1839-1914. Pennsylvania: Pennsylvania State University Press. MARIEN, M. 1997. Photography and its Critics. Cambridge: Cambridge University Press. MUNRO, J. F. July 2009 The Optical Stranger: Photographic anxieties in British periodical literature of the 1840s and 1850s. Journal of early popular visual culture 7(2) pp167-183. UNKNOWN. 1860 Punch magazine October 6th. p.140 UNKNOWN. 1861 Punch magazine June 1st pg.221 ARGO, F. 1930 Bulletin de la Socià ©tà © Fran?aise de Photographie NEWELL, B., and R. DOTY. 1962. The value of photography to the artist, 1839. The Bulletin of the George Eastman House of Photography [online]. 11 (6), [Accessed December 2nd 2009], pp. 25-40. Available From: http://image.eastmanhouse.org/files/GEH_1962_11_06.pdf Daumier, H. 1862. How the Famous Photographer Nadar Elevates Photography to the Level of Art [Accessed 3rd December 2009]. Available from: http://www.superstock.com/stock-photos-images/463-5227 BEDE, C. 1855. Photographic Pleasures. London: T McLean. UNKNOWN. 1862 Once a Week. Unknown TALBOT, H. F. 1844. The Open Door [Accessed 4th December 2009]. Available from: http://cai.ucdavis.edu/waters-sites/aesthetic_movement/opendoorphoto.jpg BEARD, R. 1843. Advertisement [Accessed 2rd December 2009]. Available from: http://www.gettyimages.com/detail/73604552/Hulton-Archive Daumier, H. 1862. How the Famous Photographer Nadar Elevates Photography to the Level of Art [Accessed 3rd December 2009]. Available from: http://www.superstock.com/stock-photos-images/463-5227 TALBOT, H. F. 1844. The Open Door [Accessed 4th December 2009]. Available from: http://cai.ucdavis.edu/waters-sites/aesthetic_movement/opendoorphoto.jpg

Does Beowulf evoke a human element that allows the reader to associate :: Epic of Beowulf Essays

Does Beowulf evoke a human element that allows the reader to associate with the plot? If so, then how does such humanity affect the story? There is a human element in Beowulf that transcends time. It is a portrayal of emotions common to the human experience of life that allow Beowulf to evoke a response from all. The human element within the epic story of Beowulf is characterized by Hrothgar. Hrothgar is the most human character in the poem. He is the person with whom we can most easily identify. By not being afraid to hide his emotions in a society where it is a sign of weakness for a man to show his feelings, gives him perhaps not a heroic quality of his own , but a quality nonetheless – the quality of human nature. The virtues of a good warrior are wisdom and courage. A good king must possess not only these qualities, but he also must be concerned for the welfare of his people. Hrothgar possesses wisdom, but his courage is lacking. However upon closer inspection of the prose, one begins to see Hrothgar not as a coward, but as a symbol of basic human reaction. For example, when Grendel attacks the hall, all Hrothgar can do is hold his head in despair. While others react in violence when threatened, Hrothgar lacks the strength to do so. Although it is not a celebrated virtue of human nature, all can relate to the feeling of despair that arises when a positive solution to a negative situation is beyond one’s immediate control/ In another situation, after Grendel's mother attacks the hall and escapes with the body of Esher, we see Hrothgar trembling "in anger and grief". When Beowulf comes to find out what's wrong, Hrothgar practically begs him to kill the monster. His grief, at this point, verges on hysteria. This point in the epic allows the readers to bring the story back to something that they can relate to, a focal point. By being able to tap into the feelings expressed by Hrothgar, one can truly understand how helpless this once strong king must feel. The emotions of Hrothgar also allow the reader to compare him to Beowulf who shuns such emotional outbursts and who isn’t wise enough to realize his shortcomings due to age. Instead of admitting that he is too old to protect his country, Beowulf attempts to relive his youth by fighting the dragon.

History of Trigonometry

Running Head: History of Trigonometry History of Trigonometry Rome Fiedler History of Mathematics 501 University of Akron April 29, 2012 History of Trigonometry: An Introduction Trigonometry is useful in our world. By exploring where these concepts come from provides an understanding in putting this mathematics to use. The term Trigonometry comes from the Greek word trigon, meaning triangle and the Greek word meatria meaning measurement. However it is not native to Greek in origin. The mathematics comes from multiple people over a span of thousands of years and has touched over every major civilization.It is a combination of geometry, and astronomy and has many practical applications over history. Trigonometry is a branch of math first created by 2nd century BC by the Greek mathematician Hipparchus. The history of trigonometry and of trigonometric functions sticks to the general lines of the history of math. Early research of triangles could be found in the 2nd millennium BC, in Egyp tian and Babylonian math. Methodical research of trigonometric functions started in Greek math, and it reached India as part of Greek astronomy.In Indian astronomy, the research of trigonometric functions flourished in the Gupta dynasty, particularly as a result of Aryabhata. Throughout the Middle Ages, the research of trigonometry continued in Islamic math, while it was implemented as a discrete subject in the Latin West beginning in the Renaissance with Regiomontanus. The growth of contemporary trigonometry shifted in the western Age of Enlightenment, starting with 17th-century math and reaching its contemporary type with Leonhard Euler (1748) Etymology The word â€Å"trigonometry† originates from the Greek â€Å"trigonometria†, implying â€Å"triangle measuring†, from triangle + to measure.The name developed from the study of right triangles by applying the relation ships between the measures of its sides and angles to the study of similar triangles (Gullberg , 1996). The word was introduced by Barthoolomus ptiticus in the title of his work Trigonometria sice de solutione triangularumtractus brevis et perspicius†¦ in 1595. The contemporary word â€Å"sine†, is originated from the Latin word sinus, which implied â€Å"bay†, â€Å"bosom† or â€Å"fold†, translation from Arabic word jayb. The Arabic word is in origin of version of Sanskrit jiva â€Å"chord†.Sanskrit jiva in learned used was a synonym of jya â€Å"chord†, primarily the word for â€Å"bow-string†. Sanskrit jiva was taken into Arabic as jiba (Boyer, 1991). This word was then changed into the real Arabic word jayb, implying â€Å"bosom, fold, bay†, either by the Arabs or erroneously of the European translators such as Robert of Chester, who translated jayb into Latin as sinus. In particular Fibonacci's sinus rectus arcus was significant in creating the word sinus. Early Beginnings The origin of the subject has rich di versity. Trigonometry is not the work of one particular person or place but rather a development over time.The primitive Egyptians and Babylonians had known of theorems on the ratios of the sides of analogous triangles for many centuries. However pre-Greek societies were deficient of the concept of an angle measure and as a result, the sides of triangles were analyzed rather, a field that would be better known as â€Å"trilaterometry†(Boyer, 1991). The Babylonian astronomers kept comprehensive records on the rising and setting of stars, the movement of the planets, and the solar and lunar eclipses, all of which needed knowledge with angular distances measured on the celestial sphere.Founded on one explanation of the Plimpton 322 cuneiform tablet, some have even claimed that the primitive Babylonians had a table of secants. There was, on the other hand, much discussion as to whether it is a table of Pythagorean triples, a solution of quadratic equations, or a trigonometric tab le. The Egyptians, in contrast, applied an ancient kind of trigonometry for construction of pyramids and surveying the land in the 2nd millennium BC. The early beginnings of trigonometry ar thought to be the first numerical sequences correlating shadow lengths to time of day.Shadow tables were simple sequences of numbers which applied the shadow of a vertical stick, called a gnomon, is long in the morning and shortens to a minimum at noon. Then becomes longer and longer as the afternoon progresses (Kennedy, 1969). The shadow tables would correlate a particular hour to a particular length and were used as early as 1500 BC by the Egyptians. Similar tables were developed by other civilizations such as the Indians and Greeks. Greek mathematics Shadow tables were the primary development in creation of trigonometry however the Greeks really developed Trigonometry into an ordered science.The Greeks continued as the Babylonians astronomers did and studied the relation between angles and cir cles in lengths of chords to develop their theories on planetary position and motion (Mankiewicz, 2001). [pic] The chord of an angle subtends the arc of the angle. Ancient Greek mathematicians used the chord. Given a circle and an arc on the circle, the chord is the line that subtends the arc. A chord's perpendicular bisector traverses the center of the circle and bisects the angle. One half of the bisected chord is the sine of the bisected angle, that is, [pic] nd consequently the sine function is also known as the â€Å"half-chord†. As a result of this relationship, several trigonometric identities and theorems that are known at present were also known to Greek mathematicians, however in their equivalent chord form. Though there is no trigonometry in the works of Euclid and Archimedes, there are theorems presented in a geometric method that are similar to particular trigonometric laws or rules. Theorems on the lengths of chords are applications of the law of sines. In addit ion Archimedes' theorem on broken chords is similar to rules for sines of sums and differences of angles.From the primitive landmarks of shadow tables and the Greeks’ gain and expansion of astronomical knowledge from the Babylonians, there was a gap in the improvement of trigonometry until the time of Hipparchus. Hipparchus The first trigonometric table was in fact compiled by Hipparchus of, who is known as an as â€Å"the father of trigonometry†(Boyer, 1991). Hipparchus was the first to put into a table the corresponding values of arc and chord for a series of angles. He did this by considering every triangle was inscribed in a circle of fixed radius. Each side of the triangle became a chord, a straight line drawn between two points on a circle.To find the parts of the triangle he needed to find the length of the chord as a function of the central angle. [pic] For Example, in the diagram triangle ACB is? inscribed in circle O. So the sides of the triangle become chord ? AC, chord CB and chord AB. Hipparchus would have sought to? find the length of the chord, AC, as a function of the central? angle. He deduced a trigonometric formula for the? length of a chord sketched from one point on the circumference of? a circle to another (Motz, 1993). This could therefore be used to help understand the positioning of the planets on the sphere.Though it is not known when the methodical use of the 360 ° circle came into math, it is known that the methodical introduction of the 360 ° circle introduced a little after Aristarchus of Samos comprised of On the Sizes and Distances of the Sun and Moon, since he measured an angle a part of a quadrant. It seemed that the systematic used of the 360 ° circle was mainly as a result of Hipparchus and his table of chords. Hipparchus might have taken the idea of that division from Hypsicles who had previously divided the day into 360 parts, a division of the day that might have been recommended by Babylonian astronomy .In primeval astronomy, the zodiac had been divided into twelve â€Å"signs† or thirty-six â€Å"decans†. A recurring cycle of approximately 360 days could have corresponded to the signs and decans of the zodiac by dividing each sign into 30 parts and each decan into 10 parts. It was as a result of the Babylonian sexagesimal numeral system that each degree was divided into 60 minutes and each minute was divided into 60 seconds. Though Hipparchus is attributed as the father of trigonometry all of his work is lost except one but we gain knowledge of his work through Ptolemy. [pic] http://www. ies. co. p/math/java/vector/menela/menela. html Menelaus Menelaus of Alexandria wrote in three books his Sphaerica. In Book I, he created a basis for spherical triangles analogous to the Euclidean basis for plane triangles. He established a theorem that is without Euclidean analogue, that two spherical triangles were similar if corresponding angles are equal, however he did not diff erentiate between congruent and symmetric spherical triangles. Another theorem that he established was that the sum of the angles of a spherical triangle is more than 180 °. Book II of Sphaerica applied spherical geometry to astronomy.In addition Book III contained the â€Å"theorem of Menelaus†(Boyer, 1991). He further gave his well-known â€Å"rule of six quantities†(Needham, 1986). This theorem came to paly a major role in spherical trigonometry and astronomy. It was also believed that Melaus mya have developed a second table of chords based on Hipparchus works, however these were lost (Smith, 1958). Ptolemy Afterwards, Claudius Ptolemy developed upon Hipparchus' Chords in a Circle in his Almagest, or the Mathematical Syntaxis. The Almagest was mainly a work on astronomy, and astronomy relied on trigonometry.The 13 books of the Almagest were the most prominent and important trigonometric work of ancient times. This book was a composition of both astronomy and trig onometry and was derived from the work of Hipparchus and Menelaus. Almagest contains a table of lengths of chords in a circle and a detailed set of instructions on how to construct the table. These instructions contain some of the earliest derivtions of trigonometry. Ptolemy distinguished that Menelaus started by dividing a circle into 360o, and the diameter into 120 parts. He did this because 3 x 120 = 360, using the previous application of 3 for pi.Then each part is divided into sixty parts, each of these again into sixty parts, and so on. This system of parts was based on the Babylonian sexagesimal or base 60-numeration system, which was the only system available at the time for handling fractions (Maor, 1998). This system was based on 60 so that the number of degrees corresponding to the circumference of a circle would be the same as the number of days in a year, which the Babylonians believed to be 360 days (Ball 1960). From Menlaus Ptolemy developed the concept that the sine i s half of a chord.Ptolemy took Menelaus’ construction _ crd  · 2_ and said that the complement angle could be written as _ crd  · (180 o -2_), since 180o was half the circumference of the circle. Since today, cos_ = sin(90 o -_), it can be shown that cos_ = _ crd  · (180 o -2_), using a similar argument as the one shown above (van Brummelen, 2009). From these two expressions, one of the greatest identities known today was created. That is, (_ crd  · 2_) 2 + {_ crd  · (180 o -2_)} 2 = 1 which is exactly sin2_ + cos2_ = 1 (van Brummelen, 2009). [pic]http://nrich. maths. org/6853 [pic] http://en. ikipedia. org/wiki/Ptolemy's_table_of_chords Using his table, Ptolemy believed that one could solve any planar triangle, if given at least one side of the triangle (Maor, 1998). A theorem that was fundamental to Ptolemy's calculation of chords was what was still known at present as Ptolemy's theorem, that the sum of the products of the opposite sides of a recurring quadrilater al was equivalent to the product of the diagonals. Ptolemy used these results to develop his trigonometric tables; however whether these tables were originated from Hipparchus' work could not be proved.Neither the tables of Hipparchus nor those of Ptolemy had survived to the present day, though descriptions by other ancient authors exhibits they existed. In his work, Ptolemy founded formulas for the chord of? difference and an equivalent for our modern day half-angle? formulas. Because of Ptolemy’s discoveries, given a chord of? an arc in a circle, the chord of half an arc can be determined as? well. Ptolemy also discovered chords of sum and difference, chords of half an arc, and chords of half degree, from which he then built up his tables to the nearest second of chords of arcs from half degree.In the Almagest, a true distinction was made between plane and spherical trigonometry. Plane trigonometry is the branch of trigonometry which applies its principles to plane triangle s; Spherical trigonometry, on the other hand, is the branch of trigonometry in which its principles are applied to spherical triangles, which are triangles on the surface of the sphere. Ptolemy began with spherical trigonometry, for he worked with spherical triangles in many of his theorems and proofs. However, when calculating the chords of arcs, he unintentionally developed a theory for plane trigonometry. Trigonometry was created for use in astronomy; and because spherical trigonometry was for this purpose the more useful tool, it was the first to be developed. The use of plane trigonometry†¦ is foreign to Greek mathematicians† (Kline, 1972). Spherical trigonometry was developed out of necessity for the interest and application of astronomers. In fact, spherical trigonometry was the most prevalent branch of trigonometry until the 1450s, even though Ptolemy did introduce a basis for plane trigonometry in the Almagest in 150 A. D. IndiaThe next major contribution to trig onometry came from India. The trigonometry of Ptolemy was based on the functional relationship between chords of a circle and central angles they subtend. The Siddhantas, a book thought to be written by Hindu scholars in late fourth century, early fifth century A. D. , changed Ptolemy’s trigonometry to the study of the relationship between half of a chord of a circle and half of the angle subtended at he center by the whole chord (Kennedy, 1969). This came from the basis for the modern trigonometric function known as the sine.The Siddhantas introduction to the sine function is the chief contribution from India and marks a transformation in trigonometry. Indian mathematicians also contributed by creating their own sine table. Arya-Bhata, born in 476, was a great Indian mathematician and astronomer (Ball, 1960). He composed a book called Aryabhathiya, which contained most of the essential ideas we associate with sine and cosine. His most outstanding contribution to the topic, w hich distinguishes him from the other mathematicians of this time, was his work on sine differences (van Brummelen, 2009).His definition of sine was literally â€Å"half chord† and was abbreviated jya or jiva, which simply meant, â€Å"chord† (Smith 615). Sines were given in minutes, at intervals of 225 minutes. This measurement was not of the sines themselves, but instead, it was the measurement of the differences between the sines. His method of calculating them was as follows. The first sine was equal to 225. The second sine was defined as any particular sine being worked with in order to calculate the sine that directly follows (Clark 29).It was found using the following pattern: (225 – the previous sine) + (225 + the previous sine) 225 this total was then subtracted from 225 to obtain the sine table. Second sine: 225 – 225 = 0 225 / 225 = 1 0 + 1= 1 225 – 1 = 224 Third sine:? 225 – 224 = 1 (225 + 224) / 225 ? 2 225 – 2 = 222 (van Brummelen, 2009). Arya-Bhata concluded that dividing a quarter of the circumference of a circle (essentially one quadrant of the unit circle) into as many equal parts, with the resulting triangles and quadrilaterals would have, on the radius, the same amount of sines of equal arcs.Doing this, he was able to form a table of natural sines corresponding to the angles in the first quadrant (van Brummelen, 2009). Although much of his work had the right idea, many of Arya-Bhata’s calculations were inaccurate. Later, in 1150AD, an Indian mathematician known as Bhaskara gave a more accurate method of constructing a table of sines, which considered sines in every degree (van Brummelen, 2009). Although the Indian mathematicians made attempts at creating a table to help with astronomy, their table of sines was not as accurate as that of the Greeks. Islamic mathematicsThe ancient works were translated and developed in the medieval Islamic world by Muslim mathematicians of mostly Persian and Arab descent, who explained a large number of theorems which freed the subject of trigonometry from reliance upon the complete quadrilateral, as was the case in Greek mathematics as a result of the application of Menelaus' theorem. In accordance with E. S. Kennedy, it was following that development in Islamic math that â€Å"the first real trigonometry appeared, in the sense that only then did the object of study become the spherical or plane triangle, its sides and angles† (Kennedy, 1969).E. S. Kennedy pointed out that whilst it was possible in pre-Islamic math to calculate the magnitudes of a spherical figure, in theory, by use of the table of chords and Menelaus' theorem, the application of the theorem to spherical problems was very complex actually (Kennedy, 1969). With the aim of observing holy days on the Islamic calendar in which timings were established by phases of the moon, astronomers at first used Menalaus' method to compute the place of the moon and stars, a lthough that method proved to be ungainly and complex.It engaged creation of two intersecting right triangles; by applying Menelaus' theorem it was possible to solve one of the 6 sides, however only if the other 5 sides were known. To tell the time from the sun's elevation, for example, repeated applications of Menelaus' theorem were needed. For medieval Islamic astronomers, there was a clear challenge to find a simpler trigonometric rule (Gingerich, 1986). In the early 9th century, Muhammad ibn Musa al-Khwarizmi c a Persian Mathematician, was an early pioneer in spherical trigonometry and wrote a treatise on the subject creating accurate sine and cosine tables.By the 10th century, in the work of Abu al-Wafa' al-Buzjani, another Persian Mathematician established the angle addition formulas, e. g. , sin(a + b), and discovered the sine formula for spherical trigonometry. Abu’l-Wafa is believed to have helped introduced the concept of the tangent function. He also may have had s omething to do with the development of secant and cosecant. His trigonometry took on a more systematic form in which he proved theorems for double and half angle formulas. The law of sines, is also attributed to Abu’l-Wafa, even? hough it was first introduced by Ptolemy. This is in part? due to the fact that Abu’l-Wafa presented a? straightforward formulation of the law of sines for? spherical triangles, which states [pic] where A, B, and C are surface angles of the spherical? triangle and a, b, and c are the central angles of the? spherical triangle. In 830, Habash al-Hasib al-Marwazi created the first table of cotangents. Muhammad ibn Jabir al-Harrani al-Battani found the reciprocal functions of secant and cosecant, and created the first table of cosecants for each degree from 1 ° to 90 °.By 1151 AD, the ideas of the six trigonometric functions existed, they were just not named as we know them today. Europe It is from the Arabic influence that trigonometry reache d Europe. Western Europe favored Arabic mathematics over Greek geometry. Arabic arithmetic and algebra were on a more elementary level than Greek geometry had been during the time of the Roman Empire. Romans did not display much interest in Greek trigonometry or any facets of Greek math. Therefore, Arabic math appealed to them since it was easier for them to comprehend.Leonardo Fibonacci was one mathematician who became acquainted with trigonometry during his extensive travels in Arab countries. He then presented the knowledge he gained in Practica geometriae in 1220 AD (Gullberg, 1996). The first distinction of trigonometry as a science separate from astronomy is credited to the Persian, Nasir Eddin. He helped to differentiate plane trigonometry and spherical trigonometry. Other than that, little development occurred from the time of the 1200’s to the 1500’s, aside for the developments of the Germans in the late 15th and early 16th century.Germany was becoming a prosp erous nation at the time and was engaged in much trade. Their interests also developed in navigation, calendar formation, and astronomy. This interest in astronomy precipitated a general interest and need for trigonometry (Kline, 1972). Included in this movement around the time of 1464, the German astronomer and mathematician, Regiomontanus (also known as Iohannes Molitoris) formulated a work known as De Triangulis Omnimodis, a compilation of the trigonometry of that time.When it was finally printed in 1533, it became an important medium of spreading the knowledge of trigonometry throughout Europe (Gullberg, 1996). The first book began with fifty propositions on the solutions of triangles using the properties of right triangles. Although the word â€Å"sine† was derived from the Arabs, Regiomontanus read the term in an Arabic manuscript in Vienna and was the first to use it in Europe. The second book began with a proof of the law of sines and then included problems involving how to determine sides, angles, and areas of plane triangles.The third book contained theorems found on Greek spherics before the use of trigonometry, and the fourth was based on spherical trigonometry. In the sixteenth century, Nicholas Copernicus was a revolutionary astronomer who could also be deemed as a trigonometer. He studied law, medicine and astronomy. He completed a treatise, known as De revolutionibus orbium coelestium, the year he died in 1543. This work-contained information on trigonometry and it was similar to that of Regiomontanus, although it is not clear if they were connected or not.While this was a great achievement, Copernicus’ student, Rheticus, an Indian mathematician, who lived during the years 1514-1576, went further and combined the work of both these men and published a two-volume work, Opus palatinum de triangulus. Trigonometry really began to expand and formalize at this point as the functions with respect to arcs of circles were disregarded. Fran cois Viete who practiced law and spent his leisure time devoted to mathematics also . contributed trigonometry around this time. He came to be known as â€Å"the father of the generalized analytic approach to trigonometry† (Boyer, 1991).He thought of trigonometry as? an independent branch of mathematics, and he worked? without direct reference to chords in a circle. He made? tables for all six trigonometric functions for angles to the? nearest minute. Viete was also one of the first to use the? formula for the law of tangents, which states the following: [pic] Viete was one of the first mathematicians to focus on analytical trigonometry, the branch of trigonometry which focuses on the relations and properties of the trigonometric functions.This form of trigonometry became more prevalent around the time of 1635 with the work of Roberval and Torricelli. They developed the first sketch of half an arch of a sine curve. This important development assisted in the progression of tri gonometry from a computational emphasis to a functional approach. This formed the basis of the European contribution of trigonometry. From the influence of oriental scientists, the Europeans focused on the computation of tables and the discovery of functional relations between parts of triangles.Europe developed appropriate symbols, which replaced the verbal rules and ordinary language in which the subject was usually presented. Previously, trigonometry was expressed in lengthy passages of confusing words, but the Europeans introduced such symbols as sin, cos, tan, etc. to simplify the subject and make it more concise. Prior to the analytic approach, the main usage of trigonometry was to measure geometric figures, but the transition of its influence from geometry to calculus began with the discovery of infinite series representations for the trigonometric functions.Trigonometric series became useful in the theory of astronomy, around the time of the eighteenth century. Since astrono mical phenomena are periodic, it was useful to have trigonometric series because they are periodic functions as well. The use of trigonometric series was introduced to determine the positions of the planets and interpolation, which is a mathematical procedure that estimates the values of a function at positions between given values (Kline, 1972). Many continued to make contributions to Trigonometry looking for more accurate tables to determine the six functions.These works continued up until the invention of the Scientific Calculator in 1968. In society today, trigonometry is used in physics to aide in the understanding of space, engineering and chemistry. Within mathematics it is typically seen in mainly in calculus, but also in linear algebra and statistics. Despite the minimal information available on the history of Trigonometry it is still a vital part of mathematics. The History shows progression from astronomy and geometry and the movement from spherical to plane geometry.Toda y, Trigonometry is used to understand space, engineering, chemistry as well as mathematics. By exploring the history of trigonometry we see the importance of it in our world. References Boyer, Carl B. (1991), A History of Mathematics (Second ed. ). John Wiley & Sons, Inc. 3 Bressoud, D. M. (2010). Historical Refelctions on Teaching Trigonometry. Mathematics Teacher, 104 (2), 106-112. Brummelen, G. V. (2009). The Mathematics of the Heavens and the Earth. Princeton, NJ: Princeton University Press. Gingerich, Owen (1986), â€Å"Islamic astronomy†. Scientific American 254 (10): 74.Gullberg, Jan. (1996)Mathematics from the Birth Of Numbers. New York:W. W. Norton and Company, Inc. Joyce, D. E. (n. d. ). History of Trigonometry Outline. Retrieved 3 21, 2012, from History of Trigonometry Outline: http://aleph0. clarku. edu/~djoyce/ma105/trighist. html Kennedy, E. S. (1969), â€Å"The History of Trigonometry†. 31st Yearbook (National Council of Teachers of Mathematics, Washingt on DC) (cf. Haq, Syed Nomanul. The Indian and Persian background. pp. 60–3, in Seyyed Hossein Nasr, Oliver Leaman (1996). History of Islamic Philosophy. Routledge. pp. 52–70.Kline, Morris. (1972) Mathematical Thought from Ancient to Modern Times. New York: Oxford University Press. Kluemper, A. (2010, 3 24). History of Trigonometry. Retrieved 3 5, 2012, from www. xtimeline. com: http://www. xtimeline. com/timeline/History-of-Trigonometry Mankiewicz, Richard. (2001)The Story of Mathematics. New Jersy:Princetion University Press. Maor, E. (1998). Trigonometric Delights. New Jersey: Princeton University Press. Miller, S. (2001). Understanding Transformations of Periodic Functions through Art. Mathematics Teacher , 94 (8), 632-635.Moussa, Ali (2011), â€Å"Mathematical Methods in Abu al-Wafa's Almagest and the Qibla Determinations†. Arabic Sciences and Philosophy. Cambridge University Press. 21 (1): 1–56. Needham, Joseph (1986), Science and Civilization in Chi na: Volume 3, Mathematics and the Sciences of the Heavens and the Earth. Taipei: Caves Books, Ltd. Rogers, L. (n. d. ). The History of Trigonometry- Part 1. Retrieved 3 1, 2012, from Enriching Mathematics: http://nrich. maths. org/6843/index Suzuki, J. (2009). Mathematics in Historical Context. Washington D. C. : The Mathematical Association of America.Smith, D. E. (1958)History of Mathematics. New York:Dover Publications, Inc. Toomer, G. J. (1998), Ptolemy's Almagest, Princeton University Press. Weber, K. (2005). Students Understanding of Trigonometric Functions. Mathematics Education Research Journal , 17 (3), 91-112. www. cartage. org. (n. d. ). Trigonometry History. Retrieved 3 5, 2012, from Trigonometry History: http://www. cartage. org. lb/en/themes/sciences/Mathematics/Trigonometry/history/History%20. html van Brummelen, G. (2009)The Mathematics of the Heavens and Earth. Princeton University Press. Princeton and Oxford.

Major Battles of World War 2

Major Battles of World War 2 There were numerous battles in World War II. Some of these battles lasted only days while others took months or years. Some of the battles were notable for the material losses such as tanks or aircraft carriers while others were notable for the number of human losses. Although this is not a comprehensive list of all battles of WWII, it is a list of the major battles of World War II. A note about the dates: Somewhat surprisingly, historians dont all agree on the exact dates of battles. For instance, some use the date that a city was surrounded while others prefer the date that major fighting commenced. For this list, I have used the dates that seemed the most agreed upon. 20 Major Battles of World War II Battles Dates Atlantic September 1939 - May 1945 Berlin April 16 - May 2, 1945 Britain July 10 - October 31, 1940 Bulge December 16, 1944 - January 25, 1945 El Alamein (First Battle) July 1-27, 1942 El Alamein (Second Battle) October 23 - November 4, 1942 Guadalcanal Campaign August 7, 1942 - February 9, 1943 Iwo Jima February 19 - March 16, 1945 Kursk July 5 - August 23, 1943 Leningrad (Siege) September 8, 1941 - January 27, 1944 Leyte Gulf October 23-26, 1944 Midway June 3-6, 1942 Milne Bay August 25 - September 5, 1942 Normandy (including D-Day) June 6 - August 25, 1944 Okinawa April 1 - June 21, 1945 Operation Barbarossa June 22, 1941 - December 1941 Operation Torch November 8-10, 1942 Pearl Harbor December 7, 1941 Philippine Sea June 19-20, 1944 Stalingrad August 21, 1942 - February 2, 1943

buy custom Imaging Services Radiology essay

buy custom Imaging Services Radiology essay The role of imaging is now becoming ever more important in patient management. With the now widespread use of different imaging techniques, it has become clear that there are several ways of investigating the same condition through diagnostic imaging. Diagnostic imaging is a term used to refer to those technologies used by doctors in examining the body to establish any medical condition (Armstrong, Wastie Rockall, 2004). There are various machines and techniques that can create pictures of the human body. Doctors use various technologies in examining the body for clues about a medical condition. Many diagnostic imaging tests are painless and easy. Nevertheless, they may require one to stay for a long time in the machine. The science of radiology has its beginning towards the end of the 19th century when a Dutch physicist, Wilhelm Conrad Roentgen, discovered a form of radiation that he named x-ray since he could not understand its nature (Armstrong, Wastie Rockall, 2004). In the first decade of the discovery of x-ray, the physical effects of x-rays on patients were also observed. It was not long before a new medical specialty known as radiology was born. Traditionally, radiology was divided into diagnostic and therapeutic. The only common area between these disciplines was the use of ionizing radiation. The last quarter of the twentieth century was marked by changes in diagnostic radiology that superseded those made in the first three quarters of the century (Daffner, 2007). Developments in recent decades have revolutionized medical diagnosis, making areas of the body previously inaccessible to surgical examination clearly visible. The realm of diagnostic radiology encompasses various modalities of imaging that may be used individually or, more commonly, in combination to provide the clinician with enough information to aid in making diagnosis. Diagnostic imaging includes radiography with and without contrast enhancement, computed tomography, magnetic resonance imaging, diagnostic ultrasound, and nuclear imaging (Armstrong, Wastie Rockall, 2004). The first three of these imaging forms use X-rays. The first diagnostic imaging modality to be examined in this paper is the computed tomography. Under ordinary circumstances, the fleshy organs of the body such as the heart and kidneys are considered uniform in radiographic density if examined using conventional radiographs (Brant Helms, 2009). However, these tissues vary somehow in their chemical properties, and it is possible, using computer-enhanced techniques, to measure those differences, magnify them, and display them in varying shades of gray or in color. This is the basis for computed tomography. The first CT machine was developed by Godfrey Hounsfield in England, and for these efforts, he was awarded the Nobel Prize in medicine in 1979 (Brant Helms, 2009). In CT, the subject is irradiated using an x-ray beam, as well as a detector system that moves all around the body of the patient. This allows the system detector to measure the intensity of radiation passing through the subject (Erkonen Smith, 2009). The data obtained from the measurements are fed to a computer system foranalysis. The computer system then assigns different shades of gray to different structures based on their absorption or attenuation coefficients. A picture is reconstructed by the computer which is based on geometric plots of where the measurements were derived from. Despite the CT having being discovered in the early 1970s, the system uses a mathematical formula that had been developed by Johann Radon earlier in 1917 (Armstrong, Wastie Rockall, 2004). One of the modern versions of CT technology is known as helical or spiral CT. In helical CT, the patient table is moved at a steady pace through the CT gantry as the scanning process continues while an x-ray tube rotates about the patients body. A constant volume of data is obtained during a single breath-hold. This technique has dramatically improved the speed of acquiring image. It also makes scanning possible especially during finest contrast opacification. It also eliminates artifacts that are occasioned by mis-registration and differences in patients breathing (Brant Helms, 2009). The information obtained using CT systems is displayed on a television CRT monitor and recorded on CD or DVD. Once the information has been recorded, it is possible to alter the windows of the various densities to optimally demonstrate the various subject organs on the reading console. The data from the CT is linked to a digital display such as PACs or teleradiology (Daffner, 2007). It may also be transferred to x-ray film using a device known as a multi format camera. The appearance of certain viscera or vascular neoplasms is enhanced by injecting contrast material intravenously. The latest technical advance in CT imaging is known as multi-detector helical CT (MDCT). It uses the helical priciples; scanner, however, includes numerous rows of detector rings (Herring, 2007). This enables the attainment of many slices in every tube rotation; hence augmenting the patients area that can be enclosed by a single x-ray beam. The key benefit of MDCT is its pace. Compared to helical CT, this version is five to eight times. For body scanning, one millimeter slices can be obtained creating cubic isotropic voxels, which allows image reconstruction in any anatomic plane without losing resolution (Daffner, 2007). A disadvantage of MDCT is radiation dose, which can be three to five times higher than with single-slice CT. During a CT imaging test, the patient lies on table attached to the CT scanner. The machine then sends x-ray through the body part under study. Every rotation of the CT scanner takes slightly under one second and offers a picture of a thin slice of the body part under examination. The pictures are then saved in a computer, and can also be printed. A CT imaging test can be used to study almost all parts of the body like the lung, liver, heart, thyroid and even bones (Erkonen Smith, 2009). The second diagnostic imaging modality to be examined in this paper is magnetic resonance imaging (MRI). This is a technique that produces tomographic images by means of radio waves and magnetic fields. As examined earlier, CT evaluates only a single tissue parameter through x-ray attenuation. However, MRI analyzes multiple tissue characteristics including protonn density, T1 and T2 relaxation times of tissues, and blood flow inside the tissue. The soft tissue gap provided by MRI is considerably better compared to what can be obtained using any other imaging modality (Armstrong, Wastie Rockall, 2004). T1 is a measurement used to determine how fast a tissue can be come magnetized (Brant Helms, 2009). On the other hand, T2 coveys how quickly a given tissue loses its magnetization. MRI is grounded on the premise that a small number of protons can absorb and release radio wave energy if the body is subjected to a strong magnetic field. Dissimilar tissues absorb and emit radio wave energy at different, detectable, and characteristic rate. MRI scans are gotten when the patient is placed in a static magnetic field of 0.02 to 4 teslas in strength, depending on the particular MRI unit used. The choice of unit for imaging is based on preference and local availability (Daffner, 2007). A small number of tissue protons in the patient align with the main magnetic field and are subsequently displaced from their alignment by application of radio frequency gradients. When the RF gradient is terminated, the protons that have been terminated align again with main magnetic field, releasing a small pulse of energy that is detected, localized, and then processed by a computer algorithm similar to that used in CT to produce a cross-sectional tomogrophic anatomic image. MRI can be used to image different body parts such as the, bones, spine, joints, pelvic organs, urinary tract, and heart. It is a useful procedure for diagnosing skeletal diseases and cancer (Erkonen Smith, 2009). The last diagnostic imaging modality is ultrasound. This modality uses very high frequency sound that is directed into the body of a patient. The transducer that produces the sound is positioned in contact with the skin. A good acoustic contact is obtained by smearing the body of the patient with jelly-like substance. As the sound moves through the body, the tissue interfaces reflect it, hence producing echoes which are picked by the same transducer and afterwards is translated into an electrical signal. Ultrasound is generated by making a special crystal oscillate at a frequency that is predetermined. The crystal not to transmits the pulses of sound and listens to the bouncing echoes. The echoes are amplified by electronic means and recorded on a television monitor in the form of signals (Herring, 2007). During the scan, the ultrasound beam is electronically passed through the patients body and body part is showed instantly. The obtained image appears like a slice, and for one to get a three-dimensional assessment; a number of slices must be created by angling or moving the transducer (Brant Helms, 2009). An ultrasound scan can be used for various uses. It can be used to keep a watch on the progress of a child that is yet to be born. Ultrasound can also be used to identify problems of different body parts such as the liver, pancreas, ovaries, kidneys, and breast. In essence, the different diagnostic imaging modalities have been a milestone in the medical history as they have helped doctors in examining various body parts that could not have been examined were it not for the developments. Buy custom Imaging Services Radiology essay

Capital Budgeting of Pevensey PLC Essay Example | Topics and Well Written Essays - 1750 words

Capital Budgeting of Pevensey PLC - Essay Example The present research has identified that Capital Budgeting is an important process for any organization. No organization can make good use of their money, unless they plan, decide and assess the best use of money. Good investment decisions maximize the earning potential of an organization and help boost the firm’s overall financial position and financial health. Good financial decisions are not intuitive. They require a lot of effort and financial planning. Many firms employ people with excellent financial knowledge and skills just to enhance the use of money. These people often lie at an important level of organizational hierarchy and given a title of CFO or Chief Financial Officers. Many firms, over the years, have realized the importance having people with good financial skills and have given these people more power and authority than the CEOs. As a result, these people are consulted every time a need arises for an organization to make a good financial decision. This good f inancial decision regarding the best machine is going to improve the asset earning potential for the firm and it is also going to improve the asset turnover and return on assets ratios. Pevensey PLC is a growing company. It needs to decide on the best option of a machine purchase. Currently, the company has four different options to ponder upon. It is good for the company to use financial tools of capital budgeting to appraise each of the four options before making the purchase. This will reduce the chances of a bad decision, and will put the company in a win-win direction. Hence, the company has done the right thing by consulting someone with the financial knowledge to look at the available options and deciding the best option for the purchase (Brigham & Ehrhardt 2010). This would ensure that the best purchase is made in the given budget. The best purchase will not only be the cheapest method, but the best purchase is also going to improve the overall financial position of the orga nization in the long-run. ASSESMENT METHODS: Capital budgeting is considered to be a specialist field. The methods used that are used to determine the best option to purchase are net cash flow method, discounted cash flow method, Payback period, NPV and IRR. No one method can alone be a good guide for the company for the best decisions. All of these methods have to be studied and used in congregation for giving the best answer to the company. This would ensure the best purchase is made in terms of returns, time value of money and cost of capital. The company can raise capital at a rate of 8 percent. This means that any of the option chosen must provide a return of at least 8 percent for the company to break-even. If this is not the case, the company will be losing money in real terms. It might be making money in nominal terms. Nominal and real returns are different. Nominal returns do not take into account the inflation rate and the cost of the capital to the company. Real returns t ake into account the cost of the capital that the company has to pay for obtaining the finance needed to make a purchase. The methods used in the report would help us calculate both the nominal returns and real returns to decide the best Machine to purchase that would maximize not only the firm’s cash flow, but will also the allow the firm to earn decent rates of return. The first method used to calculate the

Resistence to Change Case Study Example | Topics and Well Written Essays - 1250 words

Resistence to Change - Case Study Example The report further asserts that, lack of communication across the organization heightened resistance because majority of employees were unaware of impending changes that were being introduced (Griffin & Moorehead, 2012). In above connection, lack of single culture to integrate the whole organization was a significant source of resistance to change because almost every department at NASA had its own culture different from other departments (Griffin & Moorehead, 2012). Lack of proper risk mitigation measures in place to consolidated organization culture, was major factor that caused resistance to change (Columbia Accident Investigation Board, 2003). The report suggested that, termination of risky flights was not solution of reducing escalated cases of accidents but rather NASA should focus at establishing structural procedures that guarantees sustainability of a safety culture (Columbia Accident Investigation Board, 2003). Therefore, this analysis focuses at providing an insight of Col umbian mishap concerning resistance to change and how it contributes to accidents. The analysis will further focus on both individual and cultural resistance as well as the impact of the board recommendation on individual and structural barriers. Individual sources of resistance to change and their causes The Sources and causes of individual resistance could be attributed to numerous factors that may include; fear for unknown. People tend to fear uncertainties that may to occur as a result of change (Griffin, & Moorehead, 2012). This is because individuals find it difficult to cope with dynamics for instance, it can be scrutinized that lack of prior cultural integration within all departments at NASA brought great resistance (Columbia Accident Investigation Board, 2003). Additionally, Inability to adjust and start doing things using new ways may make people fear change and therefore, they may develop resistance. Inability to adjust may be overcome by ensuring that there is efficient and effective integration of NASA cultural goals and mission during the earliest juncture possible (Columbia Accident Investigation Board, 2003). In above connection, it can be scrutinized that individual developed resistance to change due to a lack of effective communication, whereby, NASA engineers could not effectively communicate safety measure to the management leading to individual resistance (Columbia Accident Investigation Board, 2003). On the other hand, NASA managers failed to communicate issues raised by engineers to all the departments leading to resistance among employees because changes were introduced without a prior notification (Columbia Accident Investigation Board, 2003). Lack of proper leadership within organization contributed significantly to individual resistance because managers were not involved in directing employees on what to do to ensure that safety standard were being observed. According to a report by Columbia Accident Investigation Board 2003, misund erstanding between managers and NASA engineers was significant source and cause of resistance. Structural sources of resistance to change and their causes The most common sources of resistance to change include; inertia within the organization structure (Griffin & Moorehead, 2012). Whereby, most organizations contain some mechanisms that enhance stability and sustainability making it difficult to