Beloved Essay

Sethe has a very complicated relationship with herself. Sethe is the character that is not able to forget the trauma of the times when she was a slave and fearing that her children might not fall into the same fate, prefers to even kill them. The central theme is that Sethe is in search of her own identity and Morrison also tries to show the cruelty and disturbing consequences of slavery that existed even after they were not slaves. The ex-slaves also feel inferior to the white people and when Denver walks out of her home to find a job and finally she finds her identity. Sethe is lacking this throughout and keeps herself isolated and only plays the role of a mother. ‘Those white things have taken all I had dreamed’, she said, ‘and broke my heartstrings too. There is no bad luck in the world but white folks. ’ (Beloved, Chapter 9, Page 89) Sethe kills her baby girl so that she is not physically, spiritually or emotionally oppressed by the masters or whites of that time. Sethe suffers the guilt of her this particular act and when the first time ghost of Beloved comes in her house she gets extremely terrified and wants it to go away at any cost. But the second time, Sethe allows Beloved’s ghost to destroy her house and digests her anger at even the cost of her relationships just because she thinks that this way she can calm down her daughter’s ghost. Beloved seems to be interested in Sethe and she listens to her and this satisfies Sethe too. Sethe has faced the dark and gloomy days of slavery and the whole life she tries to protect her children from getting into that life. Sethe’s unique interactions with Beloved, her incarnated daughter reveals a completely different picture. She struggles with herself and her emotions and most of the time she is lonely. She trusts very few people and has cut herself socially, especially from the black people. She identifies herself as a different person in different stages of her life. Sethe’s relationship with Beloved takes a different shape and helps her recover from the physical and mental trauma of slavery. The use of symbolism and allusions refer only to the confused and suffered state of mind of Sethe. Beloved has many grievances and thinks that her mother abandoned her whereas Sethe is unable to explain her daughter why it was better to die that to live in such traumatic situations. At these stages Sethe seems to be helpless and becomes more and more self-centered. She feels sometimes that she had no right to kill her daughter but the love and respect she had for her children forced her to do so. Her dreams for her children and their future were definitely not to live like slaves and she did what the moment forced her mind to do. Her motherly emotions are different from a general mother and she is seen very much possessive about her children too. She says, â€Å"[A]nybody white could take your whole self for anything that came to mind. Not just work, kill or maim you, but dirty you. Dirty you so bad you couldn’t like yourself anymore. And though she and others lived through and got over it, she could never let it happen to her own. The best things she was, was her children. Whites might dirty her al, right, but not her best thing, her beautiful, magical best thing – the part of her that was clean. † (Beloved, Chapter 26, Page 251) The novel in fact is Sethe’s memories in a shattered way and one has to collect them and understand and this makes the identification of relationships of Sethe with her two daughter all the more difficult.

Teenagers – not as bad as they are portrayed?

Britain altering her ways, has successfully managed to keep up with the ever changing world. However the youth of our day, seem the only change society somewhat fails to keep pace with. Are we leading our teenagers forlorn? Teenagers are categorised under offenders and criminals and not to mention are covered by an umbrella of stereotypical views of which if its coverage of teenage Britain fails to cease would be a slow and gradual obliteration of Britain’s future. If society takes a step back and realises the sought of pressure left upon the shoulders of our future leaders, doctors , engineers etcetera we would come to the realisation that the strain put on them is a strain put on the nation’s future. Furthermore, as the well-being of the nation hangs in the balance it seems as if eyes are staring purposefully watch it lose its balance with the likes of the media broadcasting nothing but the negatives, painting a villainous image of which the public do nothing but believe. Although there are some teenagers who follow the wrong path, statistics show 10 percent of anti-social behaviour were committed by them and the increase of knife crime amongst teenagers increased by 2 percent over the past year however it seems statistics like this also fail to mention the other percentage of teenagers who actually do something valuable for the society such us charity work, and those whom constantly thrive in the aspiration of making the nation a good one to live in, until then the current government has to work on making this nation a bearable one to live in. The constant pressure from the media towards the teenage generation has yet to show the many good works of the youths. ‘’Back in my day†¦Ã¢â‚¬â„¢Ã¢â‚¬â„¢ seems to be the reoccurring statement by the nostalgic few, the few, whom believe that without the morals and discipline of the old age teenagers today show no respect for society today, however, Do they know how it is to work in a teenagers shoes. Above all, teenagers still get along with life amongst all the turmoil: postcode wars, gang warfare and peer pressure. Being at a vulnerable stage in life, youths feel pressured into becoming the image everyone expects, seen in the small town of Lancashire where a normal boy named Tom, was bullied to the extent he committed suicide, this in itself is not accepted in society. ‘’Now I will not get to see my son lead a normal life’’ said Mrs Smith tearfully. Would the outcome be different if he spoke to someone? 2011 witnessed the London riots, often described as ‘’mindless act of violence ‘’ saw parts of London set ablaze teenagers seen as the apparent cause, could this have been prevented? Or was this just a way to gain attention from the society as they have been put on the lower end of it, always put at the receiving end of pessimistic views. Although this would be seen by some to be destructive, inconsiderate and uncalled-for , this might be what teenagers think would actually make sure their voices are heard and also make sure they have an actual say on what decisions are made about them. The life of teenagers would continue to remain a mystery to some, as times change people also change, if things do not change for the better the life of a 21st century teenager would continue to be hard.

How Do I See Myself Essay Example | Topics and Well Written Essays - 1000 words

How Do I See Myself - Essay Example This author stresses that after following certain universal rules which are set in stone since ages. Alexander the great, M .K Gandhi and Bill Gates have all reaped heaps of benefits but at certain costs. To be dominant one has to blend with the colors of this world. He outlines that "similarly, I have certain habits and traits which have been molded by the environment around me. The culture and traditions of the world in which I live have and are influencing me a lot. Each moment teaches a new lesson and each experience solves yet another paradox of life. Why is life so hard and tough? Many people wonder on this question. The answer in my opinion is simple as mentioned in the introduction. Whenever I go in public or portray myself to others, I indicate certain qualities and symbols which in my opinion will lubricate success. I belong to the oriental culture where strict belief is placed in family ties and values unlike the western one where individualism is dominant. Therefore, the external factors greatly affect my behavior. My parents are not that educated but they try their best to get their children educated. Inspired by the modern world race of education and success, they strive to equip their children with the best means of survival. I have done my O-levels belonging to a local education background, I did well. Following which I went to the second best local institution to pursue A-levels. After the completion of my A-levels, I landed in one of the leading local business education institutions due to lack of finance for studying abroad. I have five siblings which along my parents make 8 of us dwelling in a two room house. Such proximity makes us rectify each others behavior. However, facing bitter experiences and challenges in the past I have two aspects which I use to portray myself to this world depending upon the target audience and their mindset."

Discussion Essay Example | Topics and Well Written Essays - 250 words - 98

Discussion - Essay Example Second, is caste immobility wherein moving from one caste to another is extremely rare. However, if a person has exceptional skills that are rare in the society, he or she can ascend to a higher caste of professionals (McMahon 1). People in the higher caste hold the political power, and within the caste, people are subdivided further under language, economic, and cultural aspects. Each member within a caste knows his or her place within the caste (N.D). The caste system is a culture practiced in many societies, though; the most known caste system is the Indian system. The Indian caste system is based on the Hindu religious scriptures; though, it is practiced in other religions. Each caste, in India, has its own rules and customs. The social orders are arranged in ranks with the first order being Brahmans that consists of priests and professionals. The second caste comprises the Kshatriyas, who include rulers and warriors. The third comprises the Vaishyas who are associated with traders. The forth is the Shudras, the laborers. A group of other people not included in the four castes exists, the untouchable. The untouchable do menial jobs, such as garbage collection that made the society regard them as the impur e ones (The US History Organization

Thomas Cook Plc Case Study Example | Topics and Well Written Essays - 3000 words

Thomas Cook Plc - Case Study Example Thomas Cool was a former Baptist minister and a very religious man and he firmly believed that alcohol was the major factor casing problems among the working class in England. It was with this in mind that the above-mentioned train journey was arranged. The first unofficial tour was this trip in open carriages, which took nearly 500 temperance supporters to Loughborough, and back in July 5, 1841. In 1845 Thomas Cook organized a tour to Liverpool which was accompanied by what must have been the first tour brochure ever printed in the world. His first international venture was to Paris during the time of an international exhibition which was held there. Further tours to other cities in Europe began and an established tour itinerary began to fall in place. A tour to Switzerland and later to Italy was conducted in 1864. With his clientele shifting from working class to middle and upper class passengers, Mr. Cook began to make arrangements with hotels in Europe by using something called t he hotel coupon. This enabled tourists to pay for the hotel rooms in advance and to stay at hotels without paying cash. Another innovation was the circular note, the forerunner of 'travellers cheque.' Trips to the US soon followed and later a trip by steamer up the river Nile was also arranged. All this success naturally led to thoughts of expanding further overseas to the US and Asia. Mr Cook himself was part of a trial world tour which covered the US, Japan, China, Singapore, Ceylon and India. This tour went on to become an annual event in the company's tour calendar.. An unexpected move by the then two owners saw the company being sold off to a Belgian tour operator called Compagnie Internationale des Wagons-Lits et des Grands Express Europens in 1928. Certain events during the world war saw the company near collapse and a deal was made where by the ownership changed back to British hands, this time by the government owned railway companies. Even though the company could benefit from the post war travel boom, things began to slow down by 1955 due to the emergence of new and dynamic tour operators. In 1972, Thomas Cook became privately owned once again through a purchase by a c onsortium of the Midland Bank, Trust House Forte and the Automobile Association. The famous red logo of Thomas Cook was introduced during this time. The company did well during this period and even managed to survive the 1970's depression. The Company came under the sole ownership of the Midland's Bank in 1980 and again sold of to Germany's third largest bank, Westdeutsche Landesbank (WestLB) and LTU group (an airline charter company). Thomas Cook later became the subsidiary of the German bank and soon acquisitions of Sun World, Time Off and Flying Colours took place. In 1999 a merger with Calrlsons Liesrue Group took place. The Company Thomas Cook Group PLC was formed in June 2007 through a merger of Thomas Cook AG and My Travel Group Plc. "It is now part of Thomas Cook Group plc (www.thomascookgroup.com) which was formed on June 19th 2007 by the merger of Thomas Cook AG and My Travel Group plc." (A Brief History). Business Strategy: Corporate growth strategy: The merger of Thomas Cook and My Travel has resulted in a very powerful tour operating company and has a string presence in UK and some European countries. This merger came about so that both the companies could compete more efficiently in a

Through referenced literature and examples, examine the range of Essay

Through referenced literature and examples, examine the range of theories of what an entrepreneur is and how they contribute to the economy and society - Essay Example the term is applied, certain elements are constant: entrepreneurs are persons of certain psychological qualities and unique abilities who, through these qualities, contribute wealth and energy to an economy and social benefits beyond business. There are a whole range of theories as to what makes an entrepreneur. Regarding the assertion that entrepreneurs are born, not made...Shane (2010) asserts this may be only half true if one is speaking about genetic traits. One of the more modern empirical investigations was done by Collins and Moore and published in their exceptional analysis in The Enterprising Man. (delete words) Seeking to prove their theory that entrepreneurs represents certain psychological traits, they employed the Thematic Apperception Tests (TAT) test. The subject, presented with a set of cards with human figures in a variety of settings, creates a story including elements describing the event shown; what has led up to it; what the characters in the picture are feeling and thinking; and the outcome of the event. The test assumes certain results about the subject’s personality in relationship to entrepreneurship—workaholics rarely every satisfied; patronizing with subordinates; suspect and rejecting of authority—that within the Collins and Moore psychological profile theory represents early childhood relationships with adults in the entrepreneurs life. (Roberts, 1991: 50). Throughout other studies, however, while there appears to be a clear relationship between entrepreneurship and achievement motivation across a number of measurement instruments (Edwards Personal Preference Scale, the Mehrabian Scale, and the TAT (1) Sexton and Bowman (1986) found inconsistencies that challenge the blind acceptance of this theory, and that ‘students and nonstudents (entrepreneurs, potential entrepreneurs, and nonentrepreneurs) differ on a variety of characteristics which are supposed to be stable across time and situations according to personality

Review of the Article Development Opportunity Essay

Review of the Article Development Opportunity - Essay Example The article gives some guidelines in toning down what is necessary in learning and development (L & D) programs. An approach called RAM is suggested. R stands for relevance, which asks, â€Å"What is it for? Why are we doing it? Has the work changed? Has the business changed?†. A stands for alignment, which asks consults the stakeholders who will benefit from it. Lastly, M stands for measurement, which looks into the impact and value of the L & D (Scott, 2010). Since options to save up on L & D expenses have been cut short, online training services have been made available by a few groups where employees can log on to the company’s learning management server and choose a program they believe will help them in an area they need training for. Such service conducts an impact and learning study to monitor how they improved from the training. When people want to learn more to improve themselves, the article said they should not be controlled but instead given freedom and opp ortunity to do so. Social learning is one option. People can work across the company to network, â€Å"share knowledge and experience, collaborate and learn for their benefit and that of the company (Butler as mentioned in Scott, 2010, p. 25). Learning from colleagues could be an effective way of improving skills and experience while keeping company costs down. Leaders may also avail of outside training first and then cascade their new knowledge and skills from the training down to their employees. It is one way of imparting the culture of the organization to its people. In any case, the training expert should keep in mind the goals of the training – to improve the business and not only the people, so it yields a return on investment. L & D should focus more on practical strategies and not just theories. Review of Related Literature The global financial crisis has turned some companies to scrimp on their budgets just keep them afloat in these difficult times. Many people hav e lost their jobs as a result of the budget cuts. For employees left to work to help their companies rise above the economic crunch, training and development are ensured in the expectation that it will contribute towards the betterment of not only the individual employee but of the whole organization as well. Employee development has been identified as key to improving overall organizational effectiveness. Jones and Washington (2003) have defined it as: â€Å"Employee development refers to an integrated set of planned programs, provided over a period of time, to help assure that all individuals have the competence necessary to perform to their fullest potential in support of the organization’s goals† ( 344). Like what the article indicated, nowadays, people have more access to learning. More and more training courses are developed and offered in schools and online for people who want to go further in what they know to gain skills and knowledge in their

The Determinants of Household Poverty in the USA - 1980 Statistics Project

The Determinants of Household Poverty in the USA - 1980 - Statistics Project Example It is the dependent variable in this analysis. Family size is basically the number of people in a single family. The county-level family sizes were obtained by dividing the total number of people within respective counties by the number of households. Large family sizes are known to increase dependency levels, thereby making it more difficult for the breadwinners to invest in productive income-generating ventures and subsequently increasing poverty levels. Urbanization refers to the percentage of the entire population in a county that resides in urban areas. According to Cali and Menon (2009), urbanization has a net poverty reduction effect, since it invigorates business aspirations and income prospects for the population. Unemployment rate is the percentage of the entire population within a locality that is unemployed. Unemployed people tend to have higher poverty levels. Higher unemployment rates correspond to higher poverty levels within a population. Income refers to the median income of all the employed individuals within a county. The higher the average income for a population, the lower the poverty levels within it. Higher income enables workers to live more comfortably since they can meet their needs and obligations more easily. Equally, better-paid people tend to have more room for investing and, therefore, diversifying their earnings to accumulate even higher income. This study aims to establish the individual strengths of each of the independent variables as a determinant of poverty (the dependent variable). Correlation analysis has been used to establish the nature of the relationship between each of the independent variables and poverty (whether positive or negative). Using regression analysis, the independent variables are investigated for their ability to predict levels of poverty within the sample population. This type of analysis also provides the basis for obtaining a predictive model that can be used to project future poverty

Drafting Introbodyconclusion Essay Example | Topics and Well Written Essays - 500 words

Drafting Introbodyconclusion - Essay Example They spend a lot of time and money in their quest for the perfect body. They spend time under the surgeon's knife, trying as hard to look the perfect person. Models on the ramp, play host to millions of probing eyes and have been taught to look their pleasing best. Life is never easy on the fast track. Leaving behind their personal feelings, and throwing caution to wind, these tall, slim-legged, hour-glass bodied women live a life of make-believe. Is life on the ramp a bed of roses, as most of us make it to be How true has the proverb, "All that shines is not gold" proved to be. Yes! The ramp is a stage, and the models, its actors. They are there to please the connoisseur and our senses. To follow them would be disastrous and to say the least, painful. Health and beauty industries thrive on women's senses. Not much can be said of men's apparel or health and beauty care. This multi-million dollar industry remains vibrant thanks to media hype and idol-worship. Not much is seen or heard of adversities. MTV shows women clad in minutiae bits and pieces of clothing flashing more of bodies than the cloth they are supposed to represent. This is far from the reality of what fashion should be today. It's true that there remains a few with genuine interest in clothing and its accessories, but for the majority, it's the flesh and blood that appeals most.

Consumer behaviour Essay Example | Topics and Well Written Essays - 2000 words

Consumer behaviour - Essay Example Discussions about external variables pointed to Wyld’s (2010) assertions that these are the general economic climate, technology, government and competition as factors affecting customers’ decision at the various stages. Scheiltz (2010) suggested other external factors such as the cultural, group and social values that sway the decision process of consumers. Decision process is defined as identification of needs, collecting of information, evaluation of alternatives, then finally going into a purchasing decision. (Chapter 6 Class Notes, n.d.) I. How do marketers persuade consumers using external variables? a. Economy The economy is the first factor considered as an external variable affecting consumers. The recent economic crisis is an external variable that affected consumers’ behavior in many states of US and in Europe, and many others. On the other hand, economy has been favorable to the emerging countries in Asia. The shrinking economy encourages shifts in bu yer demographics and the way products are used such that consumers may alter their purchasing decisions, how they perceive value and where they purchase the product. Market report of Bharatbook.com (2010) said that in Netherlands, consumers’ decisions are today influenced by the price sensitivity, value consciousness and attitudes towards private labels as about three quarters of its consumers suffered the recession in 2009. In the said market report, Dutch consumers reconsider their spending including decisions on where and when to shop; and that changes shown is that now, Dutch consumers are buying labeled products because they think they save more money in the long run. This is also true in the car landscape wherein the economic crisis has changed car-buying process of consumers. To help dealers determine changes of consumer buying process, Dealer Communications reported on a conducted a research to know the present motivations of car buyers; to know if there are opportuni ties still open for car dealers and manufacturers, and if so, how will they adjust. In issues how the products are challenged showed the way Apple has transformed how music is bought and played thru the introduction of iPod. (Wyld, 2010) Marketers also use the power of globalization to reach more and more country markets. Recent developments of off-shore business, in particular, the emerging economies of Brazil, Russia, India, Indonesia and China have encouraged multi-national companies to spread their business in these countries. Because of the improved purchasing power of consumers in these emerging countries, marketers find globalization as a driver of change in industries as motor vehicles, cell phones and credit cards (Wyld, 2010). b. Technology. One of the driving forces that encourage consumers’ buying decisions is the use of technology. It is observed that there is a growing acceptance of internet shopping, SNS websites and the constant growing series of internet appl ications. It is now easy for the company to sell products to customers using online technology, to work with suppliers and supply chain. However, because becoming an on-line seller is an easy process in the internet, this variable increases rivalry and competition among seller. An example of a successful on-line ordering system is being done by Wal-Mart stores that make shopping easy for busy people (Wal-Mart, n.d.) c. Competition An attractive market encourages competition to enter the industry. Most

The Evil of Modern Technology Essay Example for Free

The Evil of Modern Technology Essay â€Å"Many shall run to and fro, and knowledge shall be increased. † Daniel 12:4 Here I am, sitting in a house heated by a gas/forced air furnace, illuminated by an incandescent bulb, writing down my thoughts on a computer screen, accessing the internet by a wireless connection and weighing in against modern technology. I will be the first to tell you, however, that I don’t want to go back to the way it was, even a few decades ago, when I shivered over a lone heat register in the kitchen, pounded out my writing assignments on an ancient typewriter with a faded ribbon, waiting for my water to boil on a gas stove and my cinnamon toast to bake in the oven. Daily life has been so revolutionized by a steady progression of technological improvements that few of us can imagine living any other way. Conveniences have become such necessities that anyone who has no microwave, cell phone or digital alarm clock is considered deprived. Man’s inventive genius continues to prolifically breed new technologies, and with each new technology, a cottage industry springs up to feed, clothe and shelter it. Computers have generated software, music, movies, photo-shopping and enough peripheral gadgetry to fill a catalog. With the cell phone came personal ringers, phone cameras, text messaging, GPS capabilities, internet access, ebooks, and on and on. Automobiles can now do much more than transport passengers. They can pamper, comfort, entertain, advise, warn and tell drivers how to get to their destination. We now foresee the day when we won’t even have to steer the machine down the highway. There seems to be no end to our fertile imaginations. But I am haunted by the words of an old evangelist. He said, â€Å"Man will never hold out long enough morally to do what he wants to do scientifically. Even as we mount up to the heavens in the space age, we mire down in the mud of sin and shame. † I see this chilling prediction coming true before our very eyes and ears in the twenty-first century. Our heads cannot out-smart our hearts. Something is insanely wrong with all of this progress. Not only have promises of utopia not materialized for the bulk of civilization, in many cases we have regressed back to prehistoric levels. We have not eliminated murder; we have made murder easier. We have not eliminated theft; we have made stealing easier. We have not eliminated racism; we have made racism easier. We have not eliminated pornography; we have made pornography easier. Inherent within the new technologies we find all the old maladies. Good things undeniably come from our scientific and technological breakthroughs. Unfortunately, these developments have also been subverted for evil purposes. Indeed, the evil we have enabled may end up canceling out the good we have created in society at large. The most obvious example of this is nuclear technology. The fascinating capabilities of nuclear fission for energy also gave rise to the most destructive weapon ever invented. Regardless of how atomic weaponry is used—whether for defensive purposes or aggressive military action—the fact remains that it is used to kill and destroy. Other scientific discoveries have also been channeled into military uses, like rocketry, aerodynamics, fiber optics, laser beams, radar, modulated radio and television signals, satellites, etc. If it helps, we can make it hurt. If it heals, we can make it injure. If it does good, we can make it do bad. This position has been argued in philosophical terms as well. Regent University’s website on communication contains this paragraph: â€Å"Whether one accepts the neutrality of technology depends on one’s valuing philosophy—whether one tends toward the pragmatic and situational, or the absolute and authoritarian. Those who believe that technology is neutral argue that â€Å"guns don’t kill people, people do†, or that a knife can be used to â€Å"cook, kill, or cure. Those who believe the opposite counter with evidence that technology cannot be evaluated in a vacuum. Monsma (1986) argued for the â€Å"value-ladenness† of technology (chapter 3). He based his premise on two traits that he believed are common to all technological developments: (1) technological objects are unique; they are designed to function in a particular and limited way, and (2) technological objects are intertwined with their environment; they interact in unique ways with the rest of reality. † In medical science we can find an alarming example of the limits of technology. Jerome Groopman wrote an article in the New Yorker Magazine, August 11, 2008, entitled â€Å"Superbug: The new generation of resistant infections is almost impossible to treat. † He said, â€Å"In August, 2000, Dr. Roger Wetherbee, an infectious-disease expert at New York University’s Tisch Hospital, received a disturbing call from the hospital’s microbiology laboratory. At the time, Wetherbee was in charge of handling outbreaks of dangerous microbes in the hospital, and the laboratory had isolated a bacterium called Klebsiella pneumoniae from a patient in an intensive-care unit. It was literally resistant to every meaningful antibiotic that we had,† Wetherbee recalled recently. The microbe was sensitive only to a drug called colistin, which had been developed decades earlier and largely abandoned as a systemic treatment, because it can severely damage the kidneys. â€Å"So we had this report, and I looked at it and said to myself, ‘My God, this is an organism that basically we can’t treat. ’ † Much of the toxic social climate we experience today comes to us at the hands of modern technology. Who can dispute the widespread conviction that television has had a deleterious effect on culture? It is a waster of time, numbing minds and killing creativity. It has also piped pure filth from a godless and immoral Hollywood into the living rooms of the world. The radio has dispensed anarchy, vulgarity and corruption through the powerful medium of music, especially targeting adolescents and teenagers. In the last decade, pornography has spread wildly throughout the internet, victimizing viewers who would seldom or never come in contact with sexual perversion any other way. Amazingly, these same technologies have transmitted as much or more truth, virtue, goodness and love as they have depravity. How is this possible? Is technology, then, culpable? Innocent? Morally neutral? In The Gutenberg Galaxy (1962), Marshall McLuhan wrote, â€Å"The theme of this book is not that there is anything good or bad about print but that unconsciousness of the effect of any force is a disaster, especially a force that we have made ourselves† (p. 248). Regent University comments â€Å"Insert any technology for the word â€Å"print† and you realize that for McLuhan it is not the content that really matters. In this case it is not even the channel but rather our knowledge and understanding of the medium’s potential impact. † They then ask, â€Å"Is print an amoral technology? Can any technology be amoral? These are issues that must be addressed and answered before we can begin to develop a philosophical system to address the convergence of media and technology, and its impact on society. † I contend that communication technology has the greatest potential for evil of all the developments of modern science. This should not surprise us who are in the business of spreading the gospel. After all, Jesus commissioned the church to â€Å"Go ye therefore, and teach all nations. † The very means and methods used by the church to carry out the work of Christ has been co-opted by Satanic forces to destroy the gospel and spew corruption throughout the world. The advent of the online community was initially envisioned as a dynamic way to connect the inventive genius, the soaring imaginations and the scientific knowledge of individuals, groups, schools and cultures together, thus exponentially multiplying the positive impact they were making on the world. But in the parallel universe of evil, it was also appropriated by malevolent forces to connect with people who shared the same destructive designs. Roger Cohen expresses the same view in the New York Times column of March 10, 2008. â€Å"The main forces in the world today are the modernizing, barrier-breaking sweep of globalization and the tribal reaction to it, which lies in the assertion of religious, national, linguistic, racial or ethnic identity against the unifying technological tide. â€Å"Connection and fragmentation vie. The Internet opens worlds and minds, but also offers opinions to reinforce every prejudice. You’re never alone out there; some idiot will always back you. The online world doesn’t dissolve tribes. It gives them global reach. † The very internet I access to research my topics is simultaneously used to teach people to build bombs, incite hatred, instigate anarchy, commit fraud, buy and sell illicit drugs, learn witchcraft, poison minds and dismantle Christian traditions. More specifically, it provides a way for terrorist organizations to plot destructive acts, devise conspiracies, obtain funding for their violent activities and inspire each other’s dark causes. If this world is facing global chaos and apocalyptic demise, it will undoubtedly be facilitated by the technology now in existence or soon to be developed. Groups of people who otherwise had no way to unify and combine forces to wreak havoc upon the world now find it easy to locate each other and strengthen their hands. One only has to recall the tragedy of September 11, 2001 to know that cell phones and the internet aided nineteen terrorists to coordinate their diabolical plan. Without the assistance of technology, their deed would not have been possible or would have been infinitely more difficult to carry out. Technology may not be inherently evil, but neither is it inherently good. We are unforgivably naive to trust in scientific advances to spread the gospel or do the work of the church. Technology certainly will never be our savior. In fact, the future holocaust it will most assuredly precipitate may well eclipse any good that it has ever done for us. The best gifts to mankind do not come from himself, but from God. Every good gift and every perfect gift is from above, and cometh down from the Father of lights, with whom is no variableness, neither shadow of turning. † James 1:17. This warning may find application at the local congregational level where churches are growing increasingly dependent upon technology for worship, singing, preaching and witnessing. But technology in the larger arena of the world needs to be viewed by the church as susp ect. It’s potential for evil means that it will never be the best friend of the church. Let us use it, work it and enjoy it. Let us also keep it at arms length, distant from our souls. We do not need computers, cell phones, radios, televisions, headphones, iPods, CD’s, DVD’s, satellites, telescopes or any other technological devices to have a meaningful relationship with God. Paul’s Mars Hill sermon said this, â€Å"That they should seek the Lord, if haply they might feel after him, and find him, though he be not far from every one of us: For in him we live, and move, and have our being. † Acts 17:27-28. The greatest technology to ever come to man may be the glorified body that God has prepared for them that love him. How close will that body allow us to be to God in a physiological sense? I’m not sure, but I do know what the scripture says. â€Å"Dear friends, now we are children of God, and what we will be has not yet been made known. But we know that when he appears, we shall be like him, for we shall see him as he is. † 1 John 3:2. (NIV) That’s the technological advance that excites me more than any other. In an instant, all worldly innovations will be rendered obsolete. We must not sell ourselves short by losing our soul to earthly things.

The Beloved, by Toni Morrison | Summary and Analysis

The Beloved, by Toni Morrison | Summary and Analysis 124 was spiteful. 124 was loud. 124 was quiet. The house 124 that Sethes family lives in is haunted by the ghost of the baby who drives her two sons away as well as the rest of the neighbourhood. Paul D, an old friend from Sweet Home, visits 124 in search of Baby Suggs, Sethes mother-in-law, only to find she died eight years ago. Paul D is invited into the house where he meets Denver and senses the evilness of Beloved, however the ghost is soon sent away after Paul Ds arrival which upsets Denver and causes her to act coldly towards him. Recalling memories of Sweet Home of Sethes marriage to Halle, the other men at Sweet Home and Sethes escape, the notion of a future with Paul D crossed Sethes mind. That Thursday the three of them went to the carnival in town which made all three happy, however on return to 124 they found a woman sat on a tree stump who said her name was Beloved which excited Denver for she now had the company she longed for. Denver went out of her way to make Beloved feel better and although Denver loved her, Paul D thought there was something strange about her. Beloved continued to ask Sethe and Denver of their past and Denvers birth. Denver told Beloved about Baby Suggs, her Grandmother, and about the Clearing where Baby Suggs used to preach. The three women headed towards the Clearing for Sethe to think, however she was choked by someone or something who she thought was Baby Suggs. Denver thought otherwise and thought it was Beloved who choked her. Beloved seduces Paul D after he believes she has driven himself and Sethe apart. This leads Paul D to ask for him and Sethe to have a child together, thinking that this would relieve Beloveds power over him. Howev er, Paul D is infuriated by Beloved as she waits for Sethe to return home from work, which strengthens Sethes belief of Beloved being her child she gave birth to and breaks the romance between the couple because she wants Paul D to leave. In flashback, the memory of Sethe murdering her baby is then evoked. It was Stamp Paid, an old friend, who took the dead baby from Sethe and gave her Denver before Sethe was placed in custody. Then in present, Stamp visits Paul D and shows him a newspaper clipping of when Sethe murdered the baby. In disbelief, he insults Sethe and leaves her. Sethe took Baby Suggs advice; lay it all down and so she did. The three of them went ice skating and laughed endlessly resulting in Sethe to go late to work the next day, and she did so for the following weeks until she was fired. Feeling guilty for sending Paul D away, Stamp argues with Ella after finding out she didnt offer Paul D a place to stay and he was staying at the church, recalling memories of Sweet Home. Feeling she was responsible for the silence and hunger at 124, Denver felt it was only right that she left 124. All three grew tired therefore in search for a better life, Denver received help from Lady Jones and the rest of the neighbourhood. During the day she looked after Sethe She and in the evenings worked for the Bodwins. However, on the first day of work, when Edward Bodwin came to collect her, the ladies of the neighbourhood gathered together at 124. As Edward arrived, Sethe thought of him as a man who wanted slaves and attacked him with an ice pick, leaving Beloved standing on the porch alone but as everybody looked back, there was nobody standing on the porch. After the incident, Paul D came back into Denver and Sethes lives and they all forgot Beloved and thought of her as an unpleasant dream. Narrative Style This novel is written in third person singular with an omniscient style but however shifts to first person singular; Sethe had the amazing luck of six whole years of marriages to that somebody son who had fathered every one of her children and I never had to give it to nobody else and the one time I did it was took from me they held me down and took it. The pronouns he and she are frequently used and characters are continuously addressed by their names. The novel is also written in flashback whilst describing Sethes escape and the birth of Denver to Beloved. Flashback is also found when she recalls memories of Sweet Home with Paul D and when Paul D has memories of his brothers. Also there is a chapter written in stream of consciousness relating to Beloveds thoughts; I am not big small rats do not wait for us to sleep someone is thrashing but there is no room to do it in à ¢Ã¢â€š ¬Ã‚ ¦ Character Analysis Denver: is an independent, selfless young lady. This is shown through her care and devotion to Beloved when she arrives at the house sick. She is also a determined girl that devotes her time to her family, especially her mother when she is sick. Denver is an independent woman as her independence is shown when she seeks a job to support her family when her mother lost her job. Sethe: is a very kind and compassionate woman as she is devoted to her family, even during the hardest situations. This is shown because she was a slave in her past at Sweet Home and she escaped for her family. It is also portrayed when she went hungry and picked the crusts for her children to eat, especially Beloved. She is also a very proud woman as she is determined to endure the correct way of marriage at Sweet Home when marrying Halle this is shown when Sethe is adamant on having a wedding dress on the first night they are together. Beloved: at first is portrayed as a helpless woman, seeking attention and love. This is given to her by Denver as she cures her from her sickness by devoting her time. However, Beloved then becomes an untrustworthy, selfish woman. Her selfishness is shown manipulation, as she deceives Sethe by acting upon her guilt. She doesnt forgive Sethe for her past and forces power upon her to give her what she wants. Language Diction Beloved is a descriptive novel that uses informal language often including slang and vulgarity throughout dialogue. The language and diction also reflects the speech of Afro-Americans for example; Beloved, she my daughter. She mine. Long sentences are used to describe feelings and objects, for example; Although they had been polite to her during the quiet time and gave her the whole top of the bed, she remembered how it was before: the pleasure they had sitting clustered on the white stairs she between the knees of Howard or Buglar while they made up die-witch! stories with proven ways of killing her dead. Short sentences are used more often during dialogue such as; Now you. Come on, and Come on in here girls. Short sentences are also used to make impact and emphasize the meaning, for instance; 124 was spiteful. Full of a babys venom. Imagery The imagery is evident throughout the novel because all stimuli are aroused. Tactile imagery is evident when Paul D touches Sethe in the kitchen as he rubbed his cheek on her back and learned that way her sorrow. There is a sense of smell when the roses at the carnival are described; the closer the roses got to death, the louder their scent and stench of the rotten roses. Visual imagery is foreseen throughout the novel when the keeping room is described and how Baby Suggs was starved for colour. One can imagine the slate-coloured walls and the earth-brown floor and the dullness of the room. Auditory imagery is evident when Denver can hear chickens and the knock of a badly hinged gate as well as voices behind her as she walked. Taste imagery is evident when the numerous offers of foods are found on the tree stump each day, each meal provided by a different neighbour; sack of white beans, plate of cold rabbit meat, Taste imagery is also found during a memory of 124 of tonic mixed that cured a relative, as one can imagine the strength of the mixture. Themes The theme of evil is represented throughout the novel by Beloved, as a ghost and as a person. This is evident when the ghost of Beloved chases away her two brothers, Howard and Buglar as well as other people who use to walk along Bluestone Road. The evil represented through Beloved as a human being is when she manipulates Sethe and causes pain for Sethe, although Sethe only seeks forgiveness. A theme of religion is also apparent throughout the novel as God and Jesus are constantly being referred to. It is carried throughout the novel by Baby Suggs from her preaching at the Clearing then Paul D and at the end of the novel, by Denver who was given a Bible by Lady Jones. Setting This novel is set in America mainly 124 Bluestone Road. This is evident because Sethe escaped to Ohio to number 124 where Baby Suggs was living in Cincinnati. The novel is also set at a place called Sweet Home. Sweet Home is brought into the novel whilst Sethe has flashbacks of her past before she escaped. The setting is also evident because of the diction used whilst a character speaks. Genre The genre is a family drama because of the life experiences the family endure. All adult characters in the novel were previously slaves who had escaped and Baby Suggs was bought by her own sons earnings. Sethe also experienced her childs death before her own. After this, her dead daughter came back to 124 but tormented her by using her guilt against her. The novel is also an Afro-American genre because of diction used during speech and first person narrative style. Aspects I liked I enjoyed the fact that Sethe escaped from the hardships of being a slave at Sweet Home and that her present is better because she left the home. I also enjoyed the fact that Denver devoted her time to Beloved and that Sethe and Denver were accepting of her when they found Beloved sat outside their house. I didnt enjoy the fact that Paul D just left Sethe from his jealousy of Sethes love towards Beloved and his negativity and disloyalty towards Beloved. I also didnt enjoy the fact that Beloved turned against Sethe and starting making her pay for her past even though Sethe felt apologetic and guilty for what she had done and now only wanted to give Beloved the best. I was happy that Denver did everything she could to protect Sethe from Beloveds nastiness and glad when Denver and Sethe could forget the torment and pain Beloved caused. Recommendations I would recommend this novel to any high school children that is not easily offended by vulgar language but whoever understands the change from past to present as the novel is written in flashback making it a difficult read. I would also recommend this novel to one who enjoys reading about the hardships of life and devastation that can be caused in the future from mistakes in the past, affecting not just one person but a whole family.

Difference of Squares of Two Natural Numbers

Difference of Squares of Two Natural Numbers One of the basic arithmetic operations is finding squares and difference between squares of two natural numbers. Though there are various methods to find the difference between squares of two natural numbers, still there are scopes to find simplified and easy approaches. As the sequence formed using the difference between squares of two natural numbers follow a number patterns, using number patterns may facilitate more easy approach. Also, this sequence has some general properties which are already discussed by many mathematicians in different notations. Apart from these, the sequence has some special properties like sequence difference property, difference sum property, which helps to find the value easily. The sequence also has some relations that assist to form a number pattern. This paper tries to identify the general properties, special properties of finding difference between the squares of any two natural numbers using number patterns. A rhombus rule relationship between the sequences of numbers formed by considering the difference between squares of the two natural numbers has been defined. A new method to find a2 b2 also has been introduced in some simple cases. This approach will help the secondary education lower grade students in identifying and recognizing number patterns and squares of natural numbers. Mathematical Subject Classifications: (2010) 11A25, 11A51, 40C99, 03F50 DIFFERENCE BETWEEN SQUARES OF TWO NATURAL NUMBERS RELATIONS, PROPERTIES AND NEW APPROACH Introduction Mathematics, a subject of problem solving skills and applications, has wide usage in all the fields. Basic skills of mathematical applications in number systems used even in day to day life. Though calculators and computers have greater influences in calculations, still there is a need to find new easy methods of calculations to improve personal intellectual skills. As there has been growing interest, in mathematics education, in teaching and learning, many mathematicians build simple and different methods, rules and relationships in various mathematical field. Though various investigations have made important contributions to mathematics development and education (2), there still room for new research to clarify the mutual relationship between the numbers and number patterns. In natural numbers, various subsets have been recognized by ancient mathematicians. Some are odd numbers, prime numbers, oblong numbers, triangular numbers and squares. These numbers shall be identified by number patterns. Recognizing number patterns is also an important problem-solving skill. Working with number patterns leads directly to the concept of functions in mathematics: a formal description of the relationships among different quantities. One of the basic arithmetic operations is finding squares and difference between squares of two natural numbers. Already many proofs and relationships were identified and proved in finding difference between squares of two natural numbers. We use different methods to find the difference between squares of two natural numbers. That is, to find a2 b2. Though, this area of research may be discussed by early mathematicians and researchers in various aspects, still there are many interesting ways to discuss the same in teaching. Teaching number patterns in secondary level education is most important issue as the students develop their analytical and cognitive skills in this stage. Different arithmetic operations and calculations need to be introduced in such way that they help the students in lifelong learning. Easy and simplified approaches will support the students in logical reasoning. This paper tries to identify the general properties, special properties of finding difference between the squares of any two natural numbers using number patterns. Also, this paper tries to define the rhombus rule relationship between the sequences of numbers formed by the differences of squares of two natural numbers. A new method to find a2 b2 also has been introduced in some simple cases. These may be introduced in secondary school early grades, before introducing algebraic techniques of finding a2 b2 to develop the knowledge and understanding of number patterns. This will help to recognize and apply number patterns in further level. Literature Review To find the difference between the squares of any two natural numbers, we use different methods. Also, we use various rules to find the square of a natural number. Some properties were also been identified by the researchers and mathematicians. Methods used to find the difference between squares of two natural numbers Direct Method The difference between the squares of two natural numbers shall be found out by finding the squares of the numbers directly. Example: 252 52 = 625 25 = 600 Using algebraic rule The algebraic rule a2 b2 = (a b)(a + b) shall be applied to find the difference between the squares of two natural numbers. Example: 252 52 = (25 5)(25 + 5) = 20 x 30 = 600 Method when a b = 1(2) The difference between the squares of every two consecutive natural numbers is always an odd number, and that it is equal to the sum of these numbers. Example: 252 242 = 25 + 24 = 49 Methods used to find the square of a natural number Using Algebraic Method The algebraic rules shall be used to find the square of natural number other than the direct multiplication. In general, (a + b)2, (a b)2 are used to find the squares of a natural number from nearest whole number. Example: 992 = (100 1)2 = 1002 2(100)(1) + 12 = 10000 200 + 1 = 9801 Square of a number using previous number(8) The following rule may be applied to find the square of a number using previous number. (n + 1)2 = n2 + n + (n+1) Example: 312 = 302 + 30 + 31 = 900 + 30 + 31 = 961 The Gilbreth Method of finding square(9) The Gilbreth method uses binomial theorem to find the square of a natural number. The rule is n2 = 100(n 25) + (50 n)2 Example: 992 = 100(99 25) + (50 99)2 = 7400 + 2401 = 9801 Other than the above mentioned methods various methods are used based on the knowledge and requirements. Properties of differences between squares of the natural numbers 2.3.1. The difference between squares of any two consecutive natural numbers is always odd. To prove this property, let us consider two consecutive natural numbers, say 25 and 26 Now let us find 262 252 262 252 = (26 + 25)(26 25) [Using algebraic rule] = 51 x 1 = 51, an odd number 2.3.2. The difference between squares of any two alternative natural numbers is always even. To prove this property, let us consider two alternative natural numbers, say 125 and 127 Now let us find 1272 1252 1272 1252 = (127 + 125)(127 125) [Using algebraic rule] = 252 x 2 = 504, an even number Some other properties were also identified and discussed by various mathematicians and researchers. Number Patterns and Difference Between the Squares of Two Natural Numbers Discussions and Findings Some of the properties stated above shall be proved by using number pattern. Number patterns are interesting area of arithmetic that stimulates the logical reasoning. They shall be applied in various notations to identify the sequences and relations between the numbers. 3.1. Sample Table for the difference between squares of two natural numbers To find the properties and relations that are satisfied by the sequences formed by the differences between the squares of two natural numbers, let us form a number pattern. For discussion purposes, let us consider first 10 natural numbers 1, 2, 3 à ¢Ã¢â€š ¬Ã‚ ¦ 10. Now, let us find the difference between two consecutive natural numbers. That is, 22 12 = 3; 32 22 = 5; and so on. Then the sequence will be as follows: 3, 5, 7, 9, 11, 13, 15, 17 and 19. The sequence is a set of odd numbers starting from 3. i.e., Difference 1: {x| x is an odd number greater than or equal to 3, x ÃŽ N} In the same way, let us form the sequence for the difference between squares of two alternative natural numbers. That is, 32 12 = 8, 42 22 = 12, and so on. Then the sequence will be: 8, 12, 16, 20, 24, 28, 32 and 36 Thus the sequence is a set of even numbers and multiples of 4 starting from 8. i.e., Difference 2: {x| x is an multiple of 4 greater than or equal to 8, x ÃŽ N} By proceeding this way, the sequences for other differences shall be formed. Let us represent the sequences in a table for discussion purposes. In Table 1, N is the natural number. S is the square of the corresponding natural number. D1 represents the difference between the squares of two consecutive natural numbers. That is, the difference between the numbers is 1. D2 represents the difference between the squares of two alternate natural numbers. That is, the difference between the numbers is 2. D3 represents the difference between the squares of 4th and 1st number. That is, the difference between the numbers is 3, and so on. 3.2. Relationship between the row elements of each column Now, let us discuss the relationship between the elements of rows and columns of the table. From the above table, Column D1 shows that the difference between squares of two consecutive numbers is odd. Column D2 shows that the difference between squares of two alternate numbers is even. The other columns show that the difference between the squares of two numbers is either odd or even. From the above findings, the following properties shall be defined for the difference between squares of any two natural numbers. 3.3. General Properties of the difference between squares of two natural numbers: The difference between squares of any two consecutive natural numbers is always odd. Proof: Column D1 proves this property. This may also be tested randomly for big numbers. Let us consider two digit consecutive natural numbers, say 96 and 97. Now, 972 962 = 9409 9216 = 493, an odd number Let us consider three digit consecutive natural numbers, say 757 and 758. Thus, 7582 7572 = 574564 573049 = 1515, an odd number This property may also be further tested for big numbers and proved. For example, let us consider five digit two consecutive natural numbers, say 15887 and 15888. Then, 158882 158872 = 252428544 252396769 = 31775, an odd number Apart from these, the property shall also be easily derived by the natural numbers properties. As the difference between two consecutive numbers is 1, the natural number property The sum of odd and even natural numbers is always odd, shall be applied to prove this property. The difference between squares of any two alternative natural numbers is always even. Proof: Column D2 proves this property. This may also be verified for big numbers by considering different digit natural numbers as discussed above. Apart from this, as the difference between two alternate natural numbers is 2, the natural numbers property A natural number said to be even if it is a multiple of two shall also be used for proving the stated property. The difference between squares of any two natural numbers is either odd or even, depending upon the difference between the numbers. Proof: The other columns of Table 1 prove this property. In Table 1, as D3 represents the sequence formed by the difference between two natural numbers whose difference is 3, an odd number, the sequence is also odd. Thus, the property may be proved by testing the other Columns D4, D5, à ¢Ã¢â€š ¬Ã‚ ¦ Also, the addition, subtraction and multiplication properties of natural numbers prove this property. Example: 112 62 Here the difference (11 6 = 5) is odd. So, the result will be odd. i.e. 112 62 = 121 36 = 85, an odd number 122 82 Here the difference (12 8 = 4) is even. So, the result will be even. i.e. 122 82 = 144 64 = 80, an even number 3.4. Special Properties of the difference between squares of the two natural numbers Table 1 also facilitates to find some special properties stated below. Sequence Difference Property Table 1 shows that the sequences formed are following a number pattern with a common property between them. Let us consider the number sequences of each column. Let us consider the first column D1 elements. D1: 3, 5, 7, 9, 11 à ¢Ã¢â€š ¬Ã‚ ¦ à ¢Ã¢â€š ¬Ã‚ ¦ As D1 represents the difference between the squares of two consecutive natural numbers, let us say, a and b with a > b, the difference between them will be 1. That is a b = 1 Let us consider the difference between the elements in the sequence. The difference between the numbers in the sequence is 2. Thus the difference between the elements of the sequence shall be expressed as, 2 x 1. Thus, Difference = 2(a b) Now, let us consider the second column D2 elements. D2: 8, 12, 16, 26, à ¢Ã¢â€š ¬Ã‚ ¦ à ¢Ã¢â€š ¬Ã‚ ¦ à ¢Ã¢â€š ¬Ã‚ ¦ As D2 represents the difference between the squares of two alternative natural numbers, the difference between the natural numbers, say a and b is always 2. That is a b = 2 If we consider the difference between the elements in the sequence, the difference is 4. Thus, the difference between the elements in the sequence shall be expressed as 2 x 2. That is, difference = 2 (a b) In the same way, D3: 15, 21, 27, 33, à ¢Ã¢â€š ¬Ã‚ ¦ à ¢Ã¢â€š ¬Ã‚ ¦ à ¢Ã¢â€š ¬Ã‚ ¦ D3 represents the difference between squares of the 4th and 1st numbers, difference is 3. That is a b = 3 The difference between the numbers in the sequence is 6. Thus, difference = 2 x 3 = 2(a b) All other columns also show that the difference between the numbers in the corresponding sequence is 2 (a b) Thus, this may be generalized as following property: The difference between elements of the number sequence, formed by the difference between any two natural numbers, is equal to two times of the difference between those corresponding natural numbers. Difference Sum Property: From Table 1, we shall also identify another relationship between the elements of the sequence formed. Let us consider the columns from table 1 other than D1. Consider D2: 8, 12, 16, 20, à ¢Ã¢â€š ¬Ã‚ ¦ This sequence shall be formed by adding two numbers of Column D1. i.e. 8 = 3 + 5 12 = 5 + 7 16 = 7 + 9 20 = 9 + 11 And so on. Thus, if the difference between the natural numbers taken is 2, then the number sequence of the difference between the two natural numbers shall be formed by adding 2 natural numbers. Consider D3: 15, 21, 27, à ¢Ã¢â€š ¬Ã‚ ¦ This sequence shall be formed by adding three numbers from Column D1. i.e. 15 = 3 + 5 + 7 21 = 5 + 7 + 9 27 = 7 + 9 + 11 And so on. Thus, if the difference between the natural numbers taken is 3, then the number sequence of the difference between the two natural numbers shall be formed by adding 3 natural numbers. This may also be verified with respect to the other columns. Table 2 shows the above relationship between the differences of the squares of the natural numbers. Now the above relation shall be generalized as If a b = k > 1, then a2 b2 shall be written as the sum of k natural numbers As Column D1 elements are odd natural numbers, this property may be defined as If a b = k > 1, then a2 b2 shall be written as the sum of k odd natural numbers As these odd numbers are consecutive, the property may be further precisely defined as: If a b = k > 1, then a2 b2 shall be written as the sum of k consecutive odd natural numbers 3.5. New Method to find the difference between squares of two natural numbers Using the above difference sum property, the difference between squares of two natural numbers shall be found as follows. The property shows that, a2 b2 is equal to sum of k consecutive odd numbers. Now, the principal idea is to find those k consecutive odd numbers. Let us consider two natural numbers, say 7 and 10. The difference between them 10 7 = 3 Thus, 102 72 = sum of three consecutive odd numbers. 102 72 = 100 49 = 51 Now, 51 = Sum of 3 consecutive odd numbers i.e., 51 = 15 + 17 + 19 Let we try to find these 3 numbers with respect to either the first number, let us say, a or the second number, say, b. Assume, for b As general form for odd numbers is either (2n + 1) or (2n 1), as b 15 = 2(7) + 1 = 2b + 1 17 = 2(7) + 3 = 2b + 3 19 = 2(7) + 5 = 2b + 5 Thus, 102 72 shall be written as the sum of 3 consecutive odd numbers starting from 15. i.e. starting from 2b + 1 This idea may also be applied for higher digit numbers. Let us consider two 3 digit numbers, 101 and 105. Let us find 1052 1012 Here the difference is 4. Thus 1052 1012 shall be written as the sum of 4 consecutive odd numbers. The numbers shall be found as follows: Here b = 101 The first odd number = 2b + 1 = 2(101) + 1 = 203 Thus, the 4 consecutive odd numbers are: 203, 205, 207, 209 So, 1052 1012 = 203 + 205 + 207 + 209 = 824 This shall be verified for any number of digits. Let us consider two 6 digit numbers 100519, 100521. Let us find 1005212 1005192 Here the difference is 2. Thus 1005212 1005192 shall be written as the sum of two odd numbers. Applying the same idea, The first odd number = 2(100519) + 1 = 201039 Thus the 2 consecutive odd numbers are: 201039, 201041 1005212 1005192 = 201039 + 201041 = 402080 The above result shall be verified by using other methods. For example: 1052 1012 1052 1012 = 11025 10201 = 824 (Using Direct Method) 1052 1012 = (105 + 101) (105 101) = 206 x 4 = 824 (Using Algebraic Rule) Thus, this idea shall be generalized as follows: a2 b2shall be found by adding the (a b) consecutive odd numbers starting from 2b + 1 This shall also be found using the first term a. As a > b, let us consider (2n 1) form of odd numbers. From Table 1, 102 62 = 13 + 15 + 17 + 19 = 64 Here, 2a 1 = 2(10) 1 = 19 2a 3 = 2(10) 3 = 17 2a 5 = 2(10) 5 = 15 2a 7 = 2(10) 7 = 13 Thus, as the difference between the numbers is 4, 102 62 shall be written as the sum of four consecutive odd numbers in reverse order starting from 2a 1. Thus proceeding, this may be generalized as, a2 b2shall be found by adding the (a b) consecutive odd numbers starting from 2a 1 in reverse order Finding the first number of each column Let us check the number pattern followed by the first numbers of each column. From Table 1, the first numbers of each column are: 3, 8, 15, 24 à ¢Ã¢â€š ¬Ã‚ ¦ Let us find the difference between elements of this sequence. The difference between two consecutive terms of this sequence is 5, 7, 9 à ¢Ã¢â€š ¬Ã‚ ¦ i.e. D2 D1 = 8 3 = 5; D3 D2 = 7; D4 D3 = 9 and so on. As D2 represents the difference between two alternate natural numbers, (say a and b) which implies that the difference between a and b is 2. Now, 5 = 2 (2) +1 i.e. 2 times of the difference between the numbers + 1 In the same idea, D3 D2 = 15 8 = 7 As D3 represents the difference between squares of the 4th and 1st natural numbers, (say a and b) which implies that the difference between a and b is 3. Thus, 7 = 2(3) + 1 This also shows that the difference shall be found by = 2 times of the difference between the numbers + 1 Thus, The first term of the each column shall be found by adding the previous column first term with 2 times of the difference between the numbers + 1 Finding the elements row wise The elements of the table shall also be formed in row wise. If we check the elements of each row, we can find that they follow a number pattern sequence with some property. Let us consider the elements of row when N = 5: 20, 40, 60, 80 20 = 2 x 5 x 2 Here, 5 represent the row natural number. 2 represent the difference between the elements using which the column is formed. Thus Row element = 2 x N x difference In the same way, 40 = 2 x 5 x 4 = 2 x N x difference Thus, the elements shall be formed by the rule: Row Element = 2 x N x difference This shall be applied for middle rows also. For example, let us consider the row between 5 6: The elements in this intermediate row are: 11, 33, 55, 77, 99 Here N is the mid value of 5 6. i.e. N = 5.5 Let us consider the elements and apply the above stated rule. 11 = 2 x N x difference = 2 x 5.5 x 1 In the same way other elements shall also be formed. Thus the elements of the table shall be formed in row wise using the stated rule. Rhombus Rule Relation Let us consider the elements in D2, D3 and D4. Consider the elements in the rhombus drawn, 24, 33, 39 and 48 24 + 48 = 72 33 + 39 = 72 Thus the sums of the elements in the opposite corners are equal. The other column elements also prove the same. Thus, Rhombus Rule Relation: Sum of the elements the same row of the sequence of alternative columns is equal to the sum of the two elements in the intermediate column Application of the Properties in Finding the Square of a number The square of a natural number shall be found by various methods. Here is one of the suggested methods. This method uses nearest 10s and 100s to find the square of a number. This method is also based on the algebraic formula a2 b2 = (a b)(a + b) If a > b, b2 = a2 (a2 b2) If b > a, b2 = a2 + (b2 a2) Example: Square of 32 As we need to find 322, let us assume b = 32. The nearest multiple of 10 is 30. Let a = 30 Here b > a. b2 = a2 + (b2 a2) 322 = 302 + (322 302) Using the Difference Sum Property, 322 = 900 + 61 + 63 = 1024 Example 2: Square of 9972 Let b = 997 Nearest multiple 10 is 1000. Let a = 1000 Here a > b, so b2 = a2 (a2 b2) 9972 = 10002 (10002 9972) Using Difference Sum Property, 9972 = 1000000 (1995 + 1997 + 1999) = 994009 Conclusion Though this method shall be applied to find the difference between squares of any two natural numbers, if the difference is big, it will be cumbersome. Thus, this method shall be used for finding the difference between squares of any two natural numbers where the difference is manageable. The properties shall be used for easy calculation. This properties and approach shall be introduced in secondary school lower grade levels, to make the students to identify the number patterns. This approach will surely help the students to understand the properties of squares, difference and natural numbers. The new approach will surely help the students in developing their reasoning skills. Limitations As number systems, number patterns and arithmetic operations have wide applications in various fields, the above properties, rules and relations shall be further studied intensively based on the requirements. Thus, new properties and relations shall be identified and discussed with respect to other nations.

Votes For Sale :: essays research papers

Votes For Sale According to the Associated Press, lobbyist donated 633 million dollars to government representatives in the first half of 1999. A lobbyist’s job is to pass money to representatives for a vote in their favor of a bill. Up to $5000 may be given to any one congressman by a lobbyist thru Political Action Committees (PACs). Farmers, laborers, gun control activists, abortion opponents, and teachers are just a few of the numerous groups who form these committees in the United States. These interest groups employ a lobbyist to offer a cash donation on their behalf. The legislative branch of the United States government was designed to represent citizens of this nation. Congressional members are supposed to be the representatives of people in their district or state. Laws are supposed to be passed in the public’s best interest. PACs attempt to influence the passing of laws through lobbyists. Lobbyists degrade democracy, encourage improper policymaking, and likely provoke politi cal corruption. The most obvious downfall to lobbying is that representatives would be encouraged to vote for money; causing a degradation of democracy. In other words, if a pro-life group paid a representative to vote against legalizing abortion the money would influence the representative’s vote. Whether or not a bill is passed becomes an issue of who is willing and able to pay more for it. Congressmen would look to vote for bills that would get them the most money from the PACs. Even though $5,000 is the maximum donation a lobbyists can give to one particular politician; lobbyists donate to several. This can give them the upper hand in a majority decision. Lobbyists believe they are representing the people and getting bills passed that the people want, thus promoting the citizen’s role in the government. The problem with this view is that the money is getting more representation than the people are. The group that has the most money and buys the most votes will get more bills passed in their favor, regardless if they are the majority or not. This takes away from the democratic process; not allowing all the people’s votes to count. A representative should vote for those who elected him not those who pay him the most. When a representative’s vote is influenced by money the fundamentals of democracy are defeated. Secondly, representatives benefit directly from lobbyist’s donations. Therefore, representatives will use improper policymaking to assure a lobbyist’s cause is ratified.

Preventing Bioterrorism Essay -- Biodefense, Biological Attack

September 11, 2001, signifies the most pivotal moment in United States history. It marks a great paradigm shift in the attitude of United States towards terrorism. Prior to September 11, policies to protect against terrorism were perforated with in fighting between government agencies, a lack of centralized intelligence sharing, and general surprise. This event marks the beginning of the largest growth in the United States intelligence community. The United States increased security all around the board, opened up and centralized its agencies, and began to prepare for new kinds of terrorist attacks. The country never experienced a bio-terrorist attack, and yet the threat is very real. From the Cold War, the United States fully understood the harm biological weapons can inflict. The attacks of September 11 demonstrate the preparation against domestic terrorist attacks and the damage terrorist can cause. As the United States continue to increase its security against terrorism, it is imperative it understands and prepares for a potential bio-terrorist attack. There are many events throughout which demonstrate the potential catastrophe a calculated bio-terrorist attack can create. The Black Death of the 14th century illustrates how quickly and how deadly a disease can spread. The plague originated in China and arrived via trade routes to Europe by the mid-14th century. By the end of the 14th century, the disease killed more than half the world’s population. The world witnessed its first case of biological warfare during the French and Indian Wars. British commander of the North America forces, Sir Jeffrey Amherst, ordered his troops to donate to Native Americans blankets infested with smallpox. As result, Native Ame... ...emonstrated the silent nature of such attacks and the damages they can exact on large populations. The plagues of the 14th century, the use of smallpox against the Indians, and the intentional Salmonella poisoning in the 1980’s exemplify this fact. The fall of the Soviet Union in the 1990’s along with other political events, resulted in vast amounts of bio-agents disappearing and falling into the wrong hands. Opponents claim it is too complex and requires too many resources to carry out large scale attacks; however, with biological weapons, a few infected people can spread the disease to thousands. The modern tactics of terrorism are unconventional, unexpected, and able to kill thousands. As terrorists become more organized and funded, it is essential that the United States increase its capabilities at preventing and defending against bio-terrorist attacks.

Royal Foolishness in King Lear Essay -- King Lear Essays

The presentation of persistent incompetence of the elite class would seem unlikely in a Shakespearean tragedy. Yes, it in turn led to the expected downfall of almost all principle characters, but there seems to be another element of the play of King Lear – shameful ridicule. The repetition of dishonesty, superficiality, and blatant ignorance serves as an overwhelming theme of the dysfunction of nobility. Indeed, one of the main aspects of King Lear is the representation of royalty’s foolishness. A clear example of the naiveness of the nobility is Regan’s hunger for power and wealth at an extent where she demonstrates little respect towards her own father – also her beneficiary. She insults his age and rudely implies that he no longer deserves the status of king and should pass it on to someone more capable. Ironically, she has the least potential for being an adequate ruler, â€Å"O sir, you are old†¦ You should be ruled and led by some discretion that discerns your state better than yourself† (II.iv.165-169). Her shameless remark touches upon Lear’s own flaws, his d...

Course purshasing Essay

* Founded by France Dominique Mandonnaud in 1969 as a simple perfume shop. * By 1979 the company was already expanded to â€Å"several stores† * Originally, Sephora was planned to be self-service store that offers a variety of products. * Its founder Mandonnaud rebranded his combined set of stores in order to expand is market. * Mandonnaud extended its branches all over France by acquiring 8% of total French retail perfume market and was purchased by LVMH, luxury product group, for $262 million in 1997. * Sephora expanded its operations and services beyond the perfume industry and expanding its core of products to cosmetics. * Under LNMH’s ownership and opened its first U. S store in New York City in 1998 However, this presented a challenge for the company as they had a difficult time to supply the products from other prestigious brands; such as Estee Lauder and Clinique. * The Company banked on rather unknown brands to fill its shelves therefore, these relationships grew strong and eventually this fact led to the innovation and creativity of these brands to introduce new lines of products. * Sephora confronted many issues on their cosmetic line division, especially with the direct line of supply from other stores. * Bottom line, Sephora offers more than 200 brands that go from the typical classics to new and exotic brands; altogether, Sephora counts with more than 20,000 products. Among those products we could find top of line and sophisticated brands as well as not so well know products. * Sephora formed an strategic alliance with JC Penny. * Sephora. com was projected to generate 15-20% of Sephora USA sales in 2010. * Sephora. com ranked top 50 retail sites in U. S SWOT analysis Strengths * Globally distributed with more than 1000 shops worldwide * Strong parent company; LVMH * More than 20,000 products to offer. * Strong online sales * self-service approach to cosmetics * Strong emphasis on construct loyalty brand by tracking down the customers shopping habits. Weaknesses * Modest operational budget. * Low brand recognition * Lack of TV promotions and print ads. * Higher price than drugstores and supermarkets Opportunities * Enhance their customer loyalty program in order to build a â€Å"relationship† with the product consumers. * Sign contracts with famous celebrities to endorse their products. * Introduction to enter into emerging economies such as Brazil and India. Threats * Economic downturn. * Other companies in the same industry. * Amazon and other online companies that sale cosmetic, with their aggressive approach could certainly become a threat. Identification of Problem * Personnel and financial constraints needed to be addressed. * Imagination and inventiveness was greatly needed. * Budget limitation, presented a real challenge when it comes to budget allocation to different initiatives. * Outcomes assessment of social media campaigns as well as mobile applications constituted a real test to overcome. Sephora Direct Julie Bornstein took Sephora on another journey. She transforms the marketing view to a much modern and up to date campaigns. * New Budget request was introduced in order to launch a major campaign that will include social media, web site enhancement as well as the implementation of â€Å"customer relationship† campaigns. * Campaign success should be assessed thorough out Facebook â€Å"likes† and twitter followers as well as I phone application downloads. Sephora. com and Beauty Insider * Sephora. com was implement on 1999 with very imp clear short and long term goals. * Up to 25% of sales should be generated by Sephora. com by 2010. * By 2007 Sephora developed its Beauty Insider campaign. * Incentives such as 1 point for every dollar, redeem points programs are among those strategies in order to create that â€Å"relationship† with its customers Social Media Although this initiative had a rocky start, eventually become a success, Bornstein visionary initiative and her persistence, this initiate obtained 1 million product reviews posted on their web site. (Ofek, 2012). Facebook * Sephora join Facebook by 2008 in less than a year their account had close to 300,000 fans in Facebook. * Last statistics show the Sephora page with more than 900,000 Twitter * By 2010, Sephora had approx. 100,000 users. * Primarily used for current promos, contests, events, etc. * Customers used it to tweet about newly found products. You Tube * Used by Sephora to upload â€Å"How to Videos† on make-up applications; however this sharing video site could be utilized on a much more aggressive way. Cell phone applications * The rapid pace of technology forced mayor companies such as Sephora to create applications for smart phones like IPhone, Droid, Blackberry, etc. Alternatives Budget Re-distribution As stated previously the fast pace of technology constitute a real challenge not only to Sephora but to every single company. Therefore, I would like to present the following suggestions: * Cellphone applications should really receive a great attention and consequently, more financial Resources. * Pros * Instant reaching out to their customer base * Cons * Increase cost of application development fees. * Facebook, according to younger generations has become â€Å"not cool† and obviously not as attractive for younger women, therefore Sephora should look into other popular social media networks in order target new customers that eventually become loyal customers. Instagram, Pheed, thumb, Medium, etc. should be receiving at least 5% of the developmental budget for emerging social sites. * Pros * Targeting potential new buyers, young men and women that are eager to take on the world. * Cons * This target population might take some time in order to become actual customers. * Beauty Insider should remain at 20% as this constitutes the strongest campaign for Sephora when it comes to help â€Å"Sephora loyal customers†. * Pros * Continuous catering of â€Å"loyal customers† * Cons * Become obsolete if new strategies are not develop. * Retailing – print catalogs, store animations. Should receive 30% percent of their developmental budget as these tools have become obsolete for the most part. (Personal opinion) * Pros * Reduction of cost in traditional advertise. * Cons * Potential loose of mature but loyal customers. Recommendation Finally, my recommendation will be to start a comprehensive Research of outcomes in the different categories of initiates developed under Julie Bornstein leadership. Based on those findings re-restructure the entire budget and re-think some of our means to reach out to new and existing customers. We live in a fast speed life and therefore our customers are as busy as they could help. Therefore Sephora must constantly evaluate and re-design their marketing strategies in order to provide the upmost friendly user options to inform serve and sell our products and services to their consumers. Therefore I would choose the Cellphone application development to receive a greater part of the advertisement developmental budget and at the same time re-balance other line of the budgets in order to adjust the budgets accordingly to the outcomes evaluation done thorough the above suggested research.

Catch 22 By: Joseph Heller Essay

Catch 22 has many scenes of violence in it that helps to contribute to the meaning of the complete work. The first scene of violence that helps portray the complete meaning of the novel is Kid Sampson being cut in half by McWatt while flying his plane too low to the ground. The second scene of violence was when Yossarian broke Nately’s nose on Thanksgiving while some men were playing around with the machine gun. And finally the last example of violence in Catch 22 the help contributes to the meaning of the novel is Milo Minderbinder making a contract with the Germans to have him fire on his own unit to help the syndicate. These scenes give a good idea on how the violence of Catch 22 contributes to the meaning of the complete work of the novel and shows the importance of the violence to the novel. The first scene of violence that helps portray the meaning the novel Catch 22 is McWatt accidently killing Kid Sampson on the beach. McWatt was flying way too low to the ground like he does all of the time and flew over the beach. Then he went right at Kid Sampson and then sliced him to pieces with the blade of his ship. Kid Sampson was at the beach with everyone else and he was standing on a raft when he got hit by the plane. McWatt was on a training flight with two new pilots showing them how to fly when it happened. They parachuted out of the plane and he rode it into the side of a mountain. Everyone thought Doc Daneeka died in the plane accident becasue McWatt put Doc Daneeka name down for flight hours but he was really on the ground with everyone else. Yossarian warns him about flying so low but he still decides to fly low to the ground. Colonel Cathcart is so devastated about what happened he made the missions go up even more than it was before. This is how McWatt accidently ki lling Kid Sampson is important to the novel. The second scene of violence in Catch 22 is Yossarian breaking Nately’s nose on Thanksgiving when Nately tried to stop Yossarian from shooting the guys firing the machine gun at the base. Then Nately told his whore and she hated Yossarian for that. When Nately got killed in the disastrous crash on the La Spezia mission with Dobbs, Yossarian decides to go to Rome and tell her what happened to Nately. When he was there, she tired to kill and was throwing  stuff at him. Then she keeps following him around wherever he went. She was in the plane when it landed and she was at the base. Then she jumped out of a bush after he got out of the Colonel Cathcart and Colonel Korn office. They were discussing sending home Yossarian and about giving him a medal. But she stabbed him and he had to go to the hospital. This is why Yossarian breaking Nately’s nose on Thanksgiving was important to the story. The last major scene of violence in Catch 22 that was important to the novel had to do with Milo and the M &M Enterprises is in the business for finding the best deals and trading to make a profit for the syndicate. His only failure was buying Egyptian cotton was going to ruin his business because he can’t sell it. He made a deal with the Germans who by the way were the enemies of America in the war. The deal stated that he had to bomb his own outfit and many of his own men were hurt during this. Milo even decided it was best for him to tip off the Germans during a surprise attack by the Americans. But instead of getting punishes for shooting his own unit the public celebrates all of his profits he made. His explanation for playing for both sides was if it benefits the syndicate it benefits the men and it is worth taking a risk for. Then he decides he wants to fly more missions because he has only seven but Colonel Cathcart makes him agree to have the men fly his missions for him. This is the cause for more un needed deaths in the novel. This is how Milos bombing his own unite helps show how violent scenes are important to the novel. Throughout the novel Catch 22 there are many scenes of violence. These violent scenes help to contribute to t he meaning of the book. The first scene was when Yossarian broke Nately’s nose during the Thanksgiving celebration which causes Nately’s whore to hate him. The second scene of violence that contributed to the meaning of the book was when McWatt Killed Kid Sampson with his airplane. And finally the last scene was when Milo started shooting at his own unit after making a deal whit the Germans. This is how these scenes help to contribute to the whole meaning of Catch 22.

Being a Man: Rhetorical Analysis

Being a Man, by Paul Theroux, delineates the negative effects of being a man According to himself. Theroux, in his piece, argues that a man is oppressed by gender expectations, despite living in a society where women are belittled in comparison to men. Theroux attempts to explain the gap between genders which cause bad marriages, social misfits, moral degenerates, sadists, and latent rapists. Theroux proposes that the idea of manhood in America has caused some men to feel like they dislike being a men, and caused them to reject part of their own identity deep down inside.His overall purpose it to bring awareness to both genders that an oppression is happening to American society due to gender. Theroux tries to create understanding between the two opposing genders and find common ground against the same type of oppression both genders face, â€Å"This version of masculinity is a little like having to wear an ill-fitting coat for one’s entire life (by contrast, I imagine femini nity to be an oppressive sense of nakedness)†.Theroux uses parenthetical comments in order to widen the range of theme to his essay. He not only writes about man, but about women to and how they both have become affected by the gender constructs put in place from living in an American society. This allows his target audience (both men and women) to become understanding of his purpose in the essay. Not only are men able to relate, but women to as they are remembered in the fact that they face the same oppression as the one described by Theroux.This rhetorical effect is repeated to reemphasize Theroux’s purpose, â€Å"(The paradox in American letters is that it has always been easier for a woman to write and for a man to be published)† Theroux is able to not only give the message that the gender constructs oppresses only men, but also women, gender in general for that matter. Theroux is able to successfully convey his message (to both genders) that this society is harmful to both genders. Theroux appeals to the audience’s sense of emotion as he applies his arguments soundly to gender oppression, an emotion felt with both members to his target audience.His argument is that gender constructs lead to an oppression that leaves one feeling a displeasure with their own identity. This feeling of self-loathing appeals to people’s sense of emotion. This appeal allows the readers to engage and relate, which captivates them into realizing Theroux’s message. Theroux is effective in his proper use of pathos without having to consult much with the author branches of persuasion, credibility and logic. Personally I am not able to relate much with the American gender construct. Seeing as I was raised in a more Mexican household, I was raised to believe in a stricter gender construct.One that doesn’t apply much to Theroux’s description of the male gender construct setup by American society. Mine has roots in a one that emphas izes absolute respect for women and realizing that her body is nothing less than sacred. You’d think that this would be a better way of thinking, but this kind of thinking still implies that a woman is in need of more respect, which creates a kind of sexual inequality. Although making sense and persuading me in his argument, I was not able to relate to his argument, which was part of his purpose.

Crime Scene Sketching

Crime Scene Sketching The effect of modern media on crime scene investigation has led most people to believe that crimes are relatively easy to solve and may only take a day or two to complete. In actuality crime scene investigation is a lengthy process in which investigators can spend years investigating one crime. The components of crime scene investigation themselves can be rigorous and demanding depending on the circumstance.A vital piece of crime scene investigation is crime scene sketching; a tool that seems to be less in the forefront of modern television shows, perhaps because this is a less effective way to portray the gore that attracts the audience to most of these shows in comparison to crime scene photography that is often highlighted in shows like CSI. Crime scene sketching however is a critical part of crime scene investigation.Crime scene sketching in comparison to crime scene photography can capture a â€Å"bird’s eye† view of the crime scene, can show relativity between items and can offer a â€Å"whole crime scene picture† instead of being in fragmented pieces or from one particular angle like photographs. Crime scene sketching has been a long standing process in investigations and is a technique that has an abundance of benefits. It is a permanent record that provides supplemental information that is not easily accomplished with the exclusive use of crime scene photographs and notes.A crime scene sketch depicts the overall layout of a location and the relationship of evidentiary items to the surroundings. It can show the path a suspect or victim took and the distances involved. It can be used when questioning suspects and witnesses. During trial, the crime scene diagram correlates the testimony of witnesses and serves as a tool for relaying reference and orientation points to the prosecutor, judge and jury. A crime scene sketch is a rough drawing/scale model drawing composed by an investigating officer at the crime scene .The crime scene sketch is a simple line drawing that indicates the position of the body in relation to fixed and significant items in the scene (ex: a door, table or window)(Garrett). It is usually in addition to an officer’s written report and photographs. The crime scene sketch is an amazing visual aid, and because officers can choose which items to include in the sketch it can eliminate unnecessary items that photographs can’t like clutter or items that are unrelated, it also can highlight the significance of important items like the closeness between the victim and the murder weapon or unusual blood spatter. DOJ Wisconsin) It has been well established in court that a well drawn diagram is an aid to the judge, jury and witnesses in visualizing the crime scene. Their admissibility usually lies in their relevance and accuracy. This type of evidence may be referred to as illustrative or demonstrative evidence. (DOJ Wisconsin) Even poorly drawn sketches have been admit ted into evidence, as long as they are shown to be fair representations of the scene and it's surroundings. There are four types of crime scene sketches used in investigations; Overview sketches consist of a bird’s-eye-view or floor plan sketch of the scene.This is the most common type of sketch and consists of items on the horizontal plane. An elevation sketch portrays a vertical plane rather than a horizontal plane. Examples include bloodstain patterns on vertical surfaces such as walls or cabinetry and bullet holes through windows. Exploded view or cross-projection sketches consist of a combination of the first two sketches. It is similar to a floor plan except the walls have been laid out flat and objects on them have been shown in their relative positions.Perspective sketches depict the scene or item of interest in three dimensions. It is the most difficult sketch to create and requires some artistic skill. (Gerber, 216) When an investigating officer begins his sketch he must have paper (typically graph paper to include proper measurements to scale, but blank paper is often used), a pencil and eraser, a ruler or straight edge and a steel tape usually 100’ ft. It is also extremely beneficial to have a compass to determine true North.Measurements are an important part of the crime scene sketch, something that photographs cannot do. In photographs angles can make objects appear closer or further apart than they are in actuality. Drawing things to scale is not always necessary, although it is valuable to do so. Drawing sketches to scale avoids a distorted view of the scene; measurements must be reduced in proportion so that they bear correct relationship to each other; however, in drawing sketches not to scale Sketch can be accomplished more quickly than a scaled diagram.Items are placed in the diagram based on approximation by the investigator drawing the scene. This type of diagram may provide a distorted view of the scene. Correct proportions and relationships between objects may not be maintained. Measurements are recorded on the sketch or in a chart. This rough sketch may be used to complete a scaled diagram later. These diagrams should be clearly marked as not to scale. (Garrett) All measurements are taken from a fixed point, a door or window, stairs or a chimney. They should be exact and taken with a steel tape or ruler.Usually one investigator takes the sketch while another officer takes measurements and while investigators can often estimate relative distances or positions in rough sketches; measurements are taken for exact locations. In situations where no measurement instruments are available investigators can use pace measurements but these are not exact and are often less reliable and credible. (Hess and Orthmann) A crime scene drawing is one of the simplest and most effective ways to show measurements, these measurements are important because they show relativity and distance between significant items.The inv estigator has five ways to show these measurements in a crime scene drawing. These measurement techniques include: Straight-line in which two measurements are made, one from each side of the object, to a fixed point in the diagram. This method is usually used to mark positions of furniture or evidence against a wall like blood spatter. The second method an investigator can use is the rectangular coordinates or perpendicular distance method in which two measurements are taken at right angles of an item to the nearest two permanent objects, often walls.This method is usually the best way to mark the location of a body or other significant evidence. The polar coordinates or triangulation method is done by using a compass and a protractor, the investigator locates two fixed points and transfers this information to the sketch. Measurements are then taken from these two fixed points to the object, forming a triangle, where these two points intersect is the exact location of the object. Th e fourth method used for finding measurements is the base line method; this method is used for a scene that doesn’t have a straight perimeter like a large wooded area or a river.In the baseline method a straight line is drawn through the scene and each end is located and measured. A starting point is designated (ex: the north side of the river is determined the starting point) and the base line is then used as a reference for all of the other measurements. The final technique for measurements is the two fixed point method where an investigator takes two straight line measurements to two fixed points within the scene. In this method no right angle is required, but the two points used should not be close together.In a professional and legally correct crime scene sketch an officer will include a title block, this title block includes: the name and title of the investigator who drew the sketch, the date and time that the sketch was made, the classification of the crime (homicide, burglary etc. ), the identification of the victim if known, the agency’s case number, any names of persons assisting in taking measurements, the location of the location sketched, and the reference points included in the legend such as compass directions.Several CAD based programs are commercially available that can be used to create a professional and accurate crime scene diagram. With laptops becoming more common, these types of programs can be used at the scene to record measurements and generate sketches. These diagrams can also be generated back at the office using rough sketch(es) created at the scene. Portable devices now exist that can perform a 360 ° scan of a crime scene in as little as 20 minutes, capturing millions of measurements of all objects visible to the scanner. Dozens of high-resolution images are captured automatically.The device requires only the space needed by a standard photographer’s tripod. The data generated can be used to find the distan ce between any two points in the scene, to view the scene from any vantage point (including directly overhead), and to create a full-color, 3D model for investigative and courtroom purposes. (DOJ Wisconsin) With the benefits of crime scene sketching and the advancement of technology, crime scene sketching is more than ever being helpful in investigations and court. The benefit of crime scene sketching will continue to develop as more ways of crime scene sketching becomes available.