Euthanasia Essay - Religious Views on Assisted Suicide -- Euthanasia P

Official Religious Views on Euthanasia and Assisted Suicide      Ã‚  Ã‚  Ã‚   This essay is dedicated to the expression of the various official views of religious bodies within our nation. Most major denominations are represented. These religions have long been the custodians of the truth, serving to check the erratic and unpredictable tendencies of political, judicial and social bodies which would have Americans killing off their elderly and handicapped.    The National Association of Evangelicals believe that human beings are made in the image of God and are, therefore, of inestimable worth. God has given people the highest dignity of all creation. Such human dignity prohibits euthanasia, that is actively causing a person's death.    Is it moral to withdraw a life-support system which is believed to be an inappropriate extension of the dying process? The National Association of Evangelicals (NAE) believes that in cases where patients are terminally ill, death appears imminent and treatment offers no medical hope for a cure, it is morally appropriate to request the withdrawal of life-support systems, allowing natural death to occur. In such cases, every effort should be made to keep the patient free of pain and suffering, with emotional and spiritual support being provided until the patient dies. The National Association of evangelicals believes that in cases where extensive brain injury has occurred and there is clear medical indication that the patient has suffered brain death (permanent unconscious state), no medical treatment can reverse the process. Removal of any extraordinary life-support system at this time is morally appropriate and allows the dying process to proceed.(National)    The Union of Orthodox... ...rson cannot be legitimately interrupted. The use of painkillers to alleviate the sufferings of the dying, even at the risk of shortening their days, can be morally in conformity with human dignity if death is not willed as either an end or a means, but only foreseen and tolerated as inevitable. Palliative care is a special form of disinterested charity. As such it should be encouraged. (Catechism) WORKS CITED: National Association of Evangelicals of America http://www.euthanasia.com/evangel.html Union of Orthodox Jewish Congregations of America http://www.ou.org/public/statements/1999/nate43.htm   Lutheran Church - Missouri Synod http://www.euthanasia.com/missouri.html Reformed Church in America http://www.euthanasia.com/lakes.html Catechism of the Catholic Church http://www.euthanasia.com/catech.html

The Effect of the Automobile on American Life

The automobile is one of the most important inventions in our countries history. It has totally affected the American way of life. Four main areas it affected are other transportation, roadways, rural life, and urban life. Automobiles affected other ways of transportation. Horse-drawn transportation was almost completely replaced. Trains and trolleys lost rides as cars became more affordable and popular. Roadways were then created. More than 400,000 miles of new road connected people and places. The construction of the new roadways created many jobs. Along the roadways structures such as filling stations popped up. Soon after drive-in restaurants, banks, movies, and convenience stores became popular. Tourist cabins were made for travelers passing through the country. Billboards advertising restaurants and products soon lined the streets. The automobile affected the farmers’ way of life. Farmers got their good to the markets faster, giving them a better income. It created greater contact between neighbors in the country, also. People in the country also gained access to shopping and leisure activity within the cities. The urban life was also affected by the automobile. They gained access to the country. Although most affects were for the better, the cities got hectic. Between traffic snarls and pollution the cities changed. The automobile also caused depopulation of inner cities to the suburbs. As the cities depopulated and automobiles became more popular there became a lack of parking of all the people driving to work. Parking in the city was very high. As a result the automobile changed the American way of life. The way the automobile affected the way of life still continues today. It’s still a major effect on people as in how and where they live and work.

John Steinbeck’s use of Realism Essay

John Ernst Steinbeck has written many award winning novels, some of which has even been produced as plays that captured audiences everywhere. Steinbeck wrote about real life experiences using realism, characterization, and dreams to emphasize his points and make an impact on his readers in order to reform or change society. The realism used in Steinbeck’s works is not only effective in informing the reader of circumstances that should be changed, but this nineteenth century literary style also creates great feelings of empathy toward the characters and their dreams. Steinbeck used realism to convey his points for a purpose, and his main purpose was that he wanted something to be made known to the public. Of Mice and Men and The Grapes of Wrath both tell of the hardships people went through and also the harsh conditions of their situations. The characters in both of these novels play and important role in personalizing the occurring events for the reader, making the novel more effective in getting the writers’ messages across to the audience. Steinbeck’s use of the American Dream and the will for the characters to succeed is also evident throughout the two novels. These dreams help the reader to relate to the characters, therefore making a bigger impact on those who read the novel. John Steinbeck’s novel â€Å"The Grapes of Wrath†, tells of a very harsh journey to California that the Joads, like many other families in the 1930s Depression era, embarked upon in order to find work and escape their dying farms in Oklahoma. During the depression a severe drought covered the plains, called the Dust Bowl. This natural disaster destroyed any chance that the farmers had of making a living, and they were forced to travel west and leave their homes in hopes of finding a job. Part of the novel’s sense of realism comes from the setting. The Joads head to California from Oklahoma and their journey is characterized by poverty, starvation, death, and suffering (Stegener 405). Steinbeck not only utilizes the setting as a sense of realism but also uses vivid description and specific details to draw attention to the numerous hardships encountered by the families forced to travel west in search of opportunity (Jackson 316). The first evening after the Joads leave their home, they stop on the side of the road to help another family. This family  is very thankful for the Joads help, and offers their tent for the Joads’ sickly grandfather, but unfortunately Grandpa passes away that night. The family is troubled from the very start of their journey and Steinbeck creates feelings of sympathy toward the Joads as well as the other families in the same situation. As the novel progresses, the family’s disparity becomes more and more evident. Grandma Joad dies shortly after Grandpa does and since the Joads are indigent and can barely meet ends to survive, they are forced to beg for money to bury Grandma Joad. Despite family’s disappointments, they just keep going (Britch and Lewis). As they continue to travel the Joads encounter many more obstacles, but there is one incident as the novel comes to a close. Rose of Sharon, the oldest daughter, goes into labor and her baby is stillborn. Rose of Sharon notices a dying old man who is malnourished and offers him her breast milk so that he might be able to survive. As the novel closes, the reader is left with despair and a sense of loneliness. Steinbeck’s uses of realism makes a strong impact on the reader, which makes this one of the greatest American novels ever written (Jackson 316). Of Mice and Men was also written during the time of the 1930s, the depression era. This novel is a short story of two men a small, short, and smart guy named George and a big, tall, mentally retarded man named Lennie. The novel is based around these two main characters and their journey to fulfill their dream to find true happiness on a farm that they can one day call their own (Hearle) In â€Å"Of Mice and Men† the use of realism is not only seen through the depressing life of George and Lennie, but it also shows the life that Crooks, a black stable hand on the farm, had. The character of Crooks is used to symbolize the social standing of the black community occurring during the time at which the novel is set. Crooks is a lonely African American on the farm that feels out of place. As George and Lennie explain their dream to Crooks he brushes them off and says that no one around here can implement their dreams. This realism gives the reader an impression that Crooks has absolutely no hope. However, Crooks may be pessimistic, but yet even he has a dream, which is the hope of one day experiencing the joys of  his childhood again. Crooks’ character is portrayed as very lonely in the novel, this is evident when Crooks explains, â€Å"A guy needs someone.† (Mice 77). Crooks is telling the reader the need of human interaction. This realism that Steinbeck uses shows the reader the harsh realities of the black community during the time of the depression in the 1930’s Steinbeck not only uses realism to make an impact on his readers but he also uses strong characterization to his advantage as well (Howard). By using characters such as Ma Joad and Curley’s wife, he is able to personalize the novel for the reader. This technique that Steinbeck uses makes the reader feel like he/she can relate with the characters’ struggles, therefore, creating a greater sense of understanding toward the characters’ situations (Horn). These two characters can best be described as strong, courageous, and they show great amounts of integrity as well as faith. In order to write a great book that will make an impact on the reader, the author must not only use realism but also have a strong sense of characterization for the reader to relate to. Steinbeck successfully achieved both of these aspects of a great novel. John Steinbeck’s character, Ma Joad in â€Å"The Grapes of Wrath†, is the epitome of a strong character. She is a supportive, loving woman, and surprisingly the family’s center of strength (Britch and Lewis). She is intent on keeping the family whole and together. The family looks to Ma Joad for their source of hope and encouragement. She is the emotional and physical backbone of the family, and it is very important to her to provide the family with comfort, nourishment, and support. â€Å"Without warning Grandpa began to cry. His chin wavered and his old lips tightened over his mouth and he sobbed hoarsely. Ma rushed over to him and put her arms around him. She lifted him to his feet,her broad back straining, and she half lifted, half helped him to the tent† (Wrath 185). Steinbeck makes it clear to the reader in this passage that Ma is the first to step up in times of need, and she puts others before herself no matter what. â€Å"Under the spread of the tarpaulin Grandma lay on a mattress, and Ma sat beside her. The air was stifling hot, and the flies buzzed in the shade of the canvas. Grandma was naked under a long piece of pink curtain. She turned her old head restlessly from side to side, and she  muttered and choked. Ma sat on the ground beside her, and with a piece of cardboard drove the flies away and fanned a stream of moving hot air over the tight old face. Rose of Sharon sat on the other side and watched her mother† (Wrath 285). The reader notices several times throughout the novel that Ma will care for anyone in need no matter what the circumstance. â€Å"In show of her fundamental spirit she accepts Casey into the family because the Joads just do not refuse ‘food an’ shelter or lift on the road to anybody that ask[s]'† (Britch and Lewis). She takes it upon herself to look out for to avoid any discouragement to the other family. Grandma dies in the back of the wagon with Ma by her side, but trying to avoid any discouragement to the other family members, Ma does not share the news until they have reached their stopping point. The strength that Ma shows in this situation is far great that any exhibited by the other family members. â€Å"Her capacity to care marks the measure of her self-respect. â€Å"As the action progresses her caring does not change in kind but rather grows in breadth and intensity† (Britch and Lewis). By creating such a noble character, Steinbeck greatly influences his readers, and his efforts in sharing the hardships these families in the 1930s went through are successful. The character of Curley’s wife is a very vivid and unique one. She represented the way that women were viewed by society as a whole. Steinbeck portrayed Curley’s wife as a temptress, when actually the woman is just craving for attention. Steinbeck made Curley’s wife stand out by the fact that she was the only woman on the ranch, she was the only one who dressed to impress, and the only person without a full name (Thesing). Steinbeck often used very colorful statements like â€Å"She had full, rouged lips and wide-spaced eyes, heavily made up. Her fingernails were red. Her hair hung in little rolled clusters, like sausages. She wore a cotton dress and red mules, and the insteps of which were little bouquets of red ostrich feathers† (Mice 31). These vivid and wild descriptions that Steinbeck created for Curley’s wife is just one of the many characters that Steinbeck created, in order for the reader to feel or relate to what the character is going through. In Curley’s wife’s case she is an attention deprived woman that is just one of the many lonely people on the ranch. â€Å"Of Mice and Men† and â€Å"The Grapes of Wrath† both examine the morality and necessary actions the characters choose as they pursue their dreams. Steinbeck uses the concept that dreams are better that reality, but that the dream is really hard to grasp. This concept is also used by three other famous authors who are Crane, Norris, and Dreiser (Benson 256-257). What is the American dream? The American dream is the faith held by many Americans, that through hard work, courage, and determination one can adhere financial prosperity and also some believe that it is led to an emphasis of material wealth as a measure of success and/or happiness. Like many people today the characters George, Lennie, Candy, Curley’s wife, and the Joads all wanted the American dream. Most of their dreams of success, wealth and prosperity were depleted by the harsh realities of life. Most of the characters in the novel Of Mice and Men have a dream of something. George and Lennie are best friends that go everywhere together. Their dream is to someday own a farm of their own and have rabbits to tend to. The dream to Lennie is an antidote to disappointment and loneliness, and he often asks George to recite the description of the farm to him. This dream is ultimately lost when Lennie kills Curley’s wife and George kills Lennie towards the end of the novel. This dream was later shared by two other friends on the farm, Candy and Crooks. As the reader can see these dreams are one way that the characters can cover up the loneliness and hopelessness of their existence. One other character in the novel that had a dream is Curley’s wife. Curley’s wife’s dream is her fantasies in becoming a part in movies and having a life of luxury. This dream is shattered and never fulfilled, because of the dissatisfaction of her life and when she is accidentally killed by Lennie. As the reader can see the dreamers in the novel are undermined by the hard facts of reality (Astro 43). In the 1930s the country suffered ecological devastation called the depression. During this economy downfall the mid-west prairie state families suffer from a large drought that leaves them with nothing to survive. This terrible phenomenon is called the Dust Bowl. In attempt to escape this unforgettable time, a family called the Joads dream of wealth and success in  the great state of California. In order to pursue their dream they have to leave their belongings behind. This journey carries death and suffering with it when Grandma and Grandpa Joad dies and many of the family members leave the family. The family left Oklahoma in order to find jobs in California (Hearle). The Joad’s dream, which is well known as the American dream, is shattered by certain events and conditions that the Joads faced. In conclusion, John Steinbeck’s style of writing impacted society just as he had hoped. He wrote about real life experiences and hardships to show the reader what people went through, like the Joads and the many characters in â€Å"Of Mice and Men†. Steinbeck informed the reader of what families had to overcome, which ultimately impacted whoever read his novels. The use of realism, characterization, and dreams in his two novels made them the greatest American novels in history. Works Cited Astro, Richard Dictionary of Literary Biography, volume 9: American Novelists, 1910-1915. A Bruccoli Clark Layman Book. Ed. James J. Martine. Saint Bonaventure University. Gale Research 1981. 413-68 Benson, Jackson J., â€Å"John Steinbeck: Novelist as a Scientist,† in Novel: A Forum on Fiction. Spring, 1977, 228-264. Britch, Carroll and Cliff Lewis, â€Å"Growth of the family in The Grapes of Wrath,† in Critical Essays on Steinbeck’s The Grapes of Wrath, Ed. John Ditsky, G.K. Hall. 1989, 97-108. Hearle, Kevin Dictionary of Literary Biography, volume 212: Twentieth-century American western writers. Second series. A Bruccoli Clark Layman Book. Ed. Richard H. Carcoft Brigham Young University. Gale Research Group. 1999, 278-294. Horn, Jason G. Dictionary of Literary Biography: volume 275. Twentieth century American Nature Writers: Prose A Bruccoli Clark Layman Book. Ed. Roger Thompson, Virginia Military Institute, and J. Scott Bryson. St. Mary’s College. Gale Group 2003. 314-323 Jackson, Joseph Henrey. â€Å"The Finest Book John Steinbeck has written.† Contemporary Literary Criticism, volume 59. Ed. Roger Matuz. Detroit, MI: Gale Research Inc. 1990. 316-317. Levant, Howard. â€Å"The Novels of John Steinbeck: A Critical Study.† Contemporary Literary Criticism, volume 75. Ed. Thomas Volteler. Detroit, MI: Gale Research Inc. 1993, 356-351. Steinbeck, John. The Grapes of Wrath New York, New York: Penguin Books U.S.A Inc. 1992. Steinbeck, John. Of Mice and Men, New York, New York: Penguin Putnam Inc. 1993. Stegner, Wallace, â€Å"The True Adventures of John Steinbeck, Writer† Contemporary Literary Criticism, volume 34. Ed. Sharon K. Hall. Detroit, MI: Gale Research Company, 1985. 405. Thesing, William B. Dictionary of Literary Biography, volume 7: Twentieth-century American Dramatists, first series. A Bruccoli Clark Layman Book. Ed. John MacNicholas University of South Carolina, Gale Research. 1981. 271-276.

Beyond Pythagoras Essays

Beyond Pythagoras   Essays Beyond Pythagoras   Essay Beyond Pythagoras   Essay I have been asked to investigate Pythagorean triplets where the shortest side is an odd number and all the three sides are positive integers. A pythagorean triple is a set of integers (a,b,c) that specifies the lengths of a right angle triangle aà ¯Ã‚ ¿Ã‚ ½+bà ¯Ã‚ ¿Ã‚ ½=cà ¯Ã‚ ¿Ã‚ ½ in which a is the shortest side b is the middle side and c is the hypotenuse. The first set of triples (3,4,5) which has already been proved to satisfy Pythagorass theory. I have also been given two other pythagorean triples (5,12,13) and (7,24,25) I will now prove these to satisfy Pythagorass theory aà ¯Ã‚ ¿Ã‚ ½ = 5à ¯Ã‚ ¿Ã‚ ½ =25 bà ¯Ã‚ ¿Ã‚ ½ = 12à ¯Ã‚ ¿Ã‚ ½ =144 cà ¯Ã‚ ¿Ã‚ ½ = 13à ¯Ã‚ ¿Ã‚ ½ =169 aà ¯Ã‚ ¿Ã‚ ½+bà ¯Ã‚ ¿Ã‚ ½ =25+144 =169 aà ¯Ã‚ ¿Ã‚ ½+bà ¯Ã‚ ¿Ã‚ ½=cà ¯Ã‚ ¿Ã‚ ½ so Pythagorass theory holds for (5,12,13) because they satisfy the condition of aà ¯Ã‚ ¿Ã‚ ½+bà ¯Ã‚ ¿Ã‚ ½=cà ¯Ã‚ ¿Ã‚ ½ in a right angled triangle. aà ¯Ã‚ ¿Ã‚ ½ = 7à ¯Ã‚ ¿Ã‚ ½ =49 bà ¯Ã‚ ¿Ã‚ ½ = 24à ¯Ã‚ ¿Ã‚ ½ =576 cà ¯Ã‚ ¿Ã‚ ½ = 25à ¯Ã‚ ¿Ã‚ ½ =625 aà ¯Ã‚ ¿Ã‚ ½+bà ¯Ã‚ ¿Ã‚ ½ =49+576 =625 aà ¯Ã‚ ¿Ã‚ ½+bà ¯Ã‚ ¿Ã‚ ½=cà ¯Ã‚ ¿Ã‚ ½ so Pythagorass theory holds for (7,24,25) because they satisfy the condition of aà ¯Ã‚ ¿Ã‚ ½+bà ¯Ã‚ ¿Ã‚ ½=cà ¯Ã‚ ¿Ã‚ ½ in a right angled triangle. I am now going to put my results in to a table so that I can predict more values: a b c 3 4 5 5 12 13 7 24 25 I will now predict the next two values in the table so I can work out a general formula for this pythagorean family. By using the differencing method I can see that a has a difference of 2 between each pythagorean triplet I predict the next two a values to be 9 and 11 From the table I can also see that there is a quadratic sequence for the b value so I predict the next two values to be 40 and 60 Also from my table, I can see the c value is b+1 so my two next predictions Im going to prove are: a b c 9 40 41 11 60 61 aà ¯Ã‚ ¿Ã‚ ½ = 9à ¯Ã‚ ¿Ã‚ ½ =81 bà ¯Ã‚ ¿Ã‚ ½ = 40à ¯Ã‚ ¿Ã‚ ½ =1600 cà ¯Ã‚ ¿Ã‚ ½ = 41à ¯Ã‚ ¿Ã‚ ½ =1681 aà ¯Ã‚ ¿Ã‚ ½+bà ¯Ã‚ ¿Ã‚ ½ =81+1600 =1681 aà ¯Ã‚ ¿Ã‚ ½+bà ¯Ã‚ ¿Ã‚ ½=cà ¯Ã‚ ¿Ã‚ ½ so Pythagorass theory holds for (9,40,41) because they satisfy the condition of aà ¯Ã‚ ¿Ã‚ ½+bà ¯Ã‚ ¿Ã‚ ½=cà ¯Ã‚ ¿Ã‚ ½ in a right angled triangle. aà ¯Ã‚ ¿Ã‚ ½ = 11à ¯Ã‚ ¿Ã‚ ½ =121 bà ¯Ã‚ ¿Ã‚ ½ = 60à ¯Ã‚ ¿Ã‚ ½ =3600 cà ¯Ã‚ ¿Ã‚ ½ = 61à ¯Ã‚ ¿Ã‚ ½ =3721 aà ¯Ã‚ ¿Ã‚ ½+bà ¯Ã‚ ¿Ã‚ ½ =121+3600 =3721 aà ¯Ã‚ ¿Ã‚ ½+bà ¯Ã‚ ¿Ã‚ ½=cà ¯Ã‚ ¿Ã‚ ½ so Pythagorass theory holds for (11,60,61) because they satisfy the condition of aà ¯Ã‚ ¿Ã‚ ½+bà ¯Ã‚ ¿Ã‚ ½=cà ¯Ã‚ ¿Ã‚ ½ in a right angled triangle. My table now looks like this: a b c 3 4 5 5 12 13 7 24 25 9 40 41 11 60 61 When looking at the table I found a pattern so I am going to prove if it will work. 3à ¯Ã‚ ¿Ã‚ ½ =9 -4-5 (3,4,5) 5à ¯Ã‚ ¿Ã‚ ½ =25 -12-13 (5,12,13) 7à ¯Ã‚ ¿Ã‚ ½ =49 -24-25 (7,24,25) 9à ¯Ã‚ ¿Ã‚ ½ =81 -40-41 (9,40,41) 11à ¯Ã‚ ¿Ã‚ ½ =121 -60-61 (11,60,61) aà ¯Ã‚ ¿Ã‚ ½ = b+c aà ¯Ã‚ ¿Ã‚ ½ = b+b+1 aà ¯Ã‚ ¿Ã‚ ½ + 2b+1 Now to prove if it will work for Pythagoras aà ¯Ã‚ ¿Ã‚ ½ aà ¯Ã‚ ¿Ã‚ ½+bà ¯Ã‚ ¿Ã‚ ½ = (b+1) à ¯Ã‚ ¿Ã‚ ½ bà ¯Ã‚ ¿Ã‚ ½ aà ¯Ã‚ ¿Ã‚ ½+bà ¯Ã‚ ¿Ã‚ ½ = bà ¯Ã‚ ¿Ã‚ ½=2b+1 b+1à ¯Ã‚ ¿Ã‚ ½ aà ¯Ã‚ ¿Ã‚ ½ = 2b + 1 aà ¯Ã‚ ¿Ã‚ ½-1=b 2 Pythagoras theory is satisfied So now with 5 triplets that I have proved I will now find a general formula to find other pythagorean triplets in this family. By looking at the table its obvious that the formulae for a is a=2n+1 Im now going to find the general formulae for the b and c value. (b+1) à ¯Ã‚ ¿Ã‚ ½ = (2n+1)à ¯Ã‚ ¿Ã‚ ½ + b bà ¯Ã‚ ¿Ã‚ ½+2b+1 = 4nà ¯Ã‚ ¿Ã‚ ½+4n+1+bà ¯Ã‚ ¿Ã‚ ½ bà ¯Ã‚ ¿Ã‚ ½+2b-bà ¯Ã‚ ¿Ã‚ ½ = 4nà ¯Ã‚ ¿Ã‚ ½+4n+1-1 2b = 4nà ¯Ã‚ ¿Ã‚ ½+4n b = 2nà ¯Ã‚ ¿Ã‚ ½+2n c = 2nà ¯Ã‚ ¿Ã‚ ½+2n+1 I now have the formulae: a =2n+1 b = 2nà ¯Ã‚ ¿Ã‚ ½+2n c = 2nà ¯Ã‚ ¿Ã‚ ½+2n+1 I am now going to prove that these formulae work aà ¯Ã‚ ¿Ã‚ ½ = (2n+1)à ¯Ã‚ ¿Ã‚ ½ ) bà ¯Ã‚ ¿Ã‚ ½ = (2nà ¯Ã‚ ¿Ã‚ ½+2n)à ¯Ã‚ ¿Ã‚ ½ ) cà ¯Ã‚ ¿Ã‚ ½ = (2nà ¯Ã‚ ¿Ã‚ ½+2n+1)à ¯Ã‚ ¿Ã‚ ½ = aà ¯Ã‚ ¿Ã‚ ½ = (2n+1) (2n+1) 4nà ¯Ã‚ ¿Ã‚ ½+2n+2n+1 4nà ¯Ã‚ ¿Ã‚ ½+4n+1 bà ¯Ã‚ ¿Ã‚ ½ = (2nà ¯Ã‚ ¿Ã‚ ½+2n) (2nà ¯Ã‚ ¿Ã‚ ½+2n) 4n +4nà ¯Ã‚ ¿Ã‚ ½+4nà ¯Ã‚ ¿Ã‚ ½+4nà ¯Ã‚ ¿Ã‚ ½ aà ¯Ã‚ ¿Ã‚ ½+bà ¯Ã‚ ¿Ã‚ ½ = 4n + 8nà ¯Ã‚ ¿Ã‚ ½+8nà ¯Ã‚ ¿Ã‚ ½+2n+1 cà ¯Ã‚ ¿Ã‚ ½ = (2nà ¯Ã‚ ¿Ã‚ ½+2n+1) (2nà ¯Ã‚ ¿Ã‚ ½+2n+1) 4n + 4nà ¯Ã‚ ¿Ã‚ ½+2nà ¯Ã‚ ¿Ã‚ ½+ 4nà ¯Ã‚ ¿Ã‚ ½+4nà ¯Ã‚ ¿Ã‚ ½+2n+2nà ¯Ã‚ ¿Ã‚ ½+2n+1 4n + 8nà ¯Ã‚ ¿Ã‚ ½+8nà ¯Ã‚ ¿Ã‚ ½+2n+1 I will give an example of how to use the formulae for the 10th as the nth term: a =2n+1 =21 b = 2nà ¯Ã‚ ¿Ã‚ ½+2n = 220 c = 2nà ¯Ã‚ ¿Ã‚ ½+2n+1 = 221 the 10th pythagorean triple in this pythagorean family is (21,220,221) I am now going to investigate the 2nd pythagorean family. I will get this by doubling the values of the first family. (3,4,5) = (6,8,10) (5,12,13) = (10,24,26) (7,24,25) = (14,48,50) (9,40,41) = (18,80,82) (11,60,61) = (22,120,122) Using the internet for research I found out that there are in-between values so these are the pythagorean triples I have for this family now: (6,8,10) (8,15,17) (10,24,26) (12,35,37) (14,48,50) (16,63,65) (18,80,82) (20,99,101) (22,120,122) I will now prove that Pythagoras theorem holds for some of these pythagorean triplets. aà ¯Ã‚ ¿Ã‚ ½ = 6à ¯Ã‚ ¿Ã‚ ½ =36 bà ¯Ã‚ ¿Ã‚ ½ = 8à ¯Ã‚ ¿Ã‚ ½ =64 cà ¯Ã‚ ¿Ã‚ ½ = 10à ¯Ã‚ ¿Ã‚ ½ =100 aà ¯Ã‚ ¿Ã‚ ½+bà ¯Ã‚ ¿Ã‚ ½ =36+64 =100 aà ¯Ã‚ ¿Ã‚ ½+bà ¯Ã‚ ¿Ã‚ ½=cà ¯Ã‚ ¿Ã‚ ½ so Pythagorass theory holds for (6,8,10) because they satisfy the condition of aà ¯Ã‚ ¿Ã‚ ½+bà ¯Ã‚ ¿Ã‚ ½=cà ¯Ã‚ ¿Ã‚ ½ in a right angled triangle. aà ¯Ã‚ ¿Ã‚ ½ = 8à ¯Ã‚ ¿Ã‚ ½ =64 bà ¯Ã‚ ¿Ã‚ ½ = 15à ¯Ã‚ ¿Ã‚ ½ =225 cà ¯Ã‚ ¿Ã‚ ½ = 17à ¯Ã‚ ¿Ã‚ ½ =289 aà ¯Ã‚ ¿Ã‚ ½+bà ¯Ã‚ ¿Ã‚ ½ =64+225 =289 aà ¯Ã‚ ¿Ã‚ ½+bà ¯Ã‚ ¿Ã‚ ½=cà ¯Ã‚ ¿Ã‚ ½ so Pythagorass theory holds for (8,15,17) because they satisfy the condition of aà ¯Ã‚ ¿Ã‚ ½+bà ¯Ã‚ ¿Ã‚ ½=cà ¯Ã‚ ¿Ã‚ ½ in a right angled triangle. aà ¯Ã‚ ¿Ã‚ ½ = 10à ¯Ã‚ ¿Ã‚ ½ =100 bà ¯Ã‚ ¿Ã‚ ½ = 24à ¯Ã‚ ¿Ã‚ ½ =576 cà ¯Ã‚ ¿Ã‚ ½ = 26à ¯Ã‚ ¿Ã‚ ½ =676 aà ¯Ã‚ ¿Ã‚ ½+bà ¯Ã‚ ¿Ã‚ ½ =100+576 =676 aà ¯Ã‚ ¿Ã‚ ½+bà ¯Ã‚ ¿Ã‚ ½=cà ¯Ã‚ ¿Ã‚ ½ so Pythagorass theory holds for (10,24,26) because they satisfy the condition of aà ¯Ã‚ ¿Ã‚ ½+bà ¯Ã‚ ¿Ã‚ ½=cà ¯Ã‚ ¿Ã‚ ½ in a right angled triangle. I am now going to find a general formula for the 2nd pythagorean family that I will name the b+2 family. From the values I have I know a = 2n+4 by using the differencing method I will now work out the b and c values. (b+2) à ¯Ã‚ ¿Ã‚ ½ = (2n+4)à ¯Ã‚ ¿Ã‚ ½ + b bà ¯Ã‚ ¿Ã‚ ½+4b+1 = 4nà ¯Ã‚ ¿Ã‚ ½+16n+16+bà ¯Ã‚ ¿Ã‚ ½ bà ¯Ã‚ ¿Ã‚ ½+4b-bà ¯Ã‚ ¿Ã‚ ½ = 4nà ¯Ã‚ ¿Ã‚ ½+16n+16-4 4b = 4nà ¯Ã‚ ¿Ã‚ ½+16n+12 b = nà ¯Ã‚ ¿Ã‚ ½+4n+3 c = nà ¯Ã‚ ¿Ã‚ ½+4n+5 I now have the formulae: a =2n+4 b = nà ¯Ã‚ ¿Ã‚ ½+4n+3 c = nà ¯Ã‚ ¿Ã‚ ½+4n+5 I am now going to prove that these formulae work aà ¯Ã‚ ¿Ã‚ ½ = (2n+4)à ¯Ã‚ ¿Ã‚ ½ ) bà ¯Ã‚ ¿Ã‚ ½ = (nà ¯Ã‚ ¿Ã‚ ½+4n+3)à ¯Ã‚ ¿Ã‚ ½ ) cà ¯Ã‚ ¿Ã‚ ½ = (nà ¯Ã‚ ¿Ã‚ ½+4n+5)à ¯Ã‚ ¿Ã‚ ½ = aà ¯Ã‚ ¿Ã‚ ½ = (2n+4) (2n+4) 4nà ¯Ã‚ ¿Ã‚ ½+8n+8n+16 4nà ¯Ã‚ ¿Ã‚ ½+16n+16 bà ¯Ã‚ ¿Ã‚ ½ = (nà ¯Ã‚ ¿Ã‚ ½+4n+3) (nà ¯Ã‚ ¿Ã‚ ½+4n+3) n +4nà ¯Ã‚ ¿Ã‚ ½+3nà ¯Ã‚ ¿Ã‚ ½+4nà ¯Ã‚ ¿Ã‚ ½+16nà ¯Ã‚ ¿Ã‚ ½+4n+12n+3nà ¯Ã‚ ¿Ã‚ ½+12n+9 n +8nà ¯Ã‚ ¿Ã‚ ½+22nà ¯Ã‚ ¿Ã‚ ½+24n+9 aà ¯Ã‚ ¿Ã‚ ½+bà ¯Ã‚ ¿Ã‚ ½ = n + 8nà ¯Ã‚ ¿Ã‚ ½+26nà ¯Ã‚ ¿Ã‚ ½+40n+25 cà ¯Ã‚ ¿Ã‚ ½ = (nà ¯Ã‚ ¿Ã‚ ½+4n+5) (nà ¯Ã‚ ¿Ã‚ ½+4n+5) n + 4nà ¯Ã‚ ¿Ã‚ ½+5nà ¯Ã‚ ¿Ã‚ ½+ 4nà ¯Ã‚ ¿Ã‚ ½+16nà ¯Ã‚ ¿Ã‚ ½+20n+5nà ¯Ã‚ ¿Ã‚ ½+20n+25 n + 8nà ¯Ã‚ ¿Ã‚ ½+26nà ¯Ã‚ ¿Ã‚ ½+40n+25 I will give an example of how to use the formulae for the 10th as the nth term: a =2n+4 =24 b = nà ¯Ã‚ ¿Ã‚ ½+4n+3= 143 c = nà ¯Ã‚ ¿Ã‚ ½+4n+5= 145 the 10th pythagorean triple in this pythagorean family is (21,220,221) I am now going to investigate the 3rd pythagorean family. I will get this by tripling the values of the first family. (3,4,5) = (9,12,15) (5,12,13) = (15,36,39) (7,24,25) = (21,72,75) (9,40,41) = (27,120,123) (11,60,61) = (33,180,183) I will now prove that Pythagoras theorem holds for these pythagorean triplets. aà ¯Ã‚ ¿Ã‚ ½ = 9à ¯Ã‚ ¿Ã‚ ½ =81 bà ¯Ã‚ ¿Ã‚ ½ = 12à ¯Ã‚ ¿Ã‚ ½ =144 cà ¯Ã‚ ¿Ã‚ ½ = 15à ¯Ã‚ ¿Ã‚ ½ =100 aà ¯Ã‚ ¿Ã‚ ½+bà ¯Ã‚ ¿Ã‚ ½ =81+144 =225 aà ¯Ã‚ ¿Ã‚ ½+bà ¯Ã‚ ¿Ã‚ ½=cà ¯Ã‚ ¿Ã‚ ½ so Pythagorass theory holds for (9,12,15) because they satisfy the condition of aà ¯Ã‚ ¿Ã‚ ½+bà ¯Ã‚ ¿Ã‚ ½=cà ¯Ã‚ ¿Ã‚ ½ in a right angled triangle. aà ¯Ã‚ ¿Ã‚ ½ = 15à ¯Ã‚ ¿Ã‚ ½ =225 bà ¯Ã‚ ¿Ã‚ ½ = 36à ¯Ã‚ ¿Ã‚ ½ =1296 cà ¯Ã‚ ¿Ã‚ ½ = 39à ¯Ã‚ ¿Ã‚ ½ =1521 aà ¯Ã‚ ¿Ã‚ ½+bà ¯Ã‚ ¿Ã‚ ½ =225+1296 =1521 aà ¯Ã‚ ¿Ã‚ ½+bà ¯Ã‚ ¿Ã‚ ½=cà ¯Ã‚ ¿Ã‚ ½ so Pythagorass theory holds for (15,36,39) because they satisfy the condition of aà ¯Ã‚ ¿Ã‚ ½+bà ¯Ã‚ ¿Ã‚ ½=cà ¯Ã‚ ¿Ã‚ ½ in a right angled triangle. aà ¯Ã‚ ¿Ã‚ ½ = 21à ¯Ã‚ ¿Ã‚ ½ =441 bà ¯Ã‚ ¿Ã‚ ½ = 72à ¯Ã‚ ¿Ã‚ ½ =5184 cà ¯Ã‚ ¿Ã‚ ½ = 35à ¯Ã‚ ¿Ã‚ ½ =5625 aà ¯Ã‚ ¿Ã‚ ½+bà ¯Ã‚ ¿Ã‚ ½ =441+5184 =5625 aà ¯Ã‚ ¿Ã‚ ½+bà ¯Ã‚ ¿Ã‚ ½=cà ¯Ã‚ ¿Ã‚ ½ so Pythagorass theory holds for (21,72,35) because they satisfy the condition of aà ¯Ã‚ ¿Ã‚ ½+bà ¯Ã‚ ¿Ã‚ ½=cà ¯Ã‚ ¿Ã‚ ½ in a right angled triangle. aà ¯Ã‚ ¿Ã‚ ½ = 27à ¯Ã‚ ¿Ã‚ ½ =729 bà ¯Ã‚ ¿Ã‚ ½ = 120à ¯Ã‚ ¿Ã‚ ½ =14,400 cà ¯Ã‚ ¿Ã‚ ½ = 123à ¯Ã‚ ¿Ã‚ ½ =15,129 aà ¯Ã‚ ¿Ã‚ ½+bà ¯Ã‚ ¿Ã‚ ½ =729+14,400 =15,129 aà ¯Ã‚ ¿Ã‚ ½+bà ¯Ã‚ ¿Ã‚ ½=cà ¯Ã‚ ¿Ã‚ ½ so Pythagorass theory holds for (27,120,123) because they satisfy the condition of aà ¯Ã‚ ¿Ã‚ ½+bà ¯Ã‚ ¿Ã‚ ½=cà ¯Ã‚ ¿Ã‚ ½ in a right angled triangle. aà ¯Ã‚ ¿Ã‚ ½ = 33à ¯Ã‚ ¿Ã‚ ½ =1089 bà ¯Ã‚ ¿Ã‚ ½ = 180à ¯Ã‚ ¿Ã‚ ½ =32,400 cà ¯Ã‚ ¿Ã‚ ½ = 183à ¯Ã‚ ¿Ã‚ ½ =33,489 aà ¯Ã‚ ¿Ã‚ ½+bà ¯Ã‚ ¿Ã‚ ½ =441+5184 =5625 aà ¯Ã‚ ¿Ã‚ ½+bà ¯Ã‚ ¿Ã‚ ½=cà ¯Ã‚ ¿Ã‚ ½ so Pythagorass theory holds for (33,180,183) because they satisfy the condition of aà ¯Ã‚ ¿Ã‚ ½+bà ¯Ã‚ ¿Ã‚ ½=cà ¯Ã‚ ¿Ã‚ ½ in a right angled triangle. I am now going to find a general formula for the 3rd pythagorean family that I will name the b+3 family. From the values I have I have used the differencing method to find out that a = 6n+3 I will now work out the b and c values. (b+3) à ¯Ã‚ ¿Ã‚ ½ = (6n+3)à ¯Ã‚ ¿Ã‚ ½ + b bà ¯Ã‚ ¿Ã‚ ½+6b+1 = 36nà ¯Ã‚ ¿Ã‚ ½+36n+9+bà ¯Ã‚ ¿Ã‚ ½ bà ¯Ã‚ ¿Ã‚ ½+6b-bà ¯Ã‚ ¿Ã‚ ½ = 36nà ¯Ã‚ ¿Ã‚ ½+36n+9-9 6b = 36nà ¯Ã‚ ¿Ã‚ ½+36n b = 6nà ¯Ã‚ ¿Ã‚ ½+6n c = 6nà ¯Ã‚ ¿Ã‚ ½+6n+3 I now have the formulae: a = 6n+3 b = 6nà ¯Ã‚ ¿Ã‚ ½+6n c = 6nà ¯Ã‚ ¿Ã‚ ½+6n+3 I am now going to prove that these formulae work: aà ¯Ã‚ ¿Ã‚ ½ = (6n+3)à ¯Ã‚ ¿Ã‚ ½ ) bà ¯Ã‚ ¿Ã‚ ½ = (6nà ¯Ã‚ ¿Ã‚ ½+6n)à ¯Ã‚ ¿Ã‚ ½ ) cà ¯Ã‚ ¿Ã‚ ½ = (6nà ¯Ã‚ ¿Ã‚ ½+6n+3)à ¯Ã‚ ¿Ã‚ ½ = aà ¯Ã‚ ¿Ã‚ ½ = (6n+3) (6n+3) 36nà ¯Ã‚ ¿Ã‚ ½+18n+18n+9 36nà ¯Ã‚ ¿Ã‚ ½+36n+9 bà ¯Ã‚ ¿Ã‚ ½ = (6nà ¯Ã‚ ¿Ã‚ ½+6n) (6nà ¯Ã‚ ¿Ã‚ ½+6n) 36n +36nà ¯Ã‚ ¿Ã‚ ½+36nà ¯Ã‚ ¿Ã‚ ½+36nà ¯Ã‚ ¿Ã‚ ½ 36n +72nà ¯Ã‚ ¿Ã‚ ½+36nà ¯Ã‚ ¿Ã‚ ½ aà ¯Ã‚ ¿Ã‚ ½+bà ¯Ã‚ ¿Ã‚ ½ = 36n +72nà ¯Ã‚ ¿Ã‚ ½+72nà ¯Ã‚ ¿Ã‚ ½+36n+9 cà ¯Ã‚ ¿Ã‚ ½ = (6nà ¯Ã‚ ¿Ã‚ ½+6n+3) (6nà ¯Ã‚ ¿Ã‚ ½+6n+3) 36n + 36nà ¯Ã‚ ¿Ã‚ ½+18nà ¯Ã‚ ¿Ã‚ ½+36nà ¯Ã‚ ¿Ã‚ ½+36nà ¯Ã‚ ¿Ã‚ ½+18n+18nà ¯Ã‚ ¿Ã‚ ½+18n+9 36n + 72nà ¯Ã‚ ¿Ã‚ ½+82nà ¯Ã‚ ¿Ã‚ ½+36n+9 I will give an example of how to use the formulae for the 10th as the nth term: a = 6n+3 =63 b = 6nà ¯Ã‚ ¿Ã‚ ½+6n = 3660 c = 6nà ¯Ã‚ ¿Ã‚ ½+6n+3= 3663 the 10th pythagorean triple in this pythagorean family is (21,220,221)

Leslie Marmon Silko, “Lullaby” Essays

Leslie Marmon Silko, â€Å"Lullaby† Essays Leslie Marmon Silko, â€Å"Lullaby† Paper Leslie Marmon Silko, â€Å"Lullaby† Paper American Mosaic, July 2011 FOCUS: Leslie Marmon Silko, â€Å"Lullaby† â€Å"Lullaby† is a short story that first appeared in a book entitled Storyteller in 1981. This was a book written by Leslie M. Silko that uses short stories, memories, poetry, family pictures, and songs to present her message. The book is concerned, in general, with the tradition of story-telling as it pertains to the Native American culture. Lullaby seems to be a story of tradition, change, death, loss and the tensions fostered as a result of them between the old couple in the story and the Anglo-American authorities of the time. Throughout the story there are quite a few conflicts. Some are internal between Ayah and herself and others are external ones through Ayah, the white man, and Chato, her husband. The story is told by the main character, Ayah. She’s an old woman retracing tragic memories of life occurrences like the death of her son, Jimmie, in a helicopter crash during a war. She was not sure about what happened to him until a man in khakis drove up in a blue sedan and told her that he was dead and how he died. Jimmie was the one that taught Ayah to sign her name. She regrets this greatly as she relays the loss of her other two children who were taken by white doctors because they were thought to have a disease, allegedly given to them by their grandmother. They were taken because, in fear of the white men who were yelling and pointing for her signature, she â€Å"signed† the children away. Later on, when they were brought to visit, it was apparent the children were forgetting their customs and language; further evidence of the completeness of her loss. These events seem to have severely alienated Ayah towards Chato as well. Especially those specifically related to the children as indicated by, â€Å"She slept alone on the hill until the middle of November until the first snows came. Then she made a bed for herself where the children slept. She did not lie down next to Chato again until many years later when he was sick and shivering and only her body could keep him warm. † Ayah also speaks of her husband’s work (Chato) as a fence mender for a nearby rancher. She took offense at the exploitation Chato endured at the hands of the rancher that employed im, and let him go without hesitation when Chato gets too old to work. As a result they lost their home when the rancher told Chato he [and â€Å"his old woman†] had to be out of the shack [they lived in] by the next afternoon. Despite Ayah’s immense sense of devotion to Chato it seems apparent that she sees him as a weak husband and resents him deeply for it. Though much of the story is of Ayah’s reminiscences, its present tense has Ayah searching for Chato. She finds him walking along the road late on a very cold night [seemingly] in a daze brought on by illness [and wine]. While resting together beside the road she wraps Chato in the army blanket Jimmie sent her thereby eliciting comfort from a symbol of one of her greatest losses. The lullaby she sings to him at the end of the story, as they lie together in the snow, is one that her grand-mother and mother sang to her as a child and seems to provide a sense of closure for her as she sings it. It is one of the last pieces of tradition she can cling to from her own culture as she waits for death to take her and her husband from under the cold, clear winter sky.

Euhemerism and the Gods

Euhemerism and the Gods Euhemerism and the Gods Euhemerism and the Gods By Maeve Maddox As long ago as the 4th century B.C.E., a student of religion and myth named Euhemerus theorized that the gods and their stories had their origins in actual historical events. His name has given us the term euhemerism [yÃ… «-hÄ“mÉ™-rÄ ­zÉ™m]: interpretation of myths as traditional accounts of historical persons and events OED Much later, an Icelandic student of the Norse myths, Snorri Sturluson (1179-1241), suggested that the gods began as human war leaders. He speculated that cults grew up around the burial sites of kings and renowned warriors. The living visited the sites called upon the departed for help in battle. Eventually the dead heroes were remembered as supernatural beings with the power to bestow victory in war. Related words are: euhemerist: noun, one who follows the method of Euhemerus euhemeristic: adjective, ) of persons: Inclined to euhemerism; (b) of things: Of the nature of or resembling euhemerism euhemerize: verb, To subject to euhemeristic interpretation; To follow the method of Euhemerus. Want to improve your English in five minutes a day? Get a subscription and start receiving our writing tips and exercises daily! Keep learning! Browse the Vocabulary category, check our popular posts, or choose a related post below:Types of RhymeTime Words: Era, Epoch, and EonNominalized Verbs

Carnavelis Decision Making Model Essay Example | Topics and Well Written Essays - 3000 words

Carnavelis Decision Making Model - Essay Example The effectiveness of a nurse’s role is achieved through the assessment of the social, physical, mental, and spiritual and health factors which define the needs of the patient. This paper is based on a clinical case study where the roles of nurses in assessment of the patient and related factors and decision making and practice are discussed. The discussion is based on Carnevali’s model of clinical judgment and decision making which evaluated in terms of its effectiveness and impact on the execution of nursing roles in patient assessment and decision making. The assessment of Jack’s physical, social, mental, spiritual and health care needs will be based on an integration of critical thinking and observation. Wolf (2012, p. 20) explains that the ability of a nurse to identify the needs of the patient during the assessment process is effectively achieved through keen observation and application of higher cognitive processes of thought. Kearney and Penque (2012, p. 3 2) adds that the legal and ethical standards of nursing and evidence based practice should also be included in trying to identify the needs of the patient. In Jack’s case, his symptoms are used to assess his health care needs. For example his dehydration is identified through the nurse’s observation. This leads to a critical thinking process through which the nurse will make a decision of the nursing intervention and therapy which is relevant for his condition. The significance of Carnevali’s model of clinical judgment and decision making is disclosed in this case because effectiveness in assessment of the health care needs of the patient would only be achieved through observation of his symptoms. Carnival’s model presents the first stage of diagnostic reasoning process as the collection of information and data on the patient and the family (Carnevali, 2003, p. 45). Aitken, Marshall, Elliott and McKinley (2009, p. 38), add that the roles of nurses in pati ent diagnosis are guided by collection of patient data on the social and cultural aspects and applying them in the prescription of relevant intervention and therapy. Jack for example is affected by social factors such as lack of appropriate support and care from the parents. This is disclosed by the fact that the parents want to leave him in the hospital with a neighbor. Nonetheless, critical thinking and prioritization must be applied in nursing care to ensure that the health care needs of the patient are provided before further assessment achieved. Jack’s dehydration and weakness requires immediate nursing intervention even before a complete analysis of all factors surrounding his condition are ascertained. Huiqin and Thompson (2010, p. 2752) points out that nurses play a critical role in meeting the needs of patients for care with due consideration of the standards of care and maintenance of high standards in practice. However Carnevali’s model of clinical judgment and decision making fails to show emphasis on the role of ethical and evidence based nursing practice. In accordance to Carnaveli’s model of clinical judgment and decision making, the second stage in diagnostic reasoning process is entry into the patient assessment (Carnevali, 2003, p. 45). This includes priority setting. Jack’s health care needs are prioritized by the nurse because of his weak condition and continuous crying. This is the reason why the nurse must prioritize the health care needs of the patient. Sutcliffe (2011, p. 35) emphasizes that the Nursing and