Inclusive Instructional Strategies & Accommodations Essay Example for Free

Inclusive instructional Strategies Accommodations EssayDiana Pastora Carson is a special education t from each oneer and founder of talent Awareness in Action organization. She always had an interest in changing the lives of disabled people from pitiful life and exclusion to inclusion and life panoptic of dignity and hope. The concern in Dianas nature came from presence of a brother who was preserved from others as a disabled and dependent human being. Dianas Brother, Joaquin, was diagnosed with Autism at an early age. While he was in school, he had been dictated in an exclusive classroom for students with signifi mucklet mental retardation. He was twice placed in a state institute due to misunderstanding of his character and his attempts to communicate with his services. Currently, Joaquin resides in a state institute, where he is ill, emotionally and physically, from being locked up in a building away from his friends and family. He expressed his feelings ab step to the for e living in such environment to his sister in a vexing way as he once said Diana, people are so boring here. His family has been trying to get him out of there as soon as possible.They have also taken his case to the court and are waiting for the final decision to be made. They want to get Joaquin out of there and bring him in a home of his own with people who love him instead of staying in that institute any longer. The training, titled Inclusive Instructional Strategies and Accommodations, is about including all children, whether they have a disability or not, in general education classrooms specifically, and in the community, generally. Everybody deserves to belong to and live in their communities.A teacher has an enormous role in making all students belong to that classroom through her knowledge about each and every student of his/hers, and through recognizing singularity in each one of them. This should make the teacher create a supportive environment that meets each students needs, and an atmosphere that promotes acceptance of differences and diversity, learning, hope, and collaboration. Moreover, the teacher is responsible for building a curriculum that meets each students level and accommodates tests and homework. A great teacher would avoid labels that discriminate individuals with disabilities to avoid set about expectations.Those labels may help professionals recognize what disabilities the students have, in order to provide them with services that meet their needs. However, people within the same label or disabilities may exchange therefore, we cannot always judge someone based on the labels. Moreover, it is very unprofessional to address someone by his/her disabilities as no one likes to be looked at for something that they did not choose for his/her self and it may affect his/her self-confidence. Students dignity must be preserved by the teacher and whoever is around, for instance, peers, and family.Professionals working with disabled people should pleader the community about appreciation of diversity and encourage students to speak out their thoughts, make choices, and blend in the society. Most importantly, the teachers should listen to students attentively look at their body language, written expressions, and vocalization for effective communication. During the training, many strategies and activities to develop a classroom community were shared by Diana, such as setting roles for the classroom, supporting reading books that promote diversity and discussions, and different cooperative games.Diana also explained how a customized lesson should be designed as a teacher must know her/his students in order to alter lessons based on each students needs. Teachers should also know how to model, guide, and measure students independent achievements through knowledge of students strengths and limitations. Diana enlightened the immensity of giving students time to process new information, retrieve old information, and speak o ut their answers.It is very important to break the lesson into smaller parts along with intercommunicate questions in between to check students comprehension and to encourage discussions about the lesson. It is very essential to bring movement and interaction into the curriculum, serve the different types of intelligences and most importantly honor every student for who he/she is and be aware of the impact teaching will have on his/her future life. Furthermore, visual aids can assist students in organizing their thoughts, memorizing them, and make learning more enjoyable and personal to them.Finally, commitment to learning, inclusion of all children, and building a quality future for each child is a must step for developing a loving community where everyone belongs. By having a brother with a disability, whose community isolated him from others by not providing him with education programs that serves his needs, making public places inaccessible for him, and not advocating the publi c about disabilities, Diana has learned to honor diversity and anyone who is working towards treating people with disabilities with dignity and respect.It has advance her to change the lives of those who are different from normal people, whether with a disability or not. It has motivated her to include all of them in a classroom that promotes collaboration, understanding, and hope. Furthermore, it has opened her eyeball to the importance of advocating the society about disabilities and their inclusion, to change the image and future of the disabled in the community.

Explain the Differences Between Panglosss Philosophy Essay Example for Free

Explain the Differences Between Panglosss Philosophy EssayPanglosss philosophy of life is that all is for the best in the best of all manageable worlds. This optimistic philosophy actually is the key element of Voltaires satire. Panglosss philosophy is against the ideas of the Enlightenment period. Pangloss believes that a powerful God had created the world and that, and so, the world essential be perfect. When creatures of the world, see something as wrong or evil, it is because they do not understand the ultimate good that result come out of it. Voltaire satirically shows the proofreader that Pangloss is not a believable character. Voltaire illustrates this by showing us that he keeps his optimistic archetype even when he is impris angiotensin converting enzymed. Pangloss ignores any evidence that contradicts his initial opinion. He also uses illogical arguments to support his beliefs. Panglosss philosophy tries to impose a passive attitude toward all that is wrong in th e world. If the world is the best one possible, then there is no land to make any effort to change things.Martin is more believable than Pangloss, not because he is more sophisticated, but because he is smarter and more likely to draw conclusions with which we can identify. Martin had been robbed by his wife and beaten by his son and deserted by his daughter and also lived financial set(p)backs, and therefore hes a pessimist whereas Pangloss is an optimist. He uses his experiences to judge the world whereas Pangloss was merely using a theory. As a result, Martin is more insightful than Pangloss to foresee events that go out happen.Even though Martins philosophy is more believable than Panglosss, hes still not good at predicting how some people will behave because his philosophy is coming from extreme pessimism. Therefore it might not be wrong to say that Voltaire is trying to prove that we need flexible thought in our lives based on real evidence. Both philosophers will ultimatel y fail because theres no room for exceptions in their beliefs. Candide starts his journey with the diverge of Panglosss belief of best of all possible worlds.Pangloss and Candide, suffer and witness a wide variety of horrors and tragedies together. During these tragedies, Panglosss s philosophy proves to be shadowy and even destructive at the end, because it prevents them from making realistic judgments. For example while Jacques was drowning, Pangloss doesnt let Candide save him by saying that the bay of Lisbon had been form for this Anabaptist to drown in. Also when Candide was buried under the rubble of the Lisbon earthquake, he asked for oil and wine because he was dying, but Pangloss ignored him and still tried to reason with the causes of the earthquake.At the end Candide rejects his philosophy of optimism and as he and his servant Cacambo travel and go through more horrors, Candide starts believing a pessimistic view of life. When Candide meets Martin, they set sail togethe r and Martin is just the opposite of Pangloss. He does not believe that everything is for the best in this world. Even though Candide tries to oppose Martin by talking close free will but it does not solve the problem of presence of evil in the world.In general, Martins arguments seem more reasonable than Panglosss ideas. But, like Pangloss, Martin believes so firmly in his own view of the world that he is not flexible and usually dismisses real evidence that contradicts his philosophy. When Candide cannot find Cunegonde, Martin shows the naughty influence of his pessimism. Instead of attempting to comfort his friend, Martin uses Candides distress to further confirm his own world-view. Just like Panglosss optimism, Martins pessimism also keeps him from taking scuttle to improve the world.

Psychology And Its Branches Sociology Essay

Psychology And Its Branches Sociology EssayFirst of all psychology is the study of human behaviour. The sole purpose of psychology is to unravel the mystery of why and individual acts a certain way. Psychology examines an individuals specific actions, responses and factors that dictate how an individual reacts under set conditions and the surround. The behaviour of an individual has an stir on the greater fiat that surrounds the individual. Psychological theories cover many branches including organizational psychology, surroundingsal psychology, maturation psychology, forensic psychology and sports psychology.The talk about psychology and its branches start out up an individual in particular, Robert William Pickton. This former pig farmer and serial killer convicted of the second degree murders of six Canadian women in 2007. He was in any case charged with the murder of twenty additional women. The Canadian man born in British Columbia is considered a psychopath and is very ea sily unflinching as one because of his childhood. The branch of psychology that specifically affect Picktons mentality was his ontogenesis as a child and the environment he grew up in, in other words development psychology. Robert Pickton grew up in a childhood filled with denial from his mother. Due to Roberts mother heavy work regime he would never have fun, spend time with friends or time to play. If Robert was non in school, he would be found in the slaughterhouse where his environment affected his mentality. In such an environment it is easy to see the development psychology conjecture that has had a major effect on Picktons psychopath killing offer up to a total of forty-nine victims.Erik Erikson believes that human behaviour can be understood through the experiences an individual encounters during their development. This directly relates to Robert Pickton because of the violent and gruesome environment Pickton grew up in, it is easy to analyze why his psychological beha viour has become what it is today. Erikson suggests that a person may pass a stage of psychological development or they get stuck. For example, an infant either intrusts his/her cargongivers or s/he doesnt. This failure of trust unclutter can affect the persons trusting relationship afterward on in life. This same ideology goes for Pickton he grew up in an environment where killing was occurring periodically in a day. This harsh and violent environment has caused Pickton to have a violent and gruesome psychological personality. He believes that killing has no evil or wrong in it, this is because of the psychological development theory. Pickton has been stuck in this psychological environment since his childhood and has been prominent in his life.Sociology PerspectiveSociology is a accessible science persuasion that states one area of society ordain perpetually have an effect it can be either direct or indirect. This is due to society being a complex structure where in that l ocation will always be modifications and changes in it due to society itself. The ideology of society influences decisions made on marriage, economics, love, freedom, politics etc. However, recognizing these facets of life does not assist with the story of their existence. In other words, sociology is the study of the development, structure, and functioning of human society this can include cordial problems deep down society.Robert William Pickton had a criminal mind set because of his childhood as explained through psychological development. Through his childhood and Picktons brutal treatment as a child from his mother, Pickton grew intolerance for the opposite wind up. He felt that males are dominant over females and thus the feminist theory of female oppression. Through the sociological feminist perspective Pickton neglected the female figure. His behaviour as a serial killer towards women was triggered through his childhood and ever since he has developed a feminist social view where he believes males are the dominant sexual urge over females. Hostile affection from Picktons mother led to an angrier individual later on towards the opposite sex and thus the criminal acts released against women in Picktons elder years.The sociological analysis of Marxist Feminism Theory also plays a role in the behaviour of Robert William Pickton. This implies the lack of balance in society in scathe of gender classes in the economic perspective of sociology. Stereotypes within society influenced Pickton as he believed women have a lesser role in society than males. This is why Pickton would go for vulnerable areas for kidnapping and base his attacks on lower class aims. For example, Robert Pickton would target women that were prostitutes or drug addicts because on that point class level in society was lower than his. Picktons targeting specific groups of women instead of the women gender as a whole illustrated sociological perspective of feminism.Pickton tried to a chieve structural functionalism in society where there is a balance, equilibrium in society by maintaining its interdependent social structures. Talcott Parsons stated, as much as things change they stay the same. Structural Functionalism deals with the maintenance within a society it defines changes within a system and will always seek a way to return to its normal functioning state. As Parsons stated, Pickton followed this social theory as he thought he was bringing balance to society by eliminating the lower class of females. Parsons also mentioned, When part of the system breaks down, it is undeniable for the other components of the society to take over the function of the missing social structure or to assist with the recreation of the malfunctioning social structure. This supports Picktons choice in achieving structural functionalism by the removal of the lower class which consisted of females.Anthropology PerspectiveAnthropology is the social science perspective of studying muckle and their culture. Anthropology exists to explore a variety of social phenomena. A benefit associated with anthropology is that its research lies in the huge perspective on the development and sustainability of human culture. This social science perspective poses questions concerning the continuation of poverty, racism, violence and social inequality in the world. There are four main types of anthropology including linguistic anthropology, cultural anthropology, archaeology, and biological or physical anthropology. Each type studies different aspects of people and their respective cultures including questions such as why do humans have such different ways of thinking, living and acting? This is the social science perspective of anthropology.Robert Picktons social interactions and relationships were not fully established. Pickton lived his life in rejection he was rejected of all social interactions which later led to his rage and intolerance against women. Picktons childhood was lived in neglect and the omitting of social interactions with other kids his age. The entire cause for this rejection was because of his mother, a female figure who was very brutal and hostile to the young Robert Pickton. This inevitably led to pettishness being stored throughout Picktons life towards women and thus the targeted attacking of women by Pickton. Pickton thought of his values and morals over others, specifically prostitutes (again targeting women). Pickton already thought of women as measly and inferior to males, now including prostitution he believed that those women did not deserve to live amongst society and him. Robert believed that to earn a living an individual should go through wound and hardship but prostitution in his perspective clearly did not show that. He believed prostitution made an earning with pleasure in life and not pain he believed that individuals should earn a living from physical labour and pain. Robert would never feel any sympathy for wo men especially prostitutes, thus his guilt-free attitude in killing these specified group of women.Robert King Merton bases his interpretation of society using the functionalist perspective. Functionalism is a method for understanding how social institutions fill social demand.Every usage or practice in society exits a form of stability for the entire system. This seems like a grand theory but social institutions provide for the physical and psychological needs for its society members.Sex is a practice of functionalism as it is a physical and psychological need for humans. Pickton was a very fainthearted and quiet individual but he acquired sex because it stored up inside of him. Pickton would host wild parties and orgies to release his chaotic thoughts. This also explains why Pickton would have sex with the women he would kidnap and then kill her, it is a practice of Picktons functionalism and this describes the social science perspective of anthropology.Hypothesis Psychoanalys is, Functionalism and FeminismPsychoanalysis is a psychological theory founded in the late 19th century and early 20th century by Austrian neurologist Sigmund Freud. In involves the inherited constitution of personality which is an individuals development determined by events in their childhood. Cognition, human behaviour and experience are largely determined by irrational drives. Mental disturbances from psychology occur when there are conflicts between conscious and unconscious material.Functionalisms core idea is that mental states are constituted solely by their functional role. It is a theoretical level between physical implementation and behavioural output. Functionalism is a method for understanding how social institutions fill social needs. Every custom or practice in society provides a form of stability for the entire system. This seems like a grand theory but social institutions provide for the physical and psychological needs for its society members. Feminism examines the perspective of women and their rights within a society, specifically a male dominated society.To understand and comprehend a serial killer as to what his/her motives are it is important to instigate an investigation. Through this investigation it is important to determine the unconscious and conscious mind of the serial killer by taking a look at their ego. This investigation will determine the drive of the serial killer as to what they wish to achieve, what pleasure they wish to achieve etc.Functionalists call for crime as a necessary guideline in society because it sets moral guidelines and rules through legal punishment. An increase in criminal behaviour loses the societys trust whereas a decrease in criminal behaviour illustrates that individuals have no freedom or individuality.When determining a serial killer it is important to gain information of the insights of the psychoanalytic, feminist and functionalist perspectives. These three perspectives combined can determine and give a thorough understanding of a serial killers ambition, pleasure and the ego of the criminal.

Factors that affect employee motivation

F typifyors that affect employee wantMotivation has to do with the understanding of the reasons why human beings act the mode they do. It is said to be the knowledge of psychology and is come to with explaining all forms of human conducts (Phil Gorman, 2004). Motivation is a genuinely important aspect of psychology that tries to explain why humans or animals act in a certain manner (David A.H, 1995). Motivation studies stupefy to do with the study of the Human psychology and behavioural patterns, it is an attempt to explain why and what the reasons be for actions we take.Mitchell (1982) apprizes that the term motivation represents those psychological process that perk up the awakening, direction and persistence of voluntary actions that argon goal oriented. It is a psychological process vector suming from the corresponding interaction mingled with the undivided and the environment that affects a souls choices, move and persistence (Gary P. L and Christopher T, 2006).M otivation seeks to explain the why of behaviour (Phil Gorman, 2004). When we ask why a person or animal be entertains in a particular manner, we atomic number 18 essentially asking about motivation (Mook, 1996). Motivation has generally been link up to the urgency to strain specific goals. It is concerned with goal-directed behaviours that pushes us towards certain actions and not others and is as closely as the complex process that moves unmarrieds towards some goals (Phil Gorman, 2004). Robbins (1993) defined motivation as the testamentingness to exert lofty levels of trial toward organisational goals, conditioned by the efforts and energy to indulge some personal collects. gibe to David A. H (1995), Motivation examines two aspects of behaviour the direction of behaviour those concerned with the influences which cause specific actions in humans and the intensity of behaviour concerned with the strength of behaviour. It is concerned with what causes specific actions, the reasons for actions we undertake and what determines the intensity of such action. Two individuals could be incite towards a specific goal, say passing an exam. They pass on both be motivated to read, but the degree or intensity of motivation provide usually not be the same for both individuals.Motivation studies atomic number 18 undertaken in order to explain the onset, the direction,the intensity and the persistence of behaviour directed towards the learning of one or more goals or objectives (Mark R. Z ,2006).So many authors pay off written and established various motivation theories. The fol pitifuling chapters in this check up on go out discuss on the various motivation theories and contributions of renowned writers in the field of motivation studies.MOTIVATION THEORIES MAJOR CONCEPTS AND CONTRIBUTIONS.ABRAHAM H. MASLOWS HIERARCHY OF NEEDS THEORYThis surmise advocates that all individuals be born with natural needfully and if these involve are not fulfilled, the individual will be motivated to act in a manner that will alter him satisfy them. Maslow A.H (1954) suggests that all individuals have a series of human needs which are prioritised on an hike scale, with basic physiologic survival needs at the bottom and the more psychological individual needs at the top. Maslow (1954)s Hierarchy of needs stems from Physiological needs (survival), Safety needs, fond needs, Esteem needs and Self-actualization at the top.According to this system, humans have gone beyond the need of single basic survival needs but are now driven towards greater achievements and high needs up till self actualization. Maslow (1954)s surmisal also assumes that these needs are activated in a sequential order starting from the bottom and a higher need emerging when the disgrace need has been at ease and that after a need has been satisfied it ceases to dominate behaviour.Physiological needs These are the basic biological needs of man to survive. These needs are food, water, shelter and so forth Maslow (1954) deals that humans are plausibly to be motivated by physiological needs rather than any other need. Once this needs have been satisfied, he is then motivated by the next level set of needs.Safety needs This refers to the need for security, freedom from fear and anxiety, need for stability and protection. Maslow (1954) suggests that this safety needs are mostly presumable in chaotic societies and when t present is a stable, smooth running and dandy society, this need will not be so passiond.Social needs This is the need for love and social belonging. When these needs are not satisfied, individuals will do all in their power to get affection from family and friends (Maslow, 1954)Esteem needs This refers to the need for prestige and recognition from others. It refers to the need for development, maintenance of self-respect and respect from others (David A.H, 1995).Self actualization This is the individual need of achieving ones full c apability. It is the satisfaction of r from each oneing what the individual retrieves to be his/her full potential. Maslow (1954) however, was of the view that very few wad manage to satisfy the highest set of needs such as self actualization.Some strengths of the theory conjecture acknowledges that all individuals have in-born natural needs and when these needs are not satisfied the individual is compelled to act in a manner that will enable him satisfy these needs.He has been able to combine both physiological and psychological needs in his hierarchy of needs theory. Physiological having to do with the innate needs and instinctive drives to satisfy these needs in the body. While psychological needs stem from cognitive conscious judgment before actions are taken.David A.H (1995) noted that the ascending hierarchy of needs is not a one way process, if lower needs become unsatisfied, the individual will go back towards satisfying those lower needs.The theory also suggests that the hierarchy does not apply rigidly to all individuals and some individuals may seek to satisfy some higher needs at the expense of lower ones (Maslow. 1954)Pointed out below are some weaknesses of the theoryPhil Gorman (2004) pointed out that the theory doesnt attend to take account of the possibility that people who retain small achievements in their lives may feel satisfied and fulfilled believing that they have truly achieved their full potential. He suggests that this may be due to restrictions move upon them by their social background.The theory does not consider that other factors such as environment and society discount influence the individual to act in a particular manner. According to Stanworth and Curran (1973) the theory ignores the way the culture of a society and its subcultures, structure the aspirations and expectations of individuals and groups. Ivan T. R, et al (1992) bares the opinion that Maslows theory barely touches on the type of environmental factors in t he development of his hierarchy.The theory is difficult to apply in some situations. Stanworth and Curran (1973) also pointed out that most people who set up businesses would seem to be satisfying the higher level of needs in Maslows theory and going into a business is quite a risky venture. This elbow room they are more concerned about a higher need of opening a business than a lower need, security and risk of having a business.HERZBERG F.W hygiene THEORYThis theory is primarily concerned with motivation at the proceed score. According to Herzberg et al (1959) in that respect are basically two sets of factors that influence behaviour Hygiene Factors (dissatisfiers) and Motivators (satisfiers)Hygiene factors (dissatisfiers)These are factors that do not satisfy the individuals but only keep them from being dissatisfied. The presence of these factors in a work place will mean the individuals will not be unsatisfied but they will not be motivated either. These factors include, go od running(a) conditions, good salary, supervision, security, birth with peers, company policy and administration. Most of these factors are classified as being extrinsic (David A.H, 1995).Motivators (satisfiers)These are those factors that actually motivate the individuals in the work place. They give the individual a feeling of self satisfaction and achievement. These factors are essentially internal and examples of these motivators are need for recognition, personal development and advancement and the need for growth. These motivators are related to the content of the job that fall by the waysides the individual employee to develop their occupation as a source of personal growth. Employees will be motivated with such factors as they allow them satisfy the need for self actualization (Herzberg et al, 1959).Part of the strengths of this theory is that just like Maslows theory, Herzberg et al (1959) believes that all human beings have physiological needs that flock be satisfied with money e.g. Food and water and psychological needs such as the need for self-development and self-actualization. While a major weakness is that Herzberg has also neglected the influence of the environment and societal background as possible motivators. Some of his hygiene factors such as good salary which he suggests will only prevent an individual from being dissatisfied, in some case suffer actually provide motivation to the individual (David A.H, 1995).McGREGOR DOUGLAS. -THEORY X AND YMcGregor (1960), suggest that in that respect is a direct relation between the way managers treat their workers and workers motivation. McGregor believes there are two major approaches to the focussing of people and they have to do with a managers view on workers military capability towards work. He formulated the theories X and Y.Theory XIn this theory, management treats workers with little or no respect. The attitude of managers towards workers in this theory is based onThe belief that the average human being dislikes work and will avoid it if possible.That most people have to be controlled, forced, directed and punished to get them to put adequate efforts towards the achievement of organisation objectives.That the average human, prefers to be directed wish to avoid responsibility and wants security higher up all (Evans D, 1990).Theory X is patronizing and take holds no allowance for workers individualism. It is based on aspects of management such as discipline and control (David A.H, 1995).Theory YThis theory concentrates on delegation, decentralization, participation and consultation. The characteristics of management here are as followsExternal control and the threat of punishment are not the only means of bringing out efforts towards achieving organisation objectives.People are committed to objectives in proportion to the rewards associated with achieving the objectives.That the average human being learns, under proper conditions not only to accept but to seek responsibility (David A.H, 1995).The theory encourages participative management and suggests that for workers to be motivated it is necessary to allow them use their skills within the work place. This will make them feel involved as part of the organisation.ALDERFERS EXISTENCE RELATEDNESS AND GROWTH THEORY (ERG)This theory advocates that in the attempt to achieve individual satisfaction, people are motivated to act in a specific manner (Aldefer C.P, 1972). He suggests that satisfaction relies on the fulfilment of natural needs such as existence, relatedness and growth. Individuals constantly interact with their environment which as an effect in their behaviour. He believes that these 3 sets of needs are able to exist simultaneously and can be satisfied in a flexible order.Existence needs These needs are concerned with physiological and material factors related to survival such as hunger, thirst, salary and working conditions.Relatedness This has to do with the need to relate with o thers in the society. Individuals are motivated to seek satisfaction in their social relationships.Growth needs This refers to creating the optimum use of active capacities and the development of new capacities. Satisfaction of growth needs depends on the individual developing to their full potential (Alderfer C.P, 1972).This theory does suggest a rigid vertical structure and does not propose that an individual will try to satisfy one set of needs at a time (David A.H, 1995).McCLELLANDS NEED FOR motion THEORYThis theory is also based on three innate needs which are of optimum importance. They are the need for achievement, affiliation and power (McClelland, 1961). Robbins (1993) believes that those who have strong drives to succeed are searching for personal achievements rather than rewards. They have the drive to improve on better ways of doing things.Need for achievement (N.arch) This can be described as the need for success and high standards of personal excellence (David A.H, 1995). It is the drive to achieve success.Need for affiliation This is the need for a good relationship with other individuals.Need for power This is the need to want to influence and exert some level of control over others.McClelland (1961) believes that all individuals have each of these needs although the level of intensity of the needs varies between each person. This means that some people might have high needs of some and low of the others. According to McClelland et al (1953), any attempt to understand a persons motivation to achieve must take into account both the personality and situation the individual finds him or herself in. He also suggested that the desire for achievement in a society could be measured from the variant of achievement imagery presented to the children (McClelland, 1961).Stanjworth Curran (1973), pointed out that McClellands theory considers differences between groups in motivational pattern and relates this to social and cultural factors.EDWARD TOLMA NSS EXPECTANCY THEORYTolman E.C (1948), theory suggests that the motivation of individuals is not based on needs or drives but is determined by the presence of goals and the expectancy that their behaviour will lead to the attainment of this goal. He believes that human beings will be motivated in a specific manner when they are convinced that the results of the behaviour will be desired by them. The theory basically harps on individual motivation and the influence of the society.Tolmans theory recognises that people have disparate types of needs, desires and goals and proposes that the amount of effort people are prepared to put in task depends on whether the effort will pay off better performance (Ivan T.R et al, 1992).VROOM V.H EXPECTANCY, VALENCE INSRRUMENTALITY THEORYThis theory stems from Tolmans expectancy theory but in addition to expectancy roar added valence and instrumentality as determinants of motivation.Expectancy Vroom Edward (1970) suggests that expectancy is a momentary belief concerning the likelihood that a particular act will be followed by a particular outcome.Instrumentality This assumes that the behaviour of individuals is influenced by the degree to which additional desired goals can be attained as the direct result of such behaviour (Vroom Edward, 1970). The theory suggests that the amount of effort people are willing to put in a task depends on whether the performance when achieved will pay off in equipment casualty of outcomes (Ivan T.R et al, 1992).Valence This refers to the value of the outcomes. Vroom Edward (1970) suggests that individuals value some outcomes highly and hence desire them and can value outcomes down(p) and try to avoid them. He states that we are motivated by the fact that we expect specific behaviours to result in specific outcomes and that such outcomes will have a degree of valence.The main motivation points of Vroom according to David A.H (1995) areThe expectancy that specific behaviour will result i n that attainment of a specific goal, the value of the desired goal and the degree to which such behaviour is instrumental to the attainment of other additional goals.EDWIN A. LOCKE GOAL THEORYBasically this theory looks at motivation from the angle of motivating the employer. It suggests that when specific goals and targets are set out for individuals, they become motivated in order to achieve the goals. This theory has identify that human beings act in a specific way when they are faced with a particular goal (Locke E.A, 1968).The highlights of this theory are that difficult goals should be set because they result in higher performance, employees should be part of the goal setting and that there should be adequate feedback with guidance and advice (Locke Latham, 1984). Locke pointed out that incentives such as money, participation, competition and praise can influence goals. According to Ivan T. Robertson et al (1992) goals have been demonstrated to affect performance through fo ur mechanismsDirecting attention and action.Mobilizing effortIncreasing task persistence.Motivating the search for appropriate performance strategies.Ivan T. Robertson et al (1992) also added two goal attributes that could be relevant for motivation.Goal content the level of goal difficulty and how specific it is andGoal intensity strength and commitment attached to the goal.RECENT IDEAS ON MOTIVATION THEORIESThe recent theories on motivation havent authentically come up with any new idea very different from what other older writers on the subject have written instead they have built on it to make it more adaptable to the changing environment and human perspective.SHEILA RITCHIE AND PETER MARTIN 12 FACTORS OF MOTIVATIONThey gathered a list of factors that modify motivation in the work place and finally trimmed them down to 12 basic factors. Their observation method was to create a self assessment profile which was developed in other to find out what motivated people and also to weight the factors against each other. Their result was a unique motivational profile for each person which gave the relative strength of each factor when compared to each other. The 12 factors were developed from older theories of motivation (Sheila R Peter M, 1999).The 12 factors of motivation pointed out by Sheila R Peter M (1999) whereMoney and tangible rewards This is where money and tangible result is the overwhelming driving force. Where money is the motivator, people so inclined will be ready to tolerate any amount of boredom, work long hours. Undertake repetitive task over periods of months and long time and even put work before family. People who have high money needs will regard their corporal conditions at work with empty indifference. This factor relates to Tolman and Vrooms expectancy theory where they suggest that individuals act in a particular way when they expect a kind of reward that, they value (Vroom Edward, 1970). personal condition In their theory, physi cal conditions have to do with those physical factors that could motivate in a work place. This touches on the work space, work environment and how at ease it is. Some people could be motivated by the mare fact that they work in a very comfortable and beautiful environment. However, they pointed out that physical factors in relation to other motivating factors are not seen as very important.Structure This has to do with the organisational structure and administration of a work place. They believe that people with differing structure requirements need to be motivated in significantly different ways, the right approach motivates and the wrong approach will de-motivate. They suggest that very high structured people need to know where they stand. They need to know the rules and be assured that they have followed the right procedures. Anxiety may be the settle cause of their desire for structure and may find a lack of structure very stressful. Some features of structure include timing, rules and procedures, societys norm and expectation, planning, good converse and information circulation etc (Sheila R Peter M, 1999).People Contact People with this factor enjoy dealing with other people and derive comfort and satisfaction from having a number of others around them. They would prefer to work with other people nearby rather than on their own. Most are likely to be highly spacious with the rowdiness that working with others entail and will even perform better in such situation (Sheila R Peter M, 1999). This in a way is related to Maslows hierarchys third stage that refers to the need for love and human relationship.Relationship This has to do with those motivated by the need for relationships. They suggest that this need can be satisfied outside the work place but for organisations based on commitment and trust between employees will need long term relationships between employees. According to Sheila R Peter M (1999), this particular need usually depends on the organisation in question. Organisations were members of staff are interchanged, work shifts and level of skills are low, will not be in need of long term relationships. This is also related to Maslows need for love and relationship needs.Recognition This factor harps on the need for attention and praise. Sheila R Peter M (1999) pointed out that high recognition needs can make people so dependent on others for approval, that in occasions where there is no recognition, they are unable to act independently. People with high need of this will ever so take care that they consider expectation.Achievement Sheila R Peter M (1999) suggests that a strong characteristics of those with a high achievement drive is that they which to do things on their own. People with this need can find themselves voluntarily working long hours and driving themselves hard. They have to be satisfied that the targets they are aiming are achievable. High achievers are likely to be motivated, if they are not ac hieving they are likely to feel worthless. They will do whatever it takes to achieve their goals. Motivating such people has to start with the definition of the target (Sheila R Peter M, 1999).Power and Influence This is the need to possess power and influence others. The ability to lead and influence people used properly according to Sheila R Peter M (1999) is one of the most desirable human qualities. The difference of this factor from others is that it involves people impinging directly on other people. They pointed out that here is also an element of risk that other people might not react favourably.Variety and change This is the need to always want to do something different. This kind of people we need stimulation to move on to something different with boredom setting in after an initial discharge of energy. These individuals cope better where there is constant demand for new energy and new initiatives. Sheila R Peter M (1999), pointed out that the problem with this factor i s that since the stimulation to change does not always arise, there is always the likely hood of uncompleted business or no motivation.Creativity This concerns the original idea and the development of the new out of the old. They believe that the creative drive has a very important part to play in the organisation. They advocate that those who have the need for creativity to be given an enabling environment for them to operate (Sheila R Peter M, 1999).Self development This factors shows that people who have high self development needs will judge their work in terms of what it does for them. These individuals are not motivated except it has something to do with their self development. Motivating such people requires an understanding of what they are looking for and an ability to relate what the organisation requires to what the need (Sheila R Peter M, 1999).Interest and proceeds Sheila R Peter M (1999) believes that the need for job interest or usefulness is higher on average th an the need for any other motivator. They stated that Professional and managerial people are more motivated for example by feeling of usefulness or interest than for opportunities to influence, achieve or be recognised. This factor suggests that the work place has to be structured in such a way that the employees find it useful and interesting and that in the absence of this factor, all other motivators will not work to full potential. (Sheila R Peter M, 1999).These 12 factors have covered in a way most motivating factors talked about by early exploreers in the topic.REISS AND HAVERCAMPS SENSITIVITY REINFORCEMENT THEORYAccording to Reiss and Havercamp (1996), sensitivity theory suggests that individuals differ in both the types of reinforcer they desire and in the type of reinforcement they need to satisfy them and that people crave withal much love, attention, acceptance, companionship or too much of some other of import reinforce are at the risk for peculiar behaviour becaus e normative behaviour does not produce the desired amount of reinforcement. This theory generally postulates the idea of individual differences in reinforcement effectiveness. In discussing the theory, Reiss and Havercamp (1996) defined the concept of reinforcement sensitivity as an individual difference in the reinforcing effectiveness of a fundamental motivator. They mention three key phases of this theory Reinforcing effectiveness, Individual difference and fundamental motivation.The high points of the theory according to Reiss and Havercamp (1996) are that the theory identifies individual differences in desired amount of reinforcement that is individual differences in rates of satisfaction, as an understudied and potentially important variable, suggesting that because people spend considerable time and energy seeking the reinforcement they desire, these individual differences may predict some person-environment interactions. Secondly, the theory suggests the need for research t o identify the fundamental sources of motivation. And finally, that a new theory in the development of psychopathology is suggested based on the assumption that different individuals not only desire different types of reinforcement but also desire widely varying amounts of each fundamental reinforcer.CONCLUSIONAPPLICATION OF MOTIVATION THEORIES IN THE BUILT environs AND CONSTRUCTION INDUSTRYThe Built Environment and winding industry is a labour intensive industry therefore the application of motivation theories cant be ignored. The nature of the construction industry is different in the sense that it offers jobs which appeal to many people because of their interesting, challenging and rewarding nature (Birchall D.W 1977).According to Olomolaiye Ogunlana (1988) construction operatives in developing countries are faced with many problems unlike those experienced by their counterparts in developed countries. They believe the construction environment is different in terms of site org anisation, quality of supervision and availability of production resources, so also is their socio-economic environment. This environment produces a different worker probably motivated by different factors. In this situation, even when we have highly motivated labour force, it is not right to assume that their motivation will lead to higher productivity. Inability to produce as expected, could lead to frustration and de-motivation. Essentially, extrinsic factors such as good working condition, availability working materials and resources can go a long way in motivation construction workers in developing countries.In the construction industry like every other industry productivity is paramount. The motivation theories discussed in the earlier chapters have shown that productivity of workers is directly related to motivation. When workers are highly motivated the will put more efforts in order to achieve self-fulfilment from doing so, and thereby resulting in higher productivity (Lam and bladder fucus, 2003).Lam and Tang (2003), also added that motivation theories such as Maslows hierarchy of needs, Herzbergs Hygiene theory, McGregors X and Y theories, Vroomss expectancy theory, etc. are often applied to increase productivity in construction projects.Borcherding and Gamer (1981) in their view, have pointed out that there are certain factors that will cause dissatisfaction amongst construction workers. The factors include material availability, tool availability, overcrowded areas, inspection delays, incompetence of foremen, etc. and they also suggested that factors like good craftsman relationship, good orientation program, pay. Recognition, defined goals and projects well planned can motivate construction employees.In the application of motivation theories to the construction industry, Maslow and Herzbergs theories form the basis. Once a worker satisfies his/her physiological needs, he will strive towards satisfying safety and social needs. And then later on s eek to satisfy the needs of social belonging and self-actualization. In order to satisfy the construction workers physiological needs and increase motivation a suitable salary scheme and employment policy should be established (Lam and Tang, 2003). Lam and Tang (2000) also noted that though eccentric rewards such as salary and financial benefits do not motivate employees to high work performance, they could lower employee dissatisfaction.Construction companies should maintain a high level of security, health and safety policy at work environment in order to satisfy the safety needs of workers. Effective communication will also give them a g=feeling that their jobs are secured.For social and relationship needs to be satisfied in the construction industry, induction programs for new employees should be organised to introduce them to company objectives, other colleagues, the facilities and the working environment.The concepts above will motivate the construction workers in the nigglin g term.Lam Tang (2003) also suggested that to motivate the construction employees on the long term, the below listed approaches will come in handyProper resource management and job design.Life-long learning programs.Open door communication.Effective rewarding systems.Diverse and contingency style of leadership.Empowering and valuing construction employees.Continual assessments and improvement of motivation programs.In digest the study and application of motivational theories in management is a very essential tool for all managers in all works of life, especially when there are direct interactions with human beings.

Fibonacci Series And The Golden Ratio Engineering Essay

Fibonacci Series And The lucky balance Engineering EssayThe enquiry question of this extended essay is, Is there a carnal knowledge mingled with the Fibonacci serial and the fortunate Ratio? If so be the reason, what is it and explain it. The Fibonacci series, which was first introduced by da Vinci of Pisa (Fibonacci), was found to seduce had a close connection with the halcyon Ratio. The relation found was that the limit of the balances of the numbers in the Fibonacci sequence converges to the florid immoral/golden ratio. I decided to carry unwrap a some set of experiments that involved oneness-on-one concepts of both the Fibonacci series and the well-to-do Ratio. exploitation their individual applications such as the Golden Rectangle, a computerized t aloney supported by a sketched graph, I found that I could arrive at a supposition that linked the two concepts. I as well as used the Fibonacci spiral and Golden spiral to find the limit where the harbors would t end to meet. After carrying out the experiments, I decided to find the inference of the relation using the Binets expression which is essentially the variety showula for the ordinal margin of a Fibonacci sequence. However, the Binets formula was interesting enough to shuffle me find its proof and solve it myself. From there, I proceeded on to the proof of the relation between the Fibonacci series and the Golden Ratio using this formula. The Binet formula is given by . Following the proof, I carried out steps to verify it by substituting different look ons to crack its validity. After proving the validity of the conjecture, I arrived at the end point that such a relation does exist. I also learned that this relation had applications in nature, art and architecture. Apart from these, there is a possibility that there be other applications which can be subjected to further probe.Table of ContentsSl. No.ContentsPage No.1.Introduction to the Fibonacci Series42.Introduction t o the Golden Ratio53.The Relationship between them64.Forming the conjecture65.Testing the conjecture76.The proof157.Verification of the proof208.Conclusion229.Further Investigation2210.Bibliography23IntroductionThe Fibonacci SeriesThe Fibonacci series is that sequence where every term is the sum of the two toll that precedes it (in the Hindu-Arabic system) where the first two hurt of the sequence are 0 and 1. The Fibonacci series is shown below 0, 1, 1, 2, 3, 5, 8, 13, 21, 34 Where the first two scathe are 0 and 1 and the term following it is the sum of the two foothold preceding it, which in this case are 0 and 1. Hence, 0 + 1 = 1 ( terzetto term)Similarly,Fourth term = third term + second termFourth term = 1 + 1 = 2And so the sequence follows.The series was first invented by an Italian by the name of Leonardo Pisano Bigollo (1180 1250) in 1202. He is better know as Fibonacci which essentially remembers the son of Bonacci. In his book, Liber Arci, there was a crush concernin g the breeding of rabbits and the solution to this puzzle answered in the discovery of the Fibonacci series. The problem was based on the total number of rabbits that would be born starting with a couple up of rabbits first followed by the breeding of new rabbits which would also start giving birth one month after they were born themselves.1The problem was broken downhearted into parts and the answer that was obtained gave rise to the Fibonacci series. The Fibonacci series gained a worldwide acceptance soon as after its discovery and was used in some fields. It had its uses and applications in nature (such as the petals of a sunflower and the nautilus shell). Shown below is the application of the series on the whirls of a pine cone.2http//www.3villagecsd.k12.ny.us/wmhs/Departments/Math/OBrien/fib2.jpghttp//www.3villagecsd.k12.ny.us/wmhs/Departments/Math/OBrien/fib3.jpgThe Golden average / Golden RatioThe golden mean, also known as the golden ratio, as the name suggests is a rat io of distances in simple geometric figures3. This is but one of the many definitions found for the term. It is not solely confine to geometric figures but the proportion is used for art, nature and architecture as well. From pine cones to the paintings of Leonardo Da Vinci, the golden proportion is found almost everywhere. Another definition of the golden ratio is a precise way of dividing a line4 in that location has never been one concrete definition for the golden ratio which makes it susceptible to different definitions using the same concept. First claimed to be known by Pythagoreans round 500 B.C., the golden proportion was established in print in one of Euclids major works namely, Elements, once and for all in 300 B.C. Euclid, the renowned Greek mathematician was the first to establish what the golden section really was with respect to a line. According to him, the division of a line in a mean and extreme ratio5such a way that the point where this division takes place, the ratio of the parts of the line would be the Golden proportion. He determined that the Golden Ratio was such that The golden ratio is denoted by the Greek alphabet which has a order of 1.6180339Since then, the golden ratio has been used in confused fields. In art, Leonardo Da Vinci coined the ratio as the Divine Proportion and used it to define the fundamental proportions of his famous painting of The Last Supper as well as Mona Lisa. http//goldennumber.net/images/davinciman.gifFinally, it was in the 1900s that the term Phi was coined and used for the first clock time by an American mathematician Mark Barr who used the Greek letter phi to name this ratio.6Hence, the term obtained a grasp of different names such as the golden mean, golden section and golden ratio as well as the Divine proportion.The Relation between the Fibonacci series and the Golden RatioAfter the discovery of the Fibonacci series and the golden ratio, a relation between the two was established. Whether thi s relation was a coincidence or not, no one was able to answer this question. However, today, the relation between the two is a very close one and it is visible in various fields. The relation is said to be The limit of the ratios of the numbers in the Fibonacci sequence converges to the golden ratio.This means that as we move to the nth term in the Fibonacci sequence, the ratios of the consecutive terms of the Fibonacci series arrive closer to the think of of the golden mean ().7Forming the ConjectureThe Fibonacci series and the golden ratio have been linked together in many ways. Hence, I shall now produce the same statement as a conjecture as I am about to prove the relation by means of a set of experiments and eventually proving the conjecture (right or wrong).The conjecture is stated below The limit of the ratios of the terms of the Fibonacci series converge to the golden mean as n , where n is the nth term of the Fibonacci sequence.In order to prove this conjecture, I have carried out a few experiments below that shall attribute to the result of the preceding(prenominal) conjecture.Testing the ConjectureExperiment No. 1The first set of experiments deal with the Golden Rectangle. The golden rectangle is that rectangle whose holdings are in the ratio (where y is the length of the rectangle and x is the breadth of the rectangle), and when a upstanding of dimensions is removed from the original rectangle, another golden rectangle is left field behind. Also, the ratio of the dimensions ( is equal to the golden mean (). I have used the concept of the Golden Rectangle to test whether the ratios of the dimensions of the two golden rectangles, when equated to each other, give the value of the golden ratio or not which is also said to be the formula for the nth term of the Fibonacci series. The latter part of the statement is in accordance with Binets formula.The following experiment shows how this works.Let us turn a rectangle with dimensions . The dotted line is the line that has divided the rectangle in such a way that the square on the left has dimensions of . Now, the rectangle on the right has the dimensions of where x is now the length of the new golden rectangle form and (y-x) is the breadth.Golden Rectangle 1yxy-xThe reason why this rectangle is called a Golden Rectangle is because the ratio of its dimensions gives the value of . Hence, the information we can gather from the to a higher place figure is that(1)The new golden rectangle formed from the to a higher place one is shown below with dimensionsGolden Rectangle 2y xxThe in a higher place new golden rectangle shown must thus also have the same property as that of any other golden rectangle. Therefore,From the higher up experiments we can establish the following relation (2)For convenience sake, I have decided to take so as to make y the subject of the equation. Hence, the above equation can now be re-written as On cross-procreateing the terms above we get Writing th e above equation in the form of a quadratic equation, we get Using the quadratic formula, , we getHence, the two roots obtained areHowever, the second root is rejected as a value as y is a dimension of the rectangle and hence cannot be a negative value. Hence we have,Evaluating this value we have But, from equation 1, we know that However, the value of x was restricted to 1 in the above test. So as to eliminate the variable in order to keep only y as the subject, I carried out the calculations below that help in doing so Rewriting the equation Cross-multiplying the variables Dividing the equation by , we get But we know that . Thus, using this substitution in the above equation we have This is the same quadratic that we obtained earlier and hence the doubt for the presence of x clears out.Experiment No. 2For my second experiment, I have decided to use the concept of the Fibonacci spiral and that of the Golden Spiral. The steps on how to draw these spirals are given below A Fibonacci spiral is formed by drawing squares with dimensions equal to the terms of he Fibonacci series.We start by first drawing a 1 x 1 square1 x 1Next, another 1 x 1 square is drawn on the left of the first square. (every new square is bordered in red)Now, a 2 x 2 square is drawn below the two 1 x 1 squares.Next, a 3 x 3 square is drawn to the right of the above figure.Now, a 5 x 5 square is adjoined to the top of the figure.Next, a 8 x 8 square is adjoined to the left of the figure.And so the figure continues in the same manner. The squares are adjoined to the original shape in a left to right spiral (from down to up) and each time the square gets bigger but with dimensions equal to the numbers in the Fibonacci series. Starting from the inner square, a quarter of an arc of a circle is drawn within the square. This step is repeated as we move outward, towards the bigger square. The spiral eventually looks like this http//library.thinkquest.org/27890/media/fibonacciSpiralBoxes.gifThe shap e shown below is the Fibonacci spiral without the squareshttp//library.thinkquest.org/27890/media/fibonacciSpiral2.gifA similar process is followed for forming the golden spiral. However, the only difference is that we draw the outer squares first and then draw the arcs starting from the larger squares. Hence, the spiral turns inwards all the way to the inner squares.Golden SpiralThe Golden spiral eventually looks like this Golden SpiralOn comparing the two spirals, it can be seen that they overlap as the arcs guide the squares with dimensions of the latter terms of the Fibonacci series. An image of how the two spirals look is shown below http//library.thinkquest.org/27890/media/spirals.gifFrom the above experiment, it can be seen that there is a connection between the Fibonacci series and the Golden Mean as their individual spirals overlap each other as the n (which is the nth term in the series) tends to infinity.Experiment No. 3My third experiment involves technology. In this ex periment, I decided to use a program of Microsoft Office, namely, Microsoft Excel in order to record the values obtained on calculating the ratio of the consecutive terms of the Fibonacci series. In the table below, I have recorded the terms of the Fibonacci series in the first column, the value of the ratio of the consecutive terms in the Fibonacci sequence in the second column, the value of8in the third column and the variation of the value of the ration from the value of in the last column. consideration of Fibonacci SeriesValue of ratio of consecutive termsvalue ofvariation of value calculated from value of0111.000000000000001.618033988749890.6180339887498922.000000000000001.61803398874989-0.3819660112501131.500000000000001.618033988749890.1180339887498951.666666666666671.61803398874989-0.0486326779167881.600000000000001.618033988749890.01803398874989131.625000000000001.61803398874989-0.00696601125011211.615384615384621.618033988749890.00264937336527341.619047619047621.61803398 874989-0.00101363029773551.617647058823531.618033988749890.00038692992636891.618181818181821.61803398874989-0.000147829431931441.617977528089891.618033988749890.000056460660002331.618055555555561.61803398874989-0.000021566805673771.618025751072961.618033988749890.000008237676936101.618037135278511.61803398874989-0.000003146528629871.618032786885251.618033988749890.0000012018646415971.618034447821681.61803398874989-0.0000004590717925841.618033813400131.618033988749890.0000001753497641811.618034055727551.61803398874989-0.0000000669776667651.618033963166711.618033988749890.00000002558318109461.618033998521801.61803398874989-0.00000000977191177111.618033985017361.618033988749890.00000000373253286571.618033990175601.61803398874989-0.00000000142571463681.618033988205321.618033988749890.00000000054457750251.618033988957901.61803398874989-0.000000000208011213931.618033988670441.618033988749890.000000000079451964181.618033988780241.61803398874989-0.000000000030353178111.618033988738301.61803 3988749890.000000000011595142291.618033988754321.61803398874989-0.00000000000443The aim of the table is to find out whether the value of the ratio reaches the value of or not, as the number of terms increases infinitely.ObservationFrom the above table, it can be seen that as we reach the nth term of the Fibonacci series, the variation in the value of the ratios from the value of , decreases. This observation is in agreement with the conjecture The limit of the ratios of the terms of the Fibonacci series converge to the golden mean as n , where n is the nth term of the Fibonacci sequence.InferenceFrom the above 3 experiments, I have found that the conjecture holds true for them all. Hence, I would like to state that the tests for the conjectures have been significantly successful.The proofreadIn order to find the relation between the Fibonacci series and the Golden Ratio, I followed the proof below that uses calculus to establish the required relation.The Fibonacci series is give n by,Assuming that 0, 1, and 1 are the first three terms of the sequence(3)This eventually goes on to form the well known sequence 0, 1, 1, 2, 3, 5, 8, 13Dividing the left(a) Hand Side (or LHS) and the Right Hand Side (or RHS) of equation 3 by F(n), gives(By taking the numerator as the denominator of F(n))By substituting the limit of the ratios of the terms (as n ) of the Fibonacci series with A, the limit is taken on both sides such that n The above is true as the ratioHence, the below quadratic equation is formedWe can find the roots of A by using the quadratic formula, .orFrom this we find thatThis value of is easily attainable using the Binet formula. The Binet formula is that formula which gives the value of by substituting the variable x with one of the n terms of the Fibonacci series. Using the concept of the golden rectangle, the quadratic that was obtained earlier Gave the value of . The proof of the Binet formula shows another possibility to arrive at the relation betwe en the Fibonacci series and the Golden Ratio. The beauty of this proof is that the quadratic first arose from the Fibonacci series calculation and the root that was obtained gave the value of phi. This is from the proof that was written above. Under the heading Testing the Conjecture that was done earlier, the quadratic arose from the dimensions of the Golden Rectangle and the equation thus obtained gave the value of phi. Using this concept, I have followed the proof below which was solved by older mathematicians.The Binet formula is given by Now, from the above tests, we got However, there were 2 values that were obtained on calculating the value of y. The value of y that was negative was rejected then as it was incorrect to consider it a valid answer for a dimension of a geometric figure. Calling this negative root as , we can rewrite the Binet formula as Going back to the quadratic equation, we can transmute in place of y and so the quadratic equation is (4)This quadratic was o btained from the Golden Rectangle. In order to arrive at the Fibonacci sequence, a series of algebraic manipulations will help us reach that step. To start off with, we have the value of in terms of . Now, to get the value of in terms of , we multiply equation (4) into .Using equation (4), we substitute for and we get Using the same method to find the value for raised to higher powers, we have Similarly,Writing the various values for raised to higher powers (5)Now if we look at the coefficients closely, we see that they are the consecutive terms of the Fibonacci series. This can be written as (6)However, the above trend is not enough proof for oecumenicalizing the above statement. Hence, I decided to prove it by using the principle of mathematical induction. measurement 1Step 2To prove that P(1) is true.Hence, P(1) is true (from equation 5)Step 3Hence, P(k) is true whereStep 4To prove that P(k+1) is true.Starting from the RHS,(from equation 3)(from equation 4)(from P(k))= RHSHence , P(k+1) is true.Therefore, P(n) is true for allNow that we have proved that P(n) is trueis true in its generalized form.Also, we know that is the other root of the quadratic equation and so the above general equation can be written in the above form as well (7)In order to obtain the Binet formula in the form of We can subtract equation (7) from equation (6) to get Substituting the original values of and in denominator of the above equation, we get Substituting the value of and in the above equation, we get This is the Binet formula which we started to prove. Hence, the formula is valid.Verifying the ProofIn order to validate a proof, it must be tested in order to check whether the conjecture is valid and can be generalized. For this reason, I have decided to use the Binet formula (that was proved above) to check the validity of the relation between the Fibonacci series and the Golden Ratio by substituting values for x in the equation UsingCase 1,Which is the first term of the Fibon acci series.Case 2,Which is the second term of the Fibonacci series.Case 3,Which is the third term of the Fibonacci series.Case 4,Which is the fourth term of the Fibonacci series.From these substitutions it is clear that the formula is a valid one which gives the desired result.Also, the above calculations have proved to be substantial examples for proving the validity of the proofs shown above. However, an important note to remember in the Binet formula is that the value of x starts from 0 and increases. So it can be said that (x belongs to the set of whole numbers). This is to account for the fact that the Fibonacci series starts from 0 and then continues.Hence, the conjecture is true and can be generalized. Hence the conjecture below can be considered true.The limit of the ratios of the terms of the Fibonacci series converge to the golden mean as n , where n is the nth term of the Fibonacci sequence.ConclusionFrom the above tests and verifications, it is clear that a relation be tween the Fibonacci series and the Golden Ratio does truly exist. The relation being The limit of the ratios of the terms of the Fibonacci series converge to the golden mean as n , where n is the nth term of the Fibonacci sequence.The Fibonacci series as well as the Golden Ratio have their individual applications as well as combined applications in various fields of nature, art, etc. As mentioned earlier, the Fibonacci series was used to find a solution to the rabbit problem. The relation between the two concepts was an integral part of the central idea in the novel The Da Vinci Code.Along with these well known ideas, other applications of the two concepts are present in the whirls of a pine cone, the paintings of Leonardo Da Vinci, the spiral of the nautilus shell, the petals of the sunflower. These are only very few examples regarding the applications of the two concepts.However, this relation has proved to be useful to environmentalists, artists and many other researches. For ex ample, artists were able to use the study of the concept in the paintings of Leonardo Da Vinci and draw old symbols. It also has given them the chance to create art of their own that by using this concept in their procedure of creating.Further InvestigationWith the prominent number of applications that were found regarding the Fibonacci series and the Golden Ratio, there is a possibility that there are other applications of the concept as well. The convergence of the ratios of the values to the value of phi may prove to be of great significance if applied to another theory that has boggled minds of mathematicians for years. Possibilities such as these give rise to the question of further investigation in this aspect of the relationship between the two concepts.

My Home Schooling Experience Essay -- Personal Narrative Essay Example

Id like to take this opportunity to elaborate on my home education. I realize that there argon umpteen different interpretations of the term home school and I feel obliged to explain my personal methods and philosophy. As copies of my curricula will be included in the unessential School Report, I will not go into detail concerning the specific nature of my studies, but rather I will discuss my home educate experience. I left traditional schooling at age nine, until which point I had attended the local public schools. Although I did well in the school system, I was often bored and complained that I was unch every last(predicate)enged. My parents had researched into home schooling and after a family discussion we decided to try it following the winter vacation of fourth part grade. Our approach was very structured when we first began and has gradually evolved to the natural style we live by now. Throughout my high school years I ware taken the majority of the responsibility for my education. Each August my mother and I plan a curriculum together, which is a combination of what I want to essay and what she feels I ought to know. I study Latin using a text with accompanying audio tapes and a reader with passages to be translated into English. I complete a detailed research project on a subject of interest in the social sciences -- Australian aborigines, for example, or the Vietnam war. My mother forms a reading appoint with approximately eight works of literature which I must read and discuss. During the year I add umpteen of my own selections, including science fiction, plays, non-fiction, and often novels which my friends recommend. My parents are always available for help, yet they do not act as teachers and do not constantly monitor ... ...with. This is true. While others my age direct been caught up on homework assignments and grades in preparation for the real world, I have been living and learning in the real world every day. My friends are of many ages, have many accents and professions, and do not eat the same type of food. They do not all live in my town or all gather in one building. Home education afforded me the time and opportunity to interact and learn in a variety of settings, and certainly my social behavior has been enriched by my experiences at the high school. I have had to use the resources in my surroundings to facilitate my own education, and Sarah Lawrence College seems the ideal place to continue that lifestyle. I have chosen to attend college in order to continue living and learning in the real world. I am looking forward to the college experience, and I am confiden

Police Brutality :: Use of Excessive Force by Police

In recent years, law actions, particularly natural law abuse, has come into view of a wide, public and critical eye. While citizens worry about protect themselves from criminals, it has now been shown that they must also keep a watchful eye on those who are supposed to protect and serve. This paper will discuss the types of police abuse prevalent today, including the use of firearms and receipt of mystical information. I will also discuss what and how citizens rights are taken advantage of by police. For these problems, solutions will be discussed, focusing on political reform, education, and citizen review boards. These measures are necessary to protect ourselves from police taking advantage of their positions as law enforcement officers with greater permissive rights than private citizens. Because of this significant differential, all citizens must take affirmative action from forcible brutality, rights violations, and information abuse. Problems arise, however, when one side is told what to do by another, as there is butt on to be conflicting viewpoints. In regard to police abuse, there will be many officers who feel that their job of fighting escalating street crime, gangs, narcotics violations, and other fierce crimes is difficult already, and that worrying about excessive policy for abusive behavior will only further decrease their ability to fight crime effectively, efficiently, and safely. Citizens, however, look at been caught up in this gung-ho attitude, and police are more and more often crossing the line of investigation and interrogation with abusive behavior. This abuse must be monitored so that police do not forget who they are serving--not themselves, but the public. This means that even the criminals, who are a part of the public, have certain rights, particularly, well-behaved rights. All citizens must be aware of these rights to protect themselves against over-aggressive officers who take advantage of their position as badge and gun h olders to intimidate and abuse civilians for personal or departmental polishs. Such conflicts have significant implications on departmental and administrative policy procedures. One of the main police abuse problems is physical brutality. The main goal here should be to get the police departments to adopt and enforce a written policy governing the use of physical force. The policy should restrict physical force to the narrowest possible range of specific situations. For example, their should be limitations on the use of hand-to-hand combat, batons, mace, stun guns, and firearms. However, limiting polices actions will bring much debate, especially from police officers and administrators themselves.