Indian Mathematicians And Their Contributions Essay

Ramanujan He was born on 22na of December 1887 in a small village of Tanjore district, Madras. He failed in English in Intermediate, so his formal studies were stopped but his self-study of mathematics continued. He sent a set of 120 theorems to Professor Hardy of Cambridge. As a result he invited Ramanujan to England. Ramanujan showed that any big number can be written as sum of not more than four prime numbers. He showed that how to divide the number into two or more squares or cubes. when Mr Litlewood came to see Ramanujan in taxi number 1729, Ramanujan said that 1729 is the smallest number which can be written in the form of sum of cubes of two numbers in two ways, i.e. 1729 = 93 + 103 = 13 + 123 since then the number 1729 is called Ramanujan’s number. In the third century B.C, Archimedes noted that the ratio of circumference of a circle to its diameter is constant. The ratio is now called ‘pi ( ÃŽ   )’ (the 16th letter in the Greek alphabet series) The largest numbers the Greeks and the Romans used were 106 whereas Hindus used numbers as big as 1053 with specific names as early as 5000 B.C. during the Vedic period. ARYABHATA Aryabhatta was born in 476A.D in Kusumpur, India. He was the first person to say that Earth is spherical and it revolves around the sun. He gave the formula (a + b)2 = a2 + b2 + 2ab He taught the method of solving the following problems: BRAHMAGUPTA Brahma Gupta was born in 598A.D in Pakistan. He gave four methods of multiplication. He gave the following formula, used in G.P series a + ar + ar2 + ar3 +†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. + arn-1 = (arn-1) à · (r – 1) He gave the following formulae : Area of a cyclic quadrilateral with side a, b, c, d= √(s -a)(s- b)(s -c)(s- d) where 2s = a + b + c + d Length of its diagonals = SHAKUNTALA DEVI She was born in 1939 In 1980, she gave the product of two, thirteen digit numbers within 28 seconds, many countries have invited her to demonstrate her extraordinary talent. In Dallas she competed with a computer to see who give the cube root of 188138517 faster, she won. At university of USA she was asked to give the 23rd root of 91674867692003915809866092758538016248310668014430862240712651642793465704086709659 32792057674808067900227830163549248523803357453169351119035965775473400756818688305 620821016129132845564895780158806771. She answered in 50seconds. The answer is 546372891. It took a UNIVAC 1108 computer, full one minute (10 seconds more) to confirm that she was right after it was fed with 13000 instructions. Now she is known to be Human Computer. BHASKARACHARYA He was born in a village of Mysore district. He was the first to give that any number divided by 0 gives infinity (00). He has written a lot about zero, surds, permutation and combination. He wrote, â€Å"The hundredth part of the circumference of a circle seems to be straight. Our earth is a big sphere and that’s why it appears to be flat.† He gave the formulae like sin(A  ± B) = sinA.cosB  ± cosA.sinB

Dementia: Cerebrum and High Blood Pressure

DEMENTIA AWARNESS 1. Understand what dementia is 1. 1 Explain what is meant by the term ‘dementia' A syndrome due to disease of the brain, usually of a chronic progressive nature in which there are multiple disturbances of higher cognitive function. These include impairment of memory, thinking and orientation, learning ability, language and judgement. 1. 2 Describe the key functions of the brain that are affected by dementia The key functions of the brain that are affected by dementia are the temporal lobe, frontal lobe, parietal lobe, occipital, cerebrum lobe and the hippocampus.Temporal lobe- responsible for vision,memory, language, hearing and learning Frontal lobe- responsible for decision making, problem solving, control behaviour and emotions Parietal lobe- responsible for sensory information from the body, also where letters are formed, putting things in order and spatial awareness. Occipital lobe- responsible for processing information related to vision Cerebrum lobe- i s responsible for for the biggest part of the brain its role is memory, attention, thought and our consciousness, senses and movement.Hippocampus- responsible for memory forming, organizing and storing and emotions 1. 3 Explain why depression, delirium and age-related memory impairment may be mistaken for dementia Because they both manifest with similar symptoms. Depression coupled with age related memory impairment looks the same as dementia to the untrained eye. The difference is that depression delirium responds to treatment with anti depressants, once you get on top of the depression you can put age related memory loss into perspective.If it is genuine dementia it won't get any better. 2. Understand key features of theoretical models of dementia 2. 1 Outline the medical model of dementia The medical model focuses on the impairment as the problem and focuses on a cure, these may be dependency, restriction of choice, dis empowering and devaluing individuals 2. 2 Outline the social model of dementia This is personal centred, focusing on the rights of the individual, in turn empowering the individual, promoting independence, giving choice and looking at what the individual is able to do. . 3 Explain why dementia should be viewed as a disability Individuals who have dementia are not aware of requirements for living, they can forget to do the essential things that are vital. Taking medication,hygiene and even eating are often forgotten. They can get lost or hurt and not understand what is necessary to correct a situation. Individuals cannot act in the manner of a responsible adult which is why dementia should be viewed as a disability 3. Know the most common types of dementia and their causes 3. List the most common causes of dementia Alzheimer disease This is the most common cause of dementia, during the course of the disease the chemistry and structure of the brain changes, leading to the death of brain cells. Vascular dementia If the oxygen supply to the brai n fails, brain cells may die, this can happen from a strokes or over time through series of small strokes Lewy body disease This form of dementia gets its name from tiny spherical structures that develop inside nerve cells, there presence in the brain cells leads to the degeneration of brain tissue. . 2 Describe the likely signs and symptoms of the most common causes of dementia Alzheimer's disease is a progressive condition, symptoms include minor memory problems, difficulty saying the right words, disorientation personality changes and behavioural changes Vascular dementia may develop suddenly and quickly, symptoms include memory loss depression, visual hallucinations, low attention span and periods of mental confusion.Lewy bodies develop gradually and gets more severe over the years, symptoms include memory loss, visual hallucinations, delusions, muscle stiffness. 3. 3 Outline the risk factor's for the most common causes of dementia The risk factor's for Alzeheimers is age, famil y history and genes Vascular dementia is increasing age, history of heart attacks, strokes or mini strokes, high cholesterol, high blood pressure and diabetes Lewy bodies is advanced age, it appears to affect more men than women, having a family member who's had it and a unhealthy lifestyle 3. Identify prevalence rates for different types of dementia The established prevalence rates for different types of dementia are 40-64yrs 1 in 1400 65-69yrs 1 in 100 70-79yrs 1 in 25 80+ 1 in 6 4. Understand factors relating to an individuals experience of dementia 4. 1 Describe how different individuals may experience living with dementia depending on age, type of dementia, and level of ability and disability Depending on the form of dementia people's ability and disability will be different. People with ementia may not necessarily always be forgetful, their memory may remain intact but their personality and behaviour could be noticeably changed. However the level of ability and disability depe nds on an individuals age and condition of dementia, people who are living with dementia in earlier age such as 60's-70's are less likely to be as dependable on others than people living with dementia at the age of over their 70's-80's. People also have different levels of stamina at different ages so their ability and disability may vary and the level of support they require will be varied as well. . 2 Outline the impact that the attitudes and behaviours of others may have on an individual with dementia People who suffer from dementia can feel excluded if people aren’t giving them enough time to finish there conservation or tasks, which can lead them to being treated differently and can cause more illness such has anger, depression and frustration , so therefore there is good combination of general awareness of the existence of dementia but poor detailed understanding of its causes, progression and implications tends to lead to inaccurate assumptions.

The Origin of the Universe Research Paper Example | Topics and Well Written Essays - 1750 words

The Origin of the Universe - Research Paper Example Not only is it difficult to figure out how a whole universe could appear from nothing, but also no plausible explanation for the mechanism of the explosion itself springs to mind. The only known force in nature capable of affecting the universe as a whole is gravity. Gravity is, however, an attractive force, whereas the explosion requires a repulsive force. The mystery of the explosion lies in the first fraction of a second of the life of the universe. At such early times, the universe was in a state of incredibly high temperature and density, a situation so foreign to laboratory conditions that it is impossible to extrapolate known physics to that realm. The cause of the explosion is shrouded in the extreme conditions of the very early universe. For a while cosmology treated the existence of the universe as a given and concentrated on the consequences of the explosion rather than its cause. In the course of the scientific step-by-step reconstruction of the chronology of the universe , a number of puzzling paradoxes surfaced, of which two are of interest here. The first deals with the strength of the explosion. The push of the Bang was exquisitely well fine-tuned, allowing for the existence of a universe with galaxies, stars, planets, and life. Any other push would have meant either a structureless universe or a universe collapsing back onto itself after a brief existence. Why was the Bang so well engineered? The second paradox deals with the large-scale properties of the universe. The extreme large-scale smoothness of the temperature and of the density of matter cannot be explained by the standard Big Bang model. No known physical process can account for it. What is the origin of this conspiracy? Is our universe very peculiar, that is, did it just start this way by sheer luck -- in the scientific jargon, with very special initial conditions -- or are there mechanisms that can account for the fine-tuned push of the explosion and for the smoothness of the univers e? Two diametrically opposite schools of thought have addressed these paradoxes. The proponents of the so-called anthropic principle state that if the universe were not so fine-tuned, there could be no life in it, and we humans would not be there to witness it. Although this statement is correct, it does not attempt to resolve the paradoxes in terms of physical mechanisms, but relegates them to the status of special initial conditions. In other words, that is the way the universe started because if it had not, we would not be there to witness it. The other school of thought has refused to accept special initial conditions but rather has searched for mechanisms that could account for the observed peculiarities. It is the purpose of this essay to present and to discuss some of the latest models advanced by the second school. The Big Bang When Einstein applied his newly created theory of General Relativity to the universe, he discovered to his dismay that the universe was not static as everybody, including himself, liked to believe at that time. His universe was either contracting or expanding. Rather than exploring the consequences of his findings, Einstein introduced an ad-hoc term into his equation that he called the cosmological term. The cosmological ter

Apply The Prescribed Ethical Decimation Making Model (P.30 ) Using The Essay

Apply The Prescribed Ethical Decimation Making Model (P.30 ) Using The case California Parks Department Scandal - Essay Example In his model, Cooper further explains the consequences of the individual decisions and alternatives. In fact, Cooper is very clear that the consequences are in four broad categories, that is, Moral Rule, Ethical Principle, Rehearsal of Defenses, and Anticipatory Self-Appraisal (Cooper, 2012). These are the virtues that an individual holds, in most cases they are propelled by religious convictions, evolution of the conscience, and the fear of being caught and being exposed. Lopez was faced with an ethical problem whose first alternative would have had a moral rule that he had a criminal record in the past and he in that he participated in hiding the parks funds. In whatever way the Lopez would try to justify his deeds, the moral judgment in either case would be that he be fired and prosecuted for having a hand in mismanaging public money. It was apparent that Lopez even had a share of the funds for himself. Ethical principles by far falls under the category of the outlined codes of conducts in this case those of a public officer. In fact, these codes are extensively spelt out in the constitution, which public officers must obey or else be prosecuted. It is expected that any public officer is conversant with these laid down guidelines. As such, Lopez acted contrary to the ethical codes he is expected to safeguard and uphold. Consequently, being delegated for such an office is an honor and the public officer is expected to serve the public’s interest first rather than act on personal gains. Lopez, has the alternatives named earlier, however, whatever alternative he chooses will lead to on ethical principle consequence; be fired from holding any public office and be prosecuted for acting centrally to the ethical codes knowingly. In this element the administrators is expected to asses and align the alternatives they have and this should be guided by the norms of the organization as well as the involved political forces. The results of cases that are

Compare Scientific Models and Religious Myths Essay

Compare Scientific Models and Religious Myths - Essay Example The ideas in defense of religion, on the other hand, are argument from causation and argument from values. A myriad of scientific models have been invented and adopted in the realm of pure science and applied sciences, which gave a strong attachment of science to scientific observation and scientific methods. Objectivity, accuracy, and verifiability are of prime importance of scientific inquiry, and are the characteristics of science. These dimensions are said not to be possessed by religion, whose central configuration is faith. The locus of science being based on material objectivity through scientific methods is said to be a far cry from that of religion, which to some people, is perceived to be a locus of mythology, false and science-unaided beliefs, and fanaticism. Thus, the debate about science and religion has a history that dates back to the beginning of modern science. Naturalism, a scientific model that defends science with its stance of reality being material, and is therefore subject to scientific scrutiny, poses that any considerations that ideas not relying in scientific investigations are foolish (Baker, 2006). The search for truth is found in the material reality - in the natural world - which can be measured and analyzed according to scientific investigations. Religion, having no scientific tools to aid such investigation, is taken as a myth. Science was able to maintain such confinement to the natural world on the basis of its ability to use testable and reproducible material data that passed through scientific methods, in which explanations lie in the domains of the natural world. It goes on to say that non-natural explanations, like the realm of religion, are non-testable and non-reproducible and are therefore non-scientific. Anything non-scientific is considered a myth or an erroneous belief by some science geeks. However, the exclusio n of non-scientific explanations from understanding the natural world does not

Leadership & Negotiation Essay Example | Topics and Well Written Essays - 1000 words

Leadership & Negotiation - Essay Example From the discussion it is clear that organizations are faced with an alarming shrinkage in the availability of funds as obtaining credit has become harder, a fact which has resulted in driving well established businesses to the point of bankruptcy. The global recession also proves to be a considerable challenge because inflation has increased the level of risk associated with business activities and in these times of the financial crunch.This essay discusses that smaller businesses will generally be much more sensitive to the on going credit crunch because of their limited sources of external funding, larger more well established organizations will face the difficulties of keeping a huge business set up going in an atmosphere of financial   vulnerability. Hence it would be safe to say that all sorts of businesses are facing considerable difficulties during these times. However, there are some ways that organizations can counter these circumstances. Leaders must aim to build their o rganization’s credit structures in a way which enable them to weather the â€Å"bitter cold shock to the credit markets† . Leaders of small to medium organizations can ensure credit approval by devising strong negotiation strategies and can also look towards other sources of external financing such as â€Å"crowd funding†.  Leaders will have to learn how to make their organizations more ‘flexible’, because surviving in today’s business environment means that organizations will have to respond to the micro-markets’ demands in a timely manner, and this can only be done if organizations are flexible.

Strategic Marketing Proposal Essay Example | Topics and Well Written Essays - 2000 words

Strategic Marketing Proposal - Essay Example Executive Summary Salad Creations has been offering fresh and natural salads in different parts of United States for years. Considering the response of the customers in United States, the company has planned to expand its services in United Kingdom as well. There are lots of reasons behind the success of Salad Creations in United States and the company would be highly relying on the brand image and management expertise to make the brand successful in London as well as it plans to expand. Salad Creations offer fresh and healthy salads. Different variety is available for customers to choose from and even if they do not like any of these, then the company gives them the freedom to prepare their own salads. Although, in United Kingdom there are few competitors offering fresh salad but considering the market research and response of the target market, the management feels that London would be the best suited area for opening a new store in the European Union. The management plans to make use of different marketing channels and has devised different short term as well as long term objectives. Strategies have been devised to achieve these objectives by the management. The company would also be making use of traditional as well as latest marketing channels to promote the offerings of the company so that they are able to reach the target market. Also the company would be evaluating different marketing channels and then prioritising the investment on different marketing channels accordingly. Online marketing strategies, social media marketing and traditional promotional channels such as direct mail, advertisements on billboards and advertisements on newspapers would be ysed by the management to promote the brand in London and in United Kingdom. Marketing Budget has also been setup by the management however the management has pre-decided that this budget would not be fixed and it would be flexible. The management would be evaluating the marketing budget on a quarterly bas is so that they can invest more in activities that yield better returns so that it helps in the long run profitability of the company. 2.0. Situational Analysis Salad Creation is a renowned name in the food industry of United States offering fresh and healthy salads. Salad Creation offers spectacular taste at affordable prices and with the growing consciousness of the people around the world to have more fresh and natural foods, the demand of salad has increased to a great extent. The proposal analyses the situation of Salad Creation to start offering the fresh salad in United Kingdom as it plans to expand the idea of fresh and natural foods in other parts of the world besides United States. Salad Creation has been evaluating to offer its services in London, United Kingdom and then afterwards to other parts of United Kingdom. In London, the management has selected the Oxford Street where the company should be opening its first outlet in United Kingdom. There are several reasons for selecting this location; accessibility of resources, ease of customers to reach, an important area in the city, availability of transport etc. In the appendix section, a map has been placed identifying the proposed location of Salad Creations. Although, the demand for such products have been increasing throughout the world. However, there are few competitors already operating in London