Nuclear Technology essays

Nuclear Technology essays The use of nuclear technology for civilian and military use is a highly controversial issue. Most people argue that nuclear technology is bad. However, they do not analyze how nuclear technology can be a good thing. To me, the advantages of nuclear technology out way the disadvantages. A comparative analysis of the advantages and disadvantages makes it easy to see how nuclear technology is the way forward. Even though nuclear proliferation and terrorists are serious threats, nuclear technology is good for civilian uses in that it produces high yields of environmentally friendly electricity and it is good for military uses in that it maintains a power balance and prevents countries from going to war. As the human population grows and more advances are made in technology, our energy demand rises greatly. To meet these energy demands, large amounts resources are used. Most of these resources are fossil fuels. Hydropower, wind power and other environmentally friendly techniques of producing power have great economic and environmental advantages but these techniques are rare. The reason is because these techniques require a great amount of technology and are very expensive. Also the yields of electricity from these techniques are much lower than that of fossil fuels. Fossil fuels are abundant these days and are widely available. Producing electricity using fossil fuels also requires little technology and are not so expensive. This is why they are widely used. However, the fossil fuels contribute greatly to pollution. Pollution is a big issue now because it poses a threat to us as it causes global warming and a greenhouse effect that is harmful to us. Therefore, environmentally frie ndly techniques of producing electricity are the alternative. What would be the ideal source of energy is something that does not pollute the environment, is cost effective and produces a high yield of energy. The closest to these criteria is nuclear technolog...

4 Types of Reference Books You Didnt Know You Need

4 Types of Reference Books You Didnt Know You Need 4 Types of Reference Books You Didn’t Know You Need 4 Types of Reference Books You Didn’t Know You Need By Mark Nichol OK, it’s time to conduct an inventory of your reference library to ensure that you have a comprehensive collection at hand. Dictionary? Check. Thesaurus? Mm-hmm. Compendium of famous quotations? Right. Visual dictionary? (Silence.) You’re telling me you don’t have a visual dictionary? Before you get too self-conscious, I’ll let you off the hook: You don’t have to own your own visual dictionary. But you should know where to find this type of resource, and three others, at your local library, or you simply must do some online research and see what electronic simulacra you can discover. 1. Visual Dictionaries The four books listed here are all superior guides to the names of physical objects and their components. Does a scene in your novel require you to distinguish the parts of a plane? Do you need to know the difference in home construction between a rafter and a joist? What is the base of a horse’s neck called? A visual dictionary knows all: The Macmillan Visual Dictionary, Jean-Claude Corbeil Merriam-Webster’s Visual Dictionary, Merriam-Webster What’s What: A Visual Glossary of the Physical World, Reginald Bragonier Jr. Ultimate Visual Dictionary, DK Publishing 2. Guides to Symbolism These five volumes, and others, will enlighten you about the religious, mythological, and folkloric significance of symbols. Perhaps you want to strew visual metaphors throughout your novel. Or you want to avoid cliched occult symbols in your supernatural thriller, and want to find something unusual. Or you want to make sure your medieval mystery accurately describes a cross without anachronistic errors. Follow the signs to these sources about symbology: An Illustrated Encyclopaedia of Traditional Symbols, by J. C. Cooper Dictionary of Symbolism: Cultural Icons and the Meanings Behind Them, Hans Biedermann 1,001 Symbols: An Illustrated Guide to Imagery and Its Meaning, Jack Tresidder The Penguin Dictionary of Symbols, Jean Chevalier Reverse Symbolism Dictionary: Symbols Listed by Subject, Steven Olderr 3. Guides to Hierarchies Do you know the order of succession among Cabinet officials in the United States in case the president, vice president, and Speaker of the House are all incapacitated? Is a battalion bigger, or smaller, than a regiment? What’s higher up the taxonomic scale a phylum, or a family? The Order of Things: How Everything in the World Is Organized into Hierarchies, Structures, and Pecking Orders, Barbara Ann Kipfer, will set you straight. 4. Reverse Dictionaries Flip Dictionary, Barbara Ann Kipfer, is the best of the class of reference books known as reverse dictionaries, for when you know how to describe something but can’t think of the word. One of the qualities that set it apart is the numerous charts and tables that group things by subject. The Describer’s Dictionary: A Treasury of Terms Literary Quotations, David Grambs, is a similar work that’ll help you transfer a word from the tip of your tongue to paper or the computer screen. Want to improve your English in five minutes a day? Get a subscription and start receiving our writing tips and exercises daily! Keep learning! Browse the Book Reviews category, check our popular posts, or choose a related post below:Dialogue Dos and Don'ts"Wracking" or "Racking" Your Brain?Honorary vs. Honourary

Landscape Painting Assignment Example | Topics and Well Written Essays - 250 words

Landscape Painting - Assignment Example Thus romanticism style of art involved exotic, more authentic, familiar and distant modes in harnessing imagination power as portrayed in landscape paintings that were prepared during this period. Romanticism went beyond the confines of population, industrialization unlike it preceding periods, the classical period and medievalism. In fact, romanticism exalted subjectivism, imagination, irrationalism and individualism. The art was highly characterized and influenced by artists’ fascination by their passions, nature, their moods, their mental potentials and the heroes. On the other hand, the Impressionism movement thrived in France between late 1860s and 1890s. This movement was inclined to optical realism since it sought to relate art to visual experience and the effect of light on appearance of various objects. The form of art in impressionism involved transcription of the artists’ visual sensation towards nature, which was unconcerned with the actual depiction of the objects. The main ideas of impressionism were, a quick painting of a landscape could depict it actual physical appearance and that art is promoted by a naà ¯ve vision, free from influence by intellectual preconceptions which were realist traditions and naturalist traditions. In comparison, the romanticism form and style of art applied to landscape paintings is distinguishable from the impression form art employed in landscape painting. This is evident from a keen observation of the following paintings, soleil levant by Claude Monet.

Operational Management Report Essay Example | Topics and Well Written Essays - 2750 words

Operational Management Report - Essay Example In the fashion world customers needs have changed and they are looking to get new styles and fashions in the market at frequent rates. The supply chain management in the fast fashion business deals with the movement of goods from the suppliers where the raw material is originated to the end customer who consumes the particular end product. In this fashion world there is a he competition among the companies for coming up with new styles and also in quick time. Thus agility in the whole operation process is a very important factor which helps the company to respond quickly to the changing demand of the customers. In 1975, Inditex a Spanish group which was been owned by Amancio Ortega established Zara as a fashion label and value chain store. In the last two decades Zara has grown in huge numbers and its profit has gone up by three times and has become the third largest fashion retail store in world. The other brands which Inditex has are Uterque, Oysho, Zara Home, Bershka, Pull and Bear, Zara kinds, Stradivarius and Massimo Dutti. Zara has around 300 designers in its headquarters in Spain where approximately 40,000 designs are made from where only 10,000 designs are selected for production. By Dec 2010, Inditex had approximately 5000 stores worldwide becoming the worldwide leader in fast fashion chain network. Zara has a strategy of maintaining a policy of generating a huge variety of products every year. Zara being n the fashion business and being the worldwide leader in 5this business the overall operations process including the supply chain management, design process, production process and procurement is very efficient and also agile. Each of the process included in the overall operations management process is been discussed below one after the other. Zara has a huge number of faculties and a huge infrastructure. The company reaches to its target market and the customers by

Cases in Financial Management Essay Example for Free

Cases in Financial Management Essay Case Synopsis Founded in 1984 Laurentian Bakeries Inc. operates in the industry of manufacturing a vast variety of frozen baked products within their three operating plants in Montreal, Winnipeg and Toronto. The operating plants produce items such as frozen pizza in Winnipeg, MB, pies in Montreal, QC and Cakes in Toronto, ON- with each representing 30%, 30% and 40% of the total revenue stream respectively. The buyers for this company include large institutional clients such domino’s pizza, etc. which have a significantly higher level of power whereas the seller of the products consists of several food producers which have a relatively low level of power. With the cost of setting up a plant of this scale being high, substitute products will also remain high in the market causing the overall profit margin to be low. With the company’s ongoing effort for continuous improvement Danielle Knowles (VP of operations) proposed to expand one of the operating plants in Winnipeg-which was based on the opportunity if the company expanded into the U.S. market. Statement The statement of the problem is how Danielle Knowles will prepare a capital project expenditure proposal to expand the company’s frozen pizza plant in Winnipeg; which is consistent and in line with the company’s capital allocation policy. The proposal should also satisfy the company’s continuous effort for improvement, identification of lost opportunities, satisfaction of HR and environmental impacts and provide sufficient ROI. Situational Analysis The strengths of the company are clearly visible through the company’s effective operations and reputable image in the industry. Being one of the top five in the industry, Laurentian Bakeries has established themselves as a dominant player in the market; however, with a shortage in capacity it can  potentially overpower the strengths due to its negative impact on the company. This includes a decrease in sales and potential decreases in retailer support. Nevertheless, with the acknowledgement of a capacity shortage and an opportunity to expand and grow in the U.S. market the company seems to be in good standing. Moving aside to a different area amongst the competition, all the products are similar which indicate there is heavy competition. The presence of numerous suppliers makes this industry highly competitive, as a result, there is high aggression amongst competitors. This is a leading factor that indicates this is not an attractive business to be in. SWOT ANALYSIS Strengths * Danielle Knowles has experience in the food industry for 13 years. This is a great benefit for the company, because she is able to use her knowledge and experience and apply it for Laurentian Bakeries in order to improve operations or even avoid errors. This in return can potentially save the company from incurring additional expenses. * Danielle has her Master’s in Business Administration which indicates that she is educated and has the credentials to maintain her position as the VP of operations. Also, Danielle is able to use that knowledge and apply it to everyday operations of the company. * Laurentian has above average consideration for human resource and environmental impacts. This benefits the company to the extent that it creates a public awareness which shows their commitment to the community which in return can potentially be used as a marketing tool to attract more sales. * Laurentian company is one of the five large firms that produce frozen foods dominating 21% of the market. This indicates that they are a dominant player in the market and have survived many difficulties from various competitions. * Well established and profitable company which indicates that they have survived one full economic cycle and have withstood their competition. * The company has a diversified revenue stream with three operating plants located in major cities which are not as risky as a single revenue stream. * All three segments are profitable. * Low cost pizza producer which is helping to expand into the US. Market. * Laurentian Bakeries has an integrated workforce such as sales, marketing, etc. for all of their operating plants. Weakness * Shortage of capacity. If this weakness is not dealt with the company can face losses in their sales because of the shortage. This in return lowers the overall profit of the company and can potentially decrease buyers if they cannot meet the demand due to the shortage. * Class 1 products are too risky and by taking such a great risk any wrong doing can have a negative impact on the company. Opportunities * Arrangement to supply large U.S. based grocery chain with private label brand. If the opportunity is taken to its advantage the company can potentially see higher figures in sales and profits. * Since U.S. pizza consumption is 3x bigger than the Canadian segment the overall US market is bigger which can potentially lead to a higher market share. * Within N.A. the economy is recovering modestly and is expected to grow. This indicates that consumer spending on discretionary items such as food products will remain strong. Threats * Inflation is forecasted to remain between 3-5%. This may cause interest rates to rise causing the cost of capital to increase higher than its current level. Capital projects such as expansion may suffer. * North American growth rate of gross domestic product slowed down which may lower the company sales. * Threat of new entrants will increase competition and is always a factor that makes the sales aggressive. * Health Conscious consumers will potentially affect sales due to the products offered by Laurentian Bakeries are considered â€Å"unhealthy.† With on-going health awareness the products offered by Laurentian Bakeries might not meet the changing demand of consumers. Porter’s Five Forces Buyer’s Power * Mixed Power. * There are two types of buyers: large institutional buyers such as  domino’s pizza pizza pizza as well as large retailers. Thousands of smaller clients have less power because of their current low clientele base. Supplier Power * Low Power. * Pizza suppliers distribute production to pizza stores, restaurants and grocery chain stores. Since there are numerous suppliers in the market for ingredients such as cheese, flour, vegetables, etc. they have low power. Barriers to Entrant * High * Due to high capital costs, skilled workforces, environmental regulations, high distribution channels, entry into this industry is high. Threat of Substitute * High * The products offered by Laurentian such as their Pizza can be made at home or even purchased fresh from fast food restaurants. Also they can easily be substituted for other products such as calzone, sandwiches, tacos, etc. Competition * High * There is high competition for the items offered by Laurentian Bakers. Competition for their pizza baked items can easily be substituted through franchised restaurants such as Pizza Pizza, Boston Pizza, Pizza Hut, etc. also competition is high through other companies offering the same goods. In addition, this company is also competing against other food products rather than frozen pizza alone. Financial Analysis Financial Summary: Laurentian Bakeries is seeing a cash increase from $6.2 million in 1993 to almost double its value of $13.1 million in 1995. At the same time long term debt for the company has increased by $7.23 million which indicated that Laurentian Bakeries is funded by its long term debt and has not utilized its cash and therefore has incurred additional interest expenses. Moving over to the sales figures, Laurentian Bakeries has seen an increase of 11% from 1993-95; however, net income is flat which indicates that their COGS and operating expenses have also risen almost at the same pace as sales. This setback has no advantage to the shareholders. Alternatives 1. Continue original plans to continue expansion in Winnipeg. 2. Build a plant in U.S. to cater to that market. 3. Buy an existing plant. 4. Expand the Toronto plant as it is the strongest plant for the company. Recommendations By carefully analyzing all the alternatives, we recommend alternative one as the best fit solution to this company due to it being most practical at the company’s current situation. We strongly believe that continuing original plans to expand in Winnipeg is the beneficial solution for the company as they already produce the same type of products and have the additional land to carry forward the expansion, because this plant is a low cost producer and is ideal to utilize the U.S private label sector. In addition, this alternative is beneficial because it is consistent with the company’s overall objectives. Given the discount rate of 18% and a $5.2 million capital investment the NPV of the expected cash flow is positive. Moreover, recommendation one is the best suited for this company because: * There is land readily available in Winnipeg. This can save the company some money in terms of the expansion because these will incur less of an expense due to Laurentian owning the extra land space. * Building a plant in U.S. will require a lot of capital, additional expenses for hiring, training, etc., and potential change in production, management or other techniques due to different regulations in U.S. * Expanding in Toronto will also require additional capital and additional time to hire and train the workforce to produce the pizza products which aren’t produced in the Toronto facility.

Free Essay on Euthanasia and Physician-Assisted Suicide - Mother Teresa :: Euthanasia Physician Assisted Suicide

Mother Teresa's Little Sisters and Euthanasia In this essay we see Mother Teresa of Calcutta's Little Sisters of the Poor responding to the Europena Parliament's pro-euthanasia measure. In their response is found an insight into death which the Western world lacks. The Little Sisters are knowledgeable from personal experience with the many whom they have seen die. They are also firmly rooted in a strong religious tradition. Both of these considerations make their advice the very best one can hear in the euthanasia debate. "How can the Little Sisters of the Poor, in the service of the elderly, not be concerned about the passing of the principle of euthanasia by a Commission in the European Parliament? We feel that the confusion caused by the text pertaining to the use of extraordinary means to prolong life, palliative care and euthanasia can easily mislead an uninformed public. Yet behind these extremely complicated phrases, the thought is clear: to give doctors the right to satisfy the request for euthanasia, that is to say, to take a person's life. Human dignity does not consist in being able to choose the time of one's death, but in being aware of the fact that one's basic right is the right of respect for life, of respect for human dignity"(Little) The Little Sisters have 150 years of experience in accompanying the elderly up until the end of their lives, and by this experience they are authorized to make known to the public what they have seen and learned. Since their foundation, 17,080 Little Sisters have lived with the dying, and today they are in 30 countries on six continents, with 74 homes in France and Belgium, First World nations. So the dear sisters have expertise with the dying of both the Third World and our world. Making the elderly happy, that is what counts!" Mother Teresa used to say, encouraging the Little Sisters to attain this goal by employing means adapted to each person, to his/her possibilities, tastes, past life, health, etc. Making the elderly happy means believing in the value of their life, and the Little Sisters are witnesses of the extraordinary resources of the elderly. Having a center of interest, doing something they like to do, feeling useful, being able to take initiatives, to communicate, to form friendships, maintaining a facilitated relationship with the family, having contacts with youth: these are factors which provide joy and happiness.

Origin of Narcocorridos

In the book, â€Å"The Handbook of Texas† Dan Dickey writes that in the late 1940’s and 1950’s when â€Å"Tex-Mex† music became commercialized, so did the Music called â€Å"corridos†. Back then it became popular to hear songs about drug smuggling and violence. Music from the genre corridos which was about drugs and drug smuggling was called narcocorrido, which some would say is â€Å"Mexico’s style of gangsta rap†. An excellent example of narcocorrido would be â€Å"El Avion de la Muerte† (The Plane of Death) performed by Los Tigres del Norte, which is arguably one of the most popular corridos bands in history. Los Tigres del Norte have written and performed many songs throughout their career. This famous Mexican band started in 1968 and was made up of three brothers (Jorge, Raul and Hernan Hernandez) and their cousin (Oscar Lara). They started to play their grandparents’ instruments in bars, and like thousands of immigrants they crossed the border to make it in America. Their first hit came in 1970 and was a song about two rival drug dealers. However, in 1972, their song â€Å"Contrabando y Traicion† (â€Å"Contraband and Betrayal†) became a topic of controversy. Not only was it about drug smuggling but how a woman killed a man before he could abandon her. Why would the act of murder committed by a woman spark such controversy? Bataille’s tells us that, â€Å"Such a divinely violent manifestation of violence elevates the victim above the humdrum world where men live out their calculated lives. To the primitive consciousness, death can only be the result of an offence, a failure to obey† (Bataille, 82). Even before Los Tigres del Norte, there was Rosalino â€Å"Chalino† Sanchez, a renegade artist from Sinaloa, a state in the north of Mexico that is well known for its abundant marijuana fields. Hodgson writes, â€Å"When he was 15, Sanchez shot and killed a man who had raped his sister, and fled to California, where for a while he worked as a ‘coyote', smuggling illegal immigrants and drugs across the border. Only when he was arrested, and spent nearly a year in Tijuana prison, did he discover his skill at song writing. He began composing corridos for fellow inmates, and once outside, found his skills in demand from both dealers and legitimate immigrants. † While not the best singer, his incredible lyricism built his reputation quickly. Having earned his street credibility in jail, he soon afterwards was contacted by famous Mexican drug lords who would commission him to write songs about them and their criminal exploits. To shed some light on this fascination with death, we can turn to writer Margaret Atwood in her book Negotiating with the Dead: â€Å"All writing of the narrative kind, and perhaps all writing, is motivated, deep down, by a fear of and a fascination with mortality — by a desire to make the risky trip to the Underworld, and to bring something or someone back from the dead† (157). Chalino, in this way, had a sought-after ability to immortalize the Mexican drug lords. Chalino, himself, portrayed the brave image of the Mexican cowboy. After dealing with the narcotraf icantes, he acquired both powerful friends and enemies. According to an informer that talked to Martin Hodgson, â€Å"The cartels used the group’s music to lay out a code of conduct for its members: ‘Through the corridos comes the philosophy, how the members of the cartel have to behave. If you listen carefully, the songs tell you what they did wrong. You learn what you have to do so they don’t kill you. ’† At the same time, the death drug-lords became heroes through corridos. Some enjoyed their hero status while still alive, but most of them earned it after death. This returns us again to Becker’s introduction to Human Nature and the Heroic in his book The Denial of Death. He explains, â€Å"†¦ [T]he problem of heroics is the central one of human life, †¦ it goes deeper into human nature than anything else because it is based on organismic narcissism and on the child’s need for self-esteem as the condition of human life. Society itself is a codified hero system, which means that society everywhere is a living myth of the significance of human life, a defiant creation of meaning. † Hence, by commissioning corridistas to write about them, narcotraficantes could satisfy that narcissism and become heroes in their own right.

Florence Nightingale Essay

The Polar Area Diagrams of Florence Nightingale If you read the article on Florence Nightingale in â€Å"The Children’s Book of Famous Lives†1 you will not learn that she had to battle with her parents to be allowed to study Mathematics. If you read the Ladybird book â€Å"Florence Nightingale†2 you will not discover that she was the first woman to be elected as a Fellow of the Royal Statistical Society. In looking around for an area of research I was intrigued to discover that Florence Nightingale, who I always thought of as the â€Å"lady with the lamp†, was a competent Mathematician who created her own type of statistical diagram which she used to save thousands of soldiers from needless death. Florence Nightingale headed a group of 38 nurses who went to clean up the hospitals for the British soldiers in the Crimea in 1854. She found that most of the deaths were due to diseases which could be prevented by basic hygiene, such as typhus and cholera. Her improvements were simple but they had an enormous effect: â€Å"She and her nurses washed and bathed the soldiers, laundered their linens, gave them clean beds to lie in, and fed them†3. When she returned to Britain she made a detailed report to the Government setting out what conditions were like and what needed to be done to reduce deaths in the hospitals. Nothing was done, so she tried again, making another statistical report and included in it three new statistical diagrams to make data collated by William Farr more accessible to people who could not get their minds around tables of figures. These were her polar area diagrams or rose diagrams, sometimes also known as ‘coxcombs’. The first showed how many men had died over the two years 1854-5, the second showed what proportions of men had died from wounds in battle, from disease and from other causes, the third showed how the number of deaths had decreased once â€Å"sanitary improvements†4 had been introduced. I decided I would try to recreate the second of these diagrams which is the most complicated and the most shocking. It is called â€Å"Diagram of the causes of mortality in the army in the east†. A copy of it is below: Mathematics SL and HL teacher support material 1 Example 6: Student work Figure 1 The basic ideas are very simple. The blue area represents deaths due to disease, the red area represents death due to wounds in battle and the black area represents death due to other causes. I tried to find a copy of the data which this diagram represented, but I had no luck, so I decided to make sure I understood exactly how the diagram was made and to make my own version of some data which I did have to hand. Once I tried to understand the diagram in detail I found there were some problems. The First Problem I wasn’t sure whether the black area in a shape such as this: was supposed to be this area or this area Mathematics SL and HL teacher support material 2 Example 6: Student work In other words, were the colours separate, or overlapping? The articles I read didn’t make it clear. O’Connor says that â€Å"The area of each coloured wedge, measured from the centre as a common point, is in proportion to the statistic it represents†5, which makes it seem that all colours are wedged shaped, or sectors, so the colours overlap. However, Lienhard commented that in the November 1854 section â€Å"battle deaths take up a very small portion of each slice†6, which makes it sound as though the slice has three separate portions, and Brasseur says that â€Å"she also divided the areas within each of the wedges to show which portion of the mortality data for that month could be allotted to each cause of death†4. I decided to construct polar area diagrams for a set of data with the colours separate and with the colours overlapping to see if putting theory into practice would make it clearer to me. The data I used was taken from the IB grade distribution statistics for the past 15 years at my own institution. I used the numbers taking Higher Mathematics, Standard Mathematics and Mathematical Studies to be represented by my three colours. I took the old Mathematical Methods course to be the same as Standard Mathematics. To fit 15 sectors into the circle I needed each arc to subtend an angle of 2Ï€ radians at 15 1 2Ï€ Ï€ the centre. The area of each sector would then be A = r 2 = 2 where r is the r Ãâ€" 2 15 15 radius of the sector. Since the area needs to be proportional to the statistic, I needed to 15A and just used a scale which would allow me to draw find the radius, so I used r = a reasonable sized diagram. To create a polar area diagram with overlapping sectors I just used this formula on each of the numbers of students taking the various options. Numbers taking Mathematics year on year Numbers (A) Higher Studies Standard 1995 1 24 0 1996 4 15 0 1997 8 10 0 1998 6 31 0 1999 9 17 0 2000 10 20 0 2001 4 31 1 2002 5 21 2 2003 4 15 4 2004 5 29 5 2005 1 28 0 2006 3 16 2 2007 8 13 0 2008 11 29 14 2009 10 23 15 Radius ( r ) Higher Studies Standard 2.2 10.7 0.0 4.4 8.5 0.0 6.2 6.9 0.0 5.4 12.2 0.0 6.6 9.0 0.0 6.9 9.8 0.0 4.4 12.2 2.2 4.9 10.0 3.1 4.4 8.5 4.4 4.9 11.8 4.9 2.2 11.6 0.0 3.8 8.7 3.1 6.2 7.9 0.0 7.2 11.8 8.2 6.9 10.5 8.5 Ï€ Mathematics SL and HL teacher support material 3 Example 6: Student work I then used a geometric program (GeoGebra) to draw the sectors all with a common 2Ï€ centre, each with an angle of radians, and with the radii as given in the table. I drew 15 the Higher sectors first with the Studies on top of these, and the Standard on top of these. This was the result: Figure 2 Polar area diagram to show students taking Mathematics at one school (colours overlapping) Blue represents the number of students taking Higher Maths. Brown represents the number of students taking Mathematical Studies. Green represents the number of students taking Standard Maths. The colours are not solid, so where colours overlap there is a different colour. The blue overlapping the brown makes a pink here, and the green overlapping the blue makes a darker green. In 2003 and in 2004 there were an equal number of students taking Higher and Standard so three separate colours cannot be seen on the diagram. Next I worked out the radii needed if the colours were not to overlap. For this I used cumulative areas to work out the radii. R1 = R3 = 15 ( A1 + A2 + A3) 15 A1 15 ( A1 + A2 ) Ï€ , R2 = Ï€ and Ï€ . Radii R2 10.9 9.5 9.3 13.3 11.1 12.0 12.9 11.1 9.5 12.7 11.8 9.5 10.0 13.8 12.6 Numbers taking Mathematics year on year Numbers (A) Higher (A1) Studies (A2) Standard (A3) 1995 1 24 0 1996 4 15 0 1997 8 10 0 1998 6 31 0 1999 9 17 0 2000 10 20 0 2001 4 31 1 2002 5 21 2 2003 4 15 4 2004 5 29 5 2005 1 28 0 2006 3 16 2 2007 8 13 0 2008 11 29 14 2009 10 23 15 R1 2.2 4.4 6.2 5.4 6.6 6.9 4.4 4.9 4.4 4.9 2.2 3.8 6.2 7.2 6.9 R3 10.9 9.5 9.3 13.3 11.1 12.0 13.1 11.6 10.5 13.6 11.8 10.0 10.0 16.1 15.1 Mathematics SL and HL teacher support material 4 Example 6: Student work This gave a diagram with Higher numbers at the centre and Standard numbers at the edge, like this: Figure 3 Polar area diagram to show students taking Mathematics at one school (colours separate) Blue represents the number of students taking Higher Maths. Brown represents the number of students taking Mathematical Studies. Green represents the number of students taking Standard Maths. This diagram is incomplete in that it has not got the dates on it, but I was interested in the basic shape it would make rather than seeing it as a finished article to represent the data. I decided to do the same thing but with Studies in the middle and Higher at the edge to see how different it would look. Figure 4 Polar area diagram to show students taking Mathematics at one school (colours separate) Blue represents the number of students taking Higher Maths. Brown represents the number of students taking Mathematical Studies. Green represents the number of students taking Standard Maths. This feels very different. The blue section actually looks less significant, to my eye, being put at the edges. This made me think of something else I had read in Brasseur’s article, â€Å"Nightingale arranged these colored areas so that the main cause of death (and the largest sections)—deaths by disease—would be at the end of the wedges and would be more easily noticed.†4 I am sure that Brasseur thought that the colours were separate, and not overlapped. However, comparing my diagrams to Nightingale’s original in Figure 1, I Mathematics SL and HL teacher support material 5 Example 6: Student work became sure that she did mean them to be overlapped. I noticed that in the lefthand rose in figure 1 (representing the second year) there is a wedge with blue at the edge followed by a wedge with blue at the edge: Figure 5 A zoom in of part of figure 1 This can happen in a diagram like my figure 2 of overlapping colours, but would be impossible if the colours are separate as in figures 3 and 4. From this I deduced that the colours on the diagram must be overlapping. The Second Problem My diagrams were unlike Nightingale’s ones in that the total area of the sectors in figure 2 represented the total number of students taking the IB at this school over the 15 years. Nightingale’s statistics were rates of mortality. Basically they can be thought of as percentages of soldiers who died, but, as before, when I read through the articles again, I was unsure what they were percentages of. Gill and Gill have table (Table 2) in their article with headings â€Å"No. of soldiers admitted to the hospital† and â€Å"No. (%) of soldiers who died†3. This might suggest that Nightingale was working with percentages of soldiers who were admitted into hospital. Lewi is more definite and refers to the actual statistic of one wedge of the third of Nightingale’s polar area diagrams as follows: â€Å"The mortality during the first period was 192 per 1,000 hospitalized soldiers (on a yearly basis)†9. However, Brasseur refers to the statistic in a wedge of Nightingale’s first diagram as being â€Å"the ratio of mortality for every 1,000 soldiers per annum in the field†4, in other words a percentage of the army actually on duty. I decided to create a polar area diagram to act as an analogy to the possible situations as follows: Nightingale’s data My data Number of soldiers in the army in a month Number of students taking the IB in a year Number of soldiers taken to hospital Number of students taking Maths Studies Number of soldiers dying of wounds Number of students gaining grade 7 Number of soldiers dyin g of disease Number of students gaining grade 6 Number of soldiers dying for other reasons Number of students gaining grade 5 My analogy of drawing a diagram showing the numbers of soldiers dying as a percentage of those admitted to hospital would then be the number of students gaining a grade above 4 as a percentage of those taking Mathematical Studies. I decided to do this one by hand, partly to prove I could, and partly to see if it would throw any extra light on the construction of the diagrams. Mathematics SL and HL teacher support material 6 Example 6: Student work I gathered the data, found the percentages and used the percentages as A in the usual 15A to find the radii needed to construct the diagram. The data is here: formula r = Ï€ Numbers gaining top three grades in Mathematical Studies As percentage of those taking Studies Radius required for each Taking Total Grade 7 Grade 6 Grade 5 Studies in year % grade 7 % grade 6 % grade 5 R7 R6 R5 1995 7 10 4 24 25 29.16667 41.66667 16.66667 11.80 14.10 8.92 1996 2 9 3 15 19 13.33333 60.00000 20.00000 7.98 16.93 9.77 1997 1 4 2 10 18 10.00000 40.00000 20.00000 6.91 13.82 9.77 1998 5 12 11 31 37 16.12903 38.70968 35.48387 8.78 13.60 13.02 1999 2 6 7 17 26 11.76471 35.29412 41.17647 7.49 12.98 14.02 2000 3 4 7 20 30 15.00000 20.00000 35.00000 8.46 9.77 12.93 2001 3 8 8 31 36 9.67742 25.80645 25.80645 6.80 11.10 11.10 2002 1 8 4 21 28 4.76190 38.09524 19.04762 4.77 13.49 9.54 2003 0 1 8 15 23 0.00000 6.66667 53.33333 0.00 5.64 15.96 2004 3 9 7 29 34 10.34483 31.03448 24.13793 7.03 12.17 10.74 2005 1 11 9 28 29 3.57143 39.28571 32.14286 4.13 13.70 12.39 2006 2 4 5 16 21 12.50000 25.00000 31.25000 7.73 10.93 12.22 2007 1 8 3 13 22 7.69231 61.53846 23.07692 6.06 17.14 10.50 2008 0 3 17 29 54 0.00000 10.34483 58.62069 0.00 7.03 16.73 2009 0 5 5 23 48 0.00000 21.73913 21.73913 0.00 10.19 10.19 And the diagram came out like this: Figure 6 Polar area diagram to show percentages of students taking Mathematical Studies who gained grades above 4 Red represents the number of students gaining grade 7. Blue represents the number of students gaining grade 6. Green represents the number of students gaining grade 5. The purple areas represent coinciding numbers of students gaining grade 5 and 6. Mathematics SL and HL teacher support material 7 Example 6: Student work One thing which I learnt from this exercise is that you have to be very careful about your scale and think through every move before you start if you don’t want to fall off the edge of the paper! It is a far more tense experience drawing a diagram by hand because you know that one slip will make the whole diagram flawed. A computer slip can be corrected before you print out the result. My admiration for Florence Nightingale’s draftsmanship was heightened by doing this. The other thing which drawing by hand brought out was that, if you draw the arcs in in the appropriate colours, the colouring of the sectors sorts itself out. You colour from the arc inwards until you come to another arc or the centre. The only problem came when two arcs of different colours came in exactly the same place. I got around this problem by colouring these areas in a totally different colour and saying so at the side. At this point in my research someone suggested some more possible websites to me, and following these up I found a copy of Nightingale’s second diagram which was clear enough for me to read her notes, and a copy of the original data she used. The first of these was in a letter by Henry Woodbury suggesting that Nightingale got her calculations wrong and the radii represented the statistics rather than the area.7 The letter had a comment posted by Ian Short which led me to an article by him8 giving the data for the second diagram and explaining how it was created. The very clear reproduction of Nightingale’s second diagram in Woodbury’s letter7 shows that Miss Nightingale wrote beside it: â€Å"The areas of the blue, red and black wedges are each measured from the centre as the common vertex†. This makes it quite clear that the colours are overlapped and so solves my first problem. She also wrote â€Å"In October 1854 & April 1855 the black area coincides with the red†. She coloured the first of these in red and the second in black, but just commented on it beside the diagram to make it clear. The article by Short8 was a joy to read, although I could only work out the mathematical equations, which were written out in a way which is strange to me ( for example â€Å"$$ ext{Area of sector B} = frac{pi r_B^2}{3}=3$$†8 ) because I already knew what they were (The example had a sector B in a diagram which I could see had 1 2Ï€ 2 Ï€ 2 = = areaB rB rB ). The two things I found exciting from this article were the 2 3 3 table of data which Nightingale used to create the second diagram, and an explanation of what rates of mortality she used. She described these as follows; â€Å"The ratios of deaths and admissions to Force per 1000 per annum are calculated from the monthly ratios given in Dr. Smith’s Table B†4 and I had not been able to understand the meaning of this from the other articles. (Brasseur adds that â€Å"Dr. Smith was the late director-general of the army.†4). Using Short’s article I was able to work out what it meant. I will use an example of data taken from the table in Short’s article, which is in turn taken from â€Å"A contribution to the sanitary history of the British army during the late war with Russia† by Florence Nightingale of 18598. In February 1855 the average size of the army was 30919. Of these 2120 died of ‘zymotic diseases’, 42 died of ‘wounds & injuries’ and 361 died of ‘all other causes’. This gives a total of 2120 + 42 + 361 = deaths. 2523 2523 Mathematics SL and HL teacher support material 8 Example 6: Student work 2523 81.6003 men died per 1000 men in the army in Ãâ€"1000 = 30919 that month. If the size of the army had stayed at 30919, with no more men being shipped in or out, and the death rate had continued at 81.6 deaths per 1000 men per month over 12 months, the number of deaths per annum would have been 81.6003 Ãâ€"12 = 979.2 per 1000 men in the army. In other words 979.2 deaths per 1000 per annum. out of 30919 means that This understanding of the units used allowed me to finally understand why O’Connor says of the death rate in January 1855, â€Å"if this rate had continued, and troops had not been replaced frequently, then disease alone would have killed the entire British army in the Crimea.†5 The number of deaths due to disease in January 1855 was 2761 and the 2761 average size of the army was 32393. This gives a rate of 1022.8 Ãâ€"1000 Ãâ€"12 = 32393 deaths from disease per 1000 per annum. Another way of looking at it is that if 2761 had dies each month from disease, 2761Ãâ€"12 = 33132 would have died in 12 months, but there were only 32393 in the army! As an aside, I noticed that O’Connor quoted the mortality rate for January 1855 as â€Å"1,023 per 10,000 being from zymotic diseases†5. Another example that we should not trust everything we see in print. Having sorted this out I was ready to attempt my recreation of figure 1. I decided to do the right hand rose only, covering April 1854 to March 1855. The following table shows the data taken from Short’s article in blue and my calculations in black: Average Wounds size of Zymotic & Z/S*1000*12 Radius W/S*1000*12 Radius O/S*1000*12 Radius (Az) (Aw) (Ao) for army diseases injuries Other for for Month (S) (Z) (W) (O) (1 d.p.) Zymtotic (1 d.p.) Wounds (1 d.p.) Other Apr-54 8571 1 0 5 1.4 2.3 0.0 0.0 7.0 5.2 May-54 23333 12 0 9 6.2 4.9 0.0 0.0 4.6 4.2 Jun-54 28333 11 0 6 4.7 4.2 0.0 0.0 2.5 3.1 Jul-54 28722 359 0 23 150.0 23.9 0.0 0.0 9.6 6.1 Aug-54 30246 828 1 30 328.5 35.4 0.4 1.2 11.9 6.7 Sep-54 30290 788 81 70 312.2 34.5 32.1 11.1 27.7 10.3 Oct-54 30643 503 132 128 197.0 27.4 51.7 14.1 50.1 13.8 Nov-54 29736 844 287 106 340.6 36.1 115.8 21.0 42.8 12.8 Dec-54 32779 1725 114 131 631.5 49.1 41.7 12.6 48.0 13.5 Jan-55 32393 2761 83 324 1022.8 62.5 30.7 10.8 120.0 21.4 Feb-55 30919 2120 42 361 822.8 56.1 16.3 7.9 140.1 23.1 Mar-55 30107 1205 32 172 480.3 42.8 12.8 7.0 68.6 16.2 Az is the death rate per 1000 per annum from disease, Aw is the death rate per 1000 per annum from wounds and Ao is the death rate per 1000 per annum from other causes. For 2Ï€ Ï€ this diagram there are 12 divisions so each sector has an angle of = and an area of 12 6 12A 1Ï€ 2 Ï€ 2 . r = r . So for each radius r = Ï€ 26 12 Mathematics SL and HL teacher support material 9 Example 6: Student work I will show my final polar area diagram side by side with Nightingale’s original version: Figure 7. Nightingale’s original â€Å"Diagram of the causes of mortality in the army in the east† and my recreation. I have to admit that I felt rather proud once I had done this! However, looking at the September 1854 wedge I realised that the two diagrams didn’t correspond. In Nightingale’s original diagram I can see that there are more deaths from other causes than from wounds. In my version there are fewer deaths from other causes than from wounds. All other versions of the original in other articles I looked at ( Gill and Gill3, Brasseur4, O’Connor5, Woodbury7, Riddle10, Small11, Lienhard6) are as the original, but the table in Short definitely shows fewer deaths from other causes than from wounds8. Conclusion I started out to try to lean how to recreate the polar area diagram which Florence Nightingale made to communicate to other people just how bad the situation was in army hospitals. This diagram shouts a need for reform. Look at it. The blue represents deaths which could be avoided with a bit of organisation and care. The red represents deaths due to the actual battles. Florence Nightingale had copies of her report containing her diagrams published at her own expense and sent them to doctors, army officers, members of parliament and the Queen. Following her persistent lobbying a commission was set up to improve military barracks and hospitals, sanitary codes were established and procedures were put in place for more organised collection of medical statistics4. It is a very shocking picture with a huge snowball of social change behind it. It has been an exciting adventure to drill down to a real understanding of its construction. Mathematics SL and HL teacher support material 10 Example 6: Student work However, the biggest lesson I have learnt from this research is that you can’t trust what you read. As I have argued in the main text, I am moderately sure that Brasseur thought the colours of the second diagram did not overlap4, I think O’Connor got his death rates wrong for January 18555, and I think Short may have transcribed the data incorrectly for September 18548. According to Brasseur, Florence Nightingale cross checked her data and was systematic about addressing objections to her analysis4. Everyone can make mistakes, and errors can propagate if we just quote what someone else says without looking for corroboration. I have been left with a desire to find out more about this tenacious woman who wouldn’t let society mould her into a genteel wife. Also, if I ever get the chance, I would like to get a look at one of the 2000 copies of â€Å"Notes on Matters Affecting the Health, Effiency and Hospital Administration of the British Army. Founded Chiefly on th e Experience of the Late War† which Florence Nightingale had published in 1858, to see the actual table of data and check the numbers for September 1854. Mathematics SL and HL teacher support material 11 Example 6: Student work References/Bibliography 1.Duthie, Eric ed. The Children’s Book of Famous Lives.Odhams Press Ltd, London 1957 2. Du Garde Peach, L. Florence Nightingale. Wills & Hepworth Ltd, Loughborough, 1959 3. Gill, Christopher J. and Gill, Gillian C. Nightingale in Scutari: Her Legacy Reexamined Center for Internatinal Health, Boston University School of Public Health, Boston, Massachusetts, viewed 26th July 2009 4. Brasseur, Lee, Florence Nightingale’s Visual Rhetoric in the Rose Diagrams. Technical Communication Quarterly, 14(2), 161-182, Lawrence Erlbaum Associates, Inc, 2005, viewed 26th July 2009 5. O’Connor, J.J. and Robertson, E.F., Florence Nightingale. viewed 26 July 2009 6. Lienhard, John H., Nightingale’s Graph, The Engines of Our Ingenuity. 2002 viewed 26th July 2009 7. Woodbury, Henry, Nightingale’s Rose. American Physical SocietyLaunches Dynamic Diagrams Redesign of Physical Review Letters, January 9, 2008, 4:05 pm, filed under Information Design, Visual Explanation View ed 30 July 2009 8. Short, Ian, Mathematics of the Coxcombs. November 5th, 2008 viewed 30th July 2009 9. Lewi, Paul J. Florence Nightingale and Polar Area Diagrams, Speaking of Graphics. 2006 < www.datascope.be/sog/SOG-Chapter5.pdf> viewed 26th July 2009 10. Riddle, Larry, Polar-Area Diagram. 2006 , viewed 26th July 2009 11. Small, Hugh, Florence Nightingale’s statistical diagrams. Presentation to Research Conference organized by the Florence Nightingale Museum St. Thomas’s Hospital, 18th March 1998 viewed 26th July 2009 Mathematics SL and HL teacher support material

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