Anglo-Saxon Warriors and the Klephts of Greece: Their Indo-European Ori

Anglo-Saxon Warriors and the Klephts of Greece: Their Indo-European Origins Anglo-Saxon warrior bands share the same code of honor as the Greek resistance fighters called Klephts both nations having a common Indo-European heritage and concept of hero. Beginning in the fifth century Germanic invasions transformed the Celtic culture of the British Isles. Anglo-Saxon warrior bands conquered the native Celts and prevailed in England from the fifth until the eleventh century. Warfare, the idea of comitatus, and the Germanic heroic code comprised the Anglo-Saxon way of life. Their warrior clans were ruled by a heroic figure, a chieftain or king, and the heroic code valued bravery, boasting, and above all allegiance to their king. Loyalty to the king gave warriors a sense of honor, identity and belonging. In Germania Tacitus writes, They choose their kings for their noble birth, their leaders for their valour. The power even of the kings is not absolute or arbitrary. As for the leaders, it is their example rather than theirauthority that wins them special admiration(7.1). It was their leaders rather than their kings who were the heroic figures whom the warriors could admire and emulate. The Kings were usually "inferior in virtue and courage to the great heroes who serve them" (Oosten, 152). Nevertheless, the Anglo-Saxon heroic code valued allegiance to the king above all else, since he was viewed not only as a protector but also the provider of plenty (Chaney, 90). On the field of battle, that loyalty was transferred to their leader or hero. Tacitus explains that Anglo-Saxon warriors were expected to support their leaders in battle unto death or live a life of infamy. Tacitus, (6.22-3). Since they were forced to struggle co... ...hop. The Divine Liturgy of St John Chrysostom Hymnal. Brookline, Mass: Greek Orthodox Diocese of North and South America, 1977. Oosten, Jarich G. The War of the gods, The Social Code in Indo European Mythology. London: Routledge & Kegan Paul, 1985. Runciman, Steven. The Great Church in Captivity, A Study of the Patriarchate of Constantinople From the Eve of the Turkish Conquest to the Greek War of Independence. Cambridge: Cambridge University Press, 1968. Stover, Leon E. and Kraig, Bruce. Stonehenge, The Indo- European Heritage. Chicago: Nelson-Hall, 1978. Winn, Shan M. M. Heaven, Heroes, and Happiness, The Indo-European Roots of Western Ideology. New York: University Press of America, 1995. Zafiropoulos, Simoni, ed. Greece in Poetry, With Painting Drawings, Photographs, and Other Works of Art. New York: Harry N. Abrahms, Inc., 1993.

Product Life Cycle

Compaq notebooks 1. 0 INTRODUCTION Compaq Computer, based in Houston, Texas, is the world’s largest personal computer manufacturer and the fourth largest information technology (IT) company. From 1992-1997, the company’s aggressive high volume PC strategy propelled it to high growth rates in revenues, while its leadership in PC servers sustained strong margins and drove profit growth. Starting in 1995, former CEO Eckhard Pfieffer began to transform Compaq from a pure PC company to a full-service IT company, with the goal of becoming a $50 billion company that could compete with the likes of IBM and Hewlett-Packard.The key strategic moves were the acquisitions of Tandem Computer and Digital Equipment Corporation in 1997 and 1998, giving Compaq a diverse line of technologies and service capabilities. Compaq began revamping its information systems in 1994, building global enterprise information systems to support its globally optimized manufacturing and order fulfillment o perations. The systems were built primarily around SAP applications, running on Compaq PC servers and the Windows NT operating system in order to demonstrate that large enterprise systems could run on Compaq hardware.Compaq’s IT people were forced to distribute the SAP applications across ten interconnected sites around the world and customize extensively in order to run on Windows NT and meet Compaq’s needs. Compaq stumbled badly in 1998 as it faced new challenges in the PC market and tried to assimilate Tandem and Digital. In particular, Compaq struggled to catch up with Dell Computer, whose direct sales; build-to-order model gave it a big advantage in cost and speed over Compaq’s indirect sales, build-to-forecast approach.When the company disappointed investors with poor results in 1999, the board removed Pfieffer, who had been credited for Compaq’s previously stellar performance. Since Pfieffer’s departure, Compaq has reorganized itself along b usiness lines, streamlined its distribution channels and developed a new electronic commerce strategy called â€Å"NonStop eBusiness. † Compaq has gone through a series of IT reorganizations aimed at giving business units more control over IT decisions and resources. Compaq’s new CEO, Michael Capellas, came to the company in 1998 as CIO and was the force behind this reshaping of the IT organization.It is likely that newly hired CIO Robert V. Napier will continue the process in order to align IT with the new corporate structure, while also working to implement Compaq’s e-business strategies. Since 2007 till now Compaq Company has many products as follow: in 2007 they provide laptop Compaq Presarios to their customer, in 2008 they improve and developed Aero 4/33c Notebooks, and in 2009 they provide new model E500S Notebooks, 2011 EZ2700 Desktops and LT 486/33 Desktops at the same year. 2. 0 Compaq Cash flow The issues of cash flow for each stage of the product lif e cycle they are complete each other.Cash flow for a product as it moves on the life cycle curve will change. It’s very important to know and plan each stage for our product to be success. 2. 1cash flow in the five stages Introduction stage, The introduction of a new product onto the market is typically characterised by very slow sales, which may grow only very slightly over a long period of time. Whilst profits will gradually improve during this stage, it may take until near the completion of the introductory stage in the PLC before the company witness’s positive profitability.The reason for such low profitability during this stage is not so much the limited success of the product – measured in terms of low, albeit growing, sales – but the high costs of production and promotion that are required to try to develop customer awareness. R&D expenses are really high for Compaq in especially in terms of smart laptop, because now Compaq is moving in a new path of technology and there is no resource for them to use in order to reduce the R&D costs.Particularly in case of their new product Compaq Notebooks and Compaq Desktops that is already in introduction stage we can see some spectacular features for the first time about the Desktops. For example one of the new technologies that are used in Compaq Desktops is that it has a high quality and high processor. So we can see clearly that all of these new technologies have a heavy cost for producers. That is the reason that Compaq invests at least 13% of its sales revenue into R&D activities every year. For example Compaq spent $45 million on R&D this year compared to its competitor Dell 25 million. Growing stageThe growth stage in the PLC typically involves a rapid growth in sales as early adopters replace pioneers as the main consumer group. Whilst pioneers are characterized as those consumers who purchase products almost immediately when new products are launched, early adopters wait until t he price starts to fall and some of the product's potential weaknesses are ironed out. Compaq sales steadily increased as the product was promoted and became well known. It maintained growth in sales until 2010 through expanding the original product with new developments of quality, style, speed and price the total of cash flow.Compaq Desktops unit sales in 2009 14. 9 million PCs units and 10 million laptop units. Actually the growth stage for each company is a start point to collect its cash flow by the time, but for Compaq it starts form the first date of the product presentation directly. There are many devices in the market with Compaq product and services, why people prefer Compaq desktop? Quality, brand, price and speed. Maturity stage The maturity stage in the PLC is a key point for a firm because it marks the turning point in the product's success.Typically, the growth in sales decreases quite significantly and manufacturer's over-capacity (that is, larger than required inve ntories) results in a reaction by the firm and its competitors to slash price. In this stage Compaq desktop has a partner and that is Compaq Notebooks and Compaq Presario. This is the best extension strategy for this stage and it is totally clear that Compaq had planned for these year; Compaq development groups knew that they have to present such a powerful product with the capability of presence in two stages at the same time.The total sales units in this year have grown fast for Compaq in 2011 4. 721 thousand units. Declination stage Clearly, at this point, Compaq had to make a key business decision. Sales were falling; the product was in decline and losing its position. Should Compaq let the product ‘die', i. e. withdraw it from the market and give space for their new product. 2. 2 The Degree of Competition Faced by the Product by Applying Porter’s Five Forces of Competitiveness. The degree of competition between the competitors is very high. Successful products attr act other competitor businesses to start selling similar products or service.This indicates the third stage of the life cycle – maturity. This is the time of maximum profitability, when profits can be used to continue to build the brand. However, competitor brands from both Compaq itself (e. g. dell) and other company (e. g. acre) offered the same benefits and this slowed down sales and chipped away at computers market position. Compaq continued to support the development of the brand but some products (such as quality, price and style), struggled in a crowded market. 3. 0 Improving the Company’s Financial PerformanceRecommendations to improve performance will be focused on the product attributes and benefits with the aims to enhance driving experience and build brand personality. 3. 1 Promotion: Sales promotions have a significant effect on the behavior of consumers and trades people. Such promotions can bring in more profits for the manufacturers because they permit price discrimination. 1. Price discrimination: Producers can introduce price discrimination through the use of sales promotions. They can charge different prices to different consumers and trade segments depending on how sensitive each segment is to particular prices.Coupons, special sales events, clearance sales and discounts are examples to explain the phenomenon. 2. Effect on consumer behaviour: as sales promotions are mostly announced for a short period, customers may feel a sense of urgency and stop comparing the alternatives. They are persuaded to act now rather than later. 3. Effect on trade behaviour: Short-term promotions present an opportunity and encourage dealers to forward buy. This forward buying ensures that retailers won’t to go out of stocks. As dealers have more than the normal stocks, they think it advisable to advertise in ocal media, arranged displays and offer attractive promotion deals to consumers. These actions help in increasing the store traffic. 4- Exterior Design Exterior design is the key product attribute that plays an important role in enhancing the overall product brand image. We will look at compaq exterior design in terms of: †¢Shape Many feel that the overall design of compaq is not unique enough. compaq must invest in building its creativity and innovative on it to have own characteristic outlook/shape of product brand image. †¢Color Product color the range offered by compaq generally not attractive or unique.As one of its core values is customer focus, compaq has to focus to be really customer oriented, knowing what the customers want and offer the range of colors that appeal to different market segment effectively. 5- Interior Design Interior design of the laptop refers to its overall instrument panels such as the keyboard, the dash board, the other accessories and special feature in the laptop which is perceived as not stylish. The materials used are also felt as average low quality. Throughout the years , there is not much improvement in this area which can WOW the consumers.In fact, all these features will help to create using experience. Interior design with aesthetic features and good sound protection will make the customer feels joy and excited thus creating a strong positive feeling with the laptop using experience. 3. 2 Length of the Product Life Cycle Be Prolonged Compaq Company has many problems and some customers needs when they solve these problems the length of product life cycle will be longer, from improving their product, quality and price and other needs such as style color etc†¦. Increasing Sales: a promotion can stimulate product sales.Manufacturers commonly reduce the price of a product to induce customers to make a purchase. In the short term this can increase the number of units sold, which can lead to increased market share in the long run if the customer permanently switches from a competitor's brand. 4-Brand Loyalty: sales promotions can also be used to increase brand awareness and loyalty. Clubs or special memberships provide consumers discounts or promotions for continued use. 5-Impulse Sales: Sales promotions can generate impulse sales. A customer may not be aware of a product until she enters a store and sees a sign advertising a sale price.Impulse sales also result from in-store demonstrations. 6- Exterior Design: Exterior design is the key product attribute that plays an important role in enhancing the overall product brand image. We will look at Compaq exterior design in terms of: †¢Shape Many feel that the overall design of Compaq is not unique enough. Compaq must invest in building its creativity and innovative on it to have own characteristic outlook/shape of product brand image. †¢Color Product color the range offered by Compaq generally not attractive or unique.As one of its core values is customer focus, Compaq has to focus to be really customer oriented, knowing what the customers want and offer the range of colors that appeal to different market segment effectively. 4. CONCLUSION Compaq business model has been analyzed in conjunction with the marketing mix that is employed to identify its target Market. They build their brand name with their tagline, Compaq philosophy of low fares is aimed to make computers affordable for everyone. Compaq also aims at making using easy, convenient and fun for its customers.Their services and their pricing work together to identify their target market, however, their promotional activities and their distributional channel is aggressive developed, planned, and executed to target both foreigners and locals alike. Moreover, more advertising model should be developed and Compaq need to identify more suitable areas for distribution as more and more loss potential target could be captured which will at end generate huge revenue for Compaq. Reference Bliss, J. (1998). â€Å"Expense May Thin Ranks Of AAP Plan,† Computer Reseller News, April 13..Business Wire, â€Å"CompuCom ‘Co-Locates’ with Compaq to Increase Manufacturing Efficiency and Reduce Product Delivery Time and Cost,† 7/7/98. Business Wire, â€Å"Compaq Leverages Microsoft Partnership In Aggressive Internal Windows 95 Transition; Global Rollout Will Enhance Customer Support,† 8/15/95. Commercial Times (Taiwan), â€Å"Compaq to Bring Taiwan Partners into Web-based Business System,†. Compaq Annual Report, 1998. Compaq Annual Report, 1999. Compaq Annual Report, 2000. Compaq Annual Report, 2001. Compaq Annual Report, 2002. Compaq Annual Report, 2003. Compaq Annual Report, 2008. CNET News. om, â€Å"Compaq inks deal with PCOrder. com,†, June 29, 1999. Crothers, Brooke, â€Å"Compaq sees shortfall, plans reorg,† CNET News. com, June 17, 1999. Dedrick, Jason and Kenneth L. Kraemer, 1998. Asia’s Computer Challenge: Threat or Opportunity for the United States and the World? New York: Oxford University Press. Hamblen, Matt and Kathleen Ohlson â€Å"Compaq : Reality Sinks In,† ComputerWorld, 6/21/99, Page 30 Hoover’s Online, Compaq profile. Industry Week, â€Å"What's Really Driving Apple's Recovery,† 3/15/99. Jackson, D. ()1998). â€Å"ERP Glitches Disrupt Compaq Order System,† The Australian 10 Nov, p36. Product life cycle The Product Life Cycle is indeed important in marketing since it tells the manufacturers when is the right time to launch a product and how should they launch it.   The cycle is concerned with the changes in the product, price, distribution, and the promotion.   The Product Life Cycle has four phases, the introduction stage, growth, stage, maturity stage, and the decline stage. The introduction stage deals with the launching of the product.   It concerns the product, price, distribution and promotion of the product.   One good example for this is the Nokia N80i.   This phone has a lot of other features that other phones do not have or it has combined features of different phones and it has turned into N80i.   It is a good example because it has just entered the market, and with the latest features, it can only be afforded by those who have extra $500 in their pockets.   It is during this stage that one promotes his product, giving out leaflets or pamphlets, having conferences, and the like.   And I believe that Nokia has done well in this part. Second, comes the growth stage.   This is the time when the company focuses on the growth of the revenue and their product being the preference product of the consumers. During this stage, the company heightens the distribution of the product.   The growth stage is when you improve and make innovations on your product.   One successful example would be the portable DVD players. Portable DVD players have been launched for quite some time now.   Furthermore, everybody is aware that there is this certain product available in the market.   As of now, there is a variety of portable DVD players.   They come in different colors and can play different kinds of file according to the buyers liking.   It is definitely a good example for this stage. The third stage or rather the maturity stage is when the product is at its peak in the market.   This is considered to be the most profitable stage.   This is when price are decreased to have more buyers.   Sales promotion is a must during this stage to maintain market share.   This is also the stage wherein the company aims their product to different from the other substitute products in the market. For instance, personal computers have long been in the market. A lot of computer brands have also arose in the market, like, BenQ, Dell, Apple, and Linux.   They have their own individuality and have their own identity.   Furthermore, the prices of their personal computers have already decreased in comparison with its prices when it was first launched in the market. The last stage would be the decline stage.   This stage is the time to decrease in production and price.   This is when the product is almost obsolete, or there has been a change in the preferences of the consumers.   Here are some ways to deal with the decline stage.   The company may close shop or to fully stop production and sales, continue production at a lower rate while hoping competitors will close or leave the market.   It can also be observed that in this stage, the distribution of the product becomes limited. This is what happened in the traditional cameras which only operate with film.   Only few companies sell this kind of cameras, unlike then, when almost all of the camera manufacturers compete to have the best kind of camera with film.   But then, it has already been replaced by digital cameras that are a lot cheaper in the long run (since there are no costs for photo developing and film), and they also provide an instant preview of the picture and are equipped with different settings for different uses. As of now, cameras that operate with film are cheaper than digital cameras.   Yes, traditional cameras are almost obsolete. It is only available for some photo and camera stores in the country.   And there are almost no promotional offers for this product. As said earlier, products have cycles, that's why they have innovations to remain attractive and profitable in the market. REFERENCES Bool, Hans. (2007).   A Normal Product Cycle-Some Examples. Ezine Articles. http://ezinearticles.com/?A-Normal-Product-Life-Cycle—Some-Examples&id=480455 Komninos, Ioannis. (2002).   Product Life Cycle Management.   Urban and Regional Innovation Research Unit. http://www.urenio.org/tools/en/Product_Life_Cycle_Management.pdf Products-Product Life Cycle. Tutor2u. http://www.tutor2u.net/business/marketing/products_lifecycle.asp The Product Life Cycle.   NetMBA. http://www.netmba.com/marketing/product/lifecycle/ The Product Life Cycle (PLC).   Marketing Teacher.   http://marketingteacher.com/Lessons/lesson_plc.htm ; ;

Assess the Sociological Explanations of the Role of Culture

Assess the sociological explanations of the role of culture in contemporary society Culture is the behaviour, beliefs and characteristics of a particular group of people. Age groups, ethnic groups and social groups etc†¦ are all examples of groups of people that possess their own unique culture. The people within a culture are expected to follow the norms and values that are passed down through generation to generation. Over the past 30 years, different cultures have gradually intermingled due to an increasing number people immigrating to different countries, which each bring their own cultures, be it religious or pop culture etc†¦ This is particular visible in many western countries such as Britain, Canada and the United States, as there is a much higher level of ethnic diversity. The amalgamation of different cultures has also shaped people’s views on things like sexuality, gender roles and age roles etc†¦ Functionalists believe that culture benefits the whole of society. They believe that if everyone in society shares the same beliefs and ideas, i. e. a value consensus is reached, and then society as a whole can be kept in a civilised manner. They also believe that socialisation is a key factor, to shaping culture and society.Primary socialisation is taught by parents who teach children what they expect of them. It also develops their own personal characteristics, beliefs and values, which are largely influenced by their parents and family. Secondary socialisation is taught mainly by teachers in schools. Teenagers and young adults learn what is expected of them in larger society, outside of their home (e. g. what is acceptable and not acceptable based on age or gender etc†¦). Tertiary socialization occurs when individuals are integrated into the world and being to gain new ideas and values of socialization.Emile Durkheim, a French sociologist during the late 19th century and early 20th century, believed that culture is collectively formed and only exists collectively, meaning that culture can only be developed by a group of people and not by an individual. He believed that culture has many relationships with society, including a logical relationship (the idea that power over individuals belongs to certain cultural categories, and beliefs such as God), a functional relationship (the idea that culture creates common beliefs amongst individuals in society, strengthening social order). However, the unctionalist explanations are based on a more traditional society. They are outdated as some ideas do fit todays multi-cultural society. The classical Marxist theory culture as a way of expressing a ruling class ideology. This is where the bourgeoisie control the superstructure of society, the proletariats (working class) creating a false class consciousness, which further creates a false description of reality and the relationships between them and the proletariats. They also believe that culture reinforces the class structure. This means that culture is a way of maintaining the ideas of what each class can achieve.For example, the classical Marxist theory believes that in society, the rich population will always achieve higher than the poorer population, as they can afford to carry on their education to the highest level, whilst the poorer population are sifted out of the educational system at the earliest possible stage. The classical Marxist theory does not take into account the times when the working class rejects their control under the ruling class. This can be in the form of riots, strikes or even a group of people, who are in their own subculture who share the same beliefs about the relationship between the working class and the ruling class (e. . skin heads, punks). Neo-Marxist believes that the working class are being distracted from revolting against the ruling class. One of the most widely adopted forms of neo Marxism is the Frankfurt school. Two of its key members, Theodor Adorno an d Max Horkheimer, came up with the theory of â€Å"the culture industry†. This is the idea that popular culture is like a factory that produces standardized cultural goods (e. g. film, radio, magazines) that are used to manipulate mass society into being content, no matter how poor the quality of their lives are.They believe that mass culture encourages the working class to buy things that are false needs, which leads to a commodity fetishism. This is when capitalism affects the way people interact with each other based on the economic class the belong to. For example, under capitalism, everything that can be exchanged becomes a commodity. Things like labour can become a commodity, by selling your labour to an employer you are commoditizing yourself, and that defines the kind of relationship you and your employer will have.Overall, the neo Marxist theory sees that the population are passive victims of mass culture, who are distracted from the realisation of the quality of the ir lives. Neo-Marxists at the Birmingham University adopted Gramsci’s idea of cultural hegemony. This was an idea thought up by the Italian Marxist Antonia Gramsci, that capitalism would have to face and tolerate oppositional cultures. These are usually sub cultures, particularly within youth culture, that stand against capitalist values.Stuart hall gave the example of the skinhead as an oppositional culture, as he argued that they do not follow the norms and values set in place by capitalism, and resist capitalist views. This theory however is highly theoretical and lacks primary data. Feminists believe that culture is dominated by male ideas. They believe that men control women to serve their own interests, and that women are seen as â€Å"second class citizens†. The idea that females from an early age, are brought up being brainwashed by culture and society into thinking that women cannot strive to achieve high goals like men can.This is visible in the mass media. F or example, in many soap operas and sitcoms, women are portrayed as home makers, cleaners or secretaries, whilst men a portrayed as having high powered jobs. In the 1950’s, all advertisements for thing like kitchen appliances or cleaning products where women orientated, and many T. V commercials for these often saw the male as the breadwinner, returning home from work to his wife. However, this theory is becoming outdated as women in contemporary society are given the same opportunities as men.For example, women now have equal job opportunities as mean, as many of them are entering previously male dominated occupations. The interpretive, interactionist approach or the action theory as it’s more commonly known, is the idea that culture is made up of every bodies individual actions in society. It believes that people’s views and explanations of culture are moulded by the social groups in which they belong to. These interpretations of culture by individuals in soci ety come together to form what is known as the actionist theory. This theory however does not take into account shared beliefs or a value consensus.It also conflicts with the idea that culture cannot be formed by an individual, and can only be formed when there is a group of people. Semiotic culture attempts to define culture as types of symbolic human activity, creation of signs and a way of giving meaning to everything around. In this idea, culture is understood as a system of meaningful symbols, signs words and images. This approach can be adopted by any theorist (e. g. Marxist, feminist) no matter where they stand on the sociological spectrum. Post modernists theories of culture are based around the idea that society is adopting new cultures all the time.This is what is known as cultural diversity. Post-modernists believe that individuals are free to choose and design their own culture and identities. They also may pick up a hybrid culture, which is a mixture of different cultur es that is usually found in countries where there is a large culture diversity. Overall, I think that most of the theories have valid plausibility and evidence, especially Horkeimer’s and Adorno’s neo_marxist theory. However, Theory I find most plausible is the functionalist theory. I find that it has the most supportive evidence out of all the theories.

Golden Ratio in the Human Body

THE GOLDEN RATIO IN THE HUMAN BODY GABRIELLE NAHAS IBDP MATH STUDIES THURSDAY, FEBRUARY 23rd 2012 WORD COUNT: 2,839 INTRODUCTION: The Golden Ratio, also known as The Divine Proportion, The Golden Mean, or Phi, is a constant that can be seen all throughout the mathematical world. This irrational number, Phi (? ) is equal to 1. 618 when rounded. It is described as â€Å"dividing a line in the extreme and mean ratio†. This means that when you divide segments of a line that always have a same quotient. When lines like these are divided, Phi is the quotient: When the black line is 1. 18 (Phi) times larger than the blue line and the blue line is 1. 618 times larger than the red line, you are able to find Phi. What makes Phi such a mathematical phenomenon is how often it can be found in many different places and situations all over the world. It is seen in architecture, nature, Fibonacci numbers, and even more amazingly,the human body. Fibonacci Numbers have proven to be closely rela ted to the Golden Ratio. They are a series of numbers discovered by Leonardo Fibonacci in 1175AD. In the Fibonacci Series, every number is the sum of the two before it.The term number is known as ‘n’. The first term is ‘Un’ so, in order to find the next term in the sequence, the last two Un and Un+1 are added. (Knott). Formula: Un + Un+1 = Un+2 Example: The second term (U2) is 1; the third term (U3) is 2. The fourth term is going to be 1+2, making U3 equal 3. Fibonacci Series: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144†¦ When each term in the Fibonacci Series is divided by the term before it, the quotient is Phi, with the exception of the first 9 terms, which are still very close to equaling Phi. Term (n)| First Term Un| SecondTerm Un+1| Second Term/First Term (Un+1 /Un)| 1| 0| 1| n/a| 2| 1| 1| 1| 3| 1| 2| 2| 4| 2| 3| 1. 5| 5| 3| 5| 1. 667| 6| 5| 8| 1. 6| 7| 8| 13| 1. 625| 8| 13| 21| 1. 615| 9| 21| 34| 1. 619| 10| 34| 55| 1. 618| 11| 55| 89| 1. 618| 12| 89| 144| 1. 618| Lines that follow the Fibonacci Series are found all over the world and are lines that can be divided to find Phi. One interesting place they are found is in the human body. Many examples of Phi can be seen in the hands, face and body. For example, when the length of a person’s forearm is divided by the length of that person’s hand, the quotient is Phi.The distance from a person’s head to their fingertips divided by the distance from that person’s head to their elbows equals Phi. (Jovanovic). Because Phi is found in so many natural places, it is called the Divine ratio. It can be tested in a number of ways, and has been by various scientists and mathematicians. I have chosen to investigate the Phi constant and its appearance in the human body, to find the ratio in different sized people and see if my results match what is expected. The aim of this investigation is to find examples of the number 1. 618 in different people and investiga te other places where Phi is found.Three ratios will be compared. The ratios investigated are the ratio of head to toe and head to fingertips, the ratio of the lowest section of the index finger to the middle section of the index finger, and the ratio of forearm to hand. FIGURE 1 FIGURE 2 FIGURE 3 The first ratio is the white line in the to the light blue line in FIGURE 1 The second ratio is the ratio of the black line to the blue line in FIGURE 2 The third ratio is the ratio of the light blue line to the dark blue line in FIGURE 3 METHOD: DESIGN: Specific body parts of people of different ages and genders were measured in centimeters.Five people were measured and each participant had these parts measured: * Distance from head to foot * Distance from head to fingertips * Length of lowest section of index finger * Length of middle section of index finger * Distance from elbow to fingertips * Distance from wrist to fingertips The ratios were found, to see how close their quotients are to Phi (1. 618). Then the percentage difference was found for each result. PARTICIPANTS: The people were of different ages and genders. For variety, a 4-year-old female, 8-year-old male, 18-year-old female, 18-year-old male and a 45-year-old male were measured.All of the measurements are in this investigation with the ratios found and how close they are to the constant Phi are analyzed. The results were put into tables by each set of measurements and the ratios were found. DATA: | Participant Measurement ( ± 0. 5 cm)| Measurement| 4/female| 8/male| 18/female| 18/male| 45/male| Distance from head to foot| 105. 5| 124. 5| 167| 180| 185| Distance from head to fingertips| 72. 5| 84| 97| 110| 115| Length of lowest section of index finger| 2| 3| 3| 3| 3| Length of middle section of index finger| 1. 2| 2| 2. 5| 2| 2| Distance from elbow to fingertips| 27| 30| 40| 48| 50|Distance from wrist to fingertips| 15| 18. 5| 25| 28| 31| RATIO 1: RATIO OF HEAD TO TOE AND HEAD TO FINGERTIPS Measure ments Participant| Distance from head to foot ( ±0. 5 cm)| Distance from head to fingertips ( ±0. 5 cm)| 4-year-old female| 105. 5| 72. 5| 8-year-old male| 124. 5| 85| 18-year-old female| 167| 97| 18-year-male| 180| 110| 45-year-old male| 185| 115| Ratios: These are the original quotients that were found from the measurements. According to the Golden Ratio, the expected quotients will all equal Phi (1. 618). Distance from head to footDistance from head to fingertips 1. 4-year-old female: 105.  ±0. 5 cm/ 72. 5 ±0. 5 cm = 1. 455  ± 1. 2% 2. 8-year-old male: 124. 5 ±0. 5 cm/ 85 ±0. 5 cm = 1. 465  ± 1. 0% 3. 18-year-old female: 167 ±0. 5 cm/ 97 ±0. 5 cm = 1. 722  ± 5. 2% 4. 18-year-old male: 180 ±0. 5 cm/ 110 ±0. 5 cm = 1. 636  ± 1. 0% 5. 45-year-old male: 185 ±0. 5 cm/ 115 ±0. 5 cm = 1. 609  ± 0. 7% How close each result is to Phi: This shows the difference between the actual quotient, what was measured, and the expected quotient (1. 618). This is foun d by subtracting the actual quotient from Phi and using the absolute value to get the difference so it does not give a negative answer. |1. 18-Actual Quotient|=difference between result and Phi The difference between each quotient and 1. 618: 1. 4-year-old female: |1. 618- 1. 455  ± 1. 2%| = 0. 163  ± 1. 2% 2. 8-year-old male: |1. 618- 1. 465  ± 1. 0%| = 0. 153  ± 1. 0% 3. 18-year-old female: |1. 618- 1. 722  ± 5. 2%| = 0. 1  ± 5. 2% 4. 18-year-old male: |1. 618- 1. 636  ± 1. 0%| = 0. 018 5. 45-year-old male: |1. 618- 1. 609  ± 0. 7%| = 0. 009 Percentage Error: To find how close the results are to the expected value of Phi, percentage error can be used. Percentage error is how close experimental results are to expected results.Percentage error is found by dividing the difference between each quotient and Phi by Phi (1. 618) and multiplying that result by 100. This gives you the difference of the actual quotient to the expected quotient, Phi, in a percentage. (Roberts ) Difference1. 618 x100=Percentage difference between result and Phi 1. 4-year-old female: 0. 163  ± 1. 2%/1. 618 x 100 = 10. 1  ± 0. 12% 2. 8-year-old male: 0. 153  ± 1. 0%/1. 618 x 100 = 9. 46  ± 0. 09% 3. 18-year-old female: 0. 1 ± 5. 2% /1. 618 x 100 = 6. 18  ± 0. 3% 4. 18-year-old male: 0. 018/1. 618 x 100 = 1. 11% 5. 45-year-old male: 0. 009/1. 618 x 100 = 0. 5% AVERAGE: 10. 1  ± 0. 12% + 9. 46  ± 0. 09% + 6. 18  ± 0. 3% + 1. 11% + 0. 55% / 5 = 5. 48  ± 0. 5% ANALYSIS: The highest percentage error, the percent difference between the result and Phi, is 10. 1  ± 0. 12%. This is a small percentage error, and means that all but one of the ratios was more than 90% accurate. This is a good example of the Golden Ratio in the human body because all the values are close to Phi. Also, as the age of the participants increases, the percentage error decreases, so as people get older, the ratio of their head to feet to the ratio of their head to fingertips gets closer to PhiRATIO 2: RATIO OF THE MIDDLE SECTION OF THE INDEX FINGER TO THE BOTTOM SECTION OF THE INDEX FINGER Measurements Participant| Length of lowest section of index finger ( ±0. 5 cm)| Length of middle section of index finger ( ±0. 5 cm)| 4 year old female| 2| 1| 8 year old male| 3| 2| 18 year old female| 3| 2. 5| 18 year male| 3| 2| 35 year old male| 3| 2| Ratios: Length of lowest section of index finger Length of middle section of index finger 1. 4-year-old female: 2  ± 0. 5 cm/ 1  ± 0. 5 cm = 2  ± 75% 2. 8-year-old male: 3  ± 0. 5 cm/ 2  ± 0. 5 cm = 1. 5  ± 42% 3. 18-year-old female: 3  ± 0. 5 cm/ 2.  ± 0. 5 cm = 1. 2  ± 37% 4. 18-year-old male: 3  ± 0. 5 cm/ 2  ± 0. 5 cm = 1. 5  ± 42% 5. 45-year-old male: 3  ± 0. 5 cm/ 2  ± 0. 5 cm = 1. 5  ± 42% How close each result is to Phi: |1. 618-Actual Quotient|=difference between result and Phi The difference between each quotient and 1. 618: 1. 4-year-old female: |1. 618- 2  ± 75%| = 0. 382  ± 75% 2 . 8-year-old male: |1. 618- 1. 5  ± 42%| = 0. 118  ± 42% 3. 18-year-old female: |1. 618- 1. 2  ± 37%| = 0. 418  ± 37% 4. 18-year-old male: |1. 618- 1. 5  ± 42%| = 0. 118  ± 42% 5. 45-year-old male: |1. 618- 1. 5  ± 42%| = 0. 118  ± 42% Percentage Error: Difference1. 18 x100=Percentage difference between result and Phi 1. 4-year-old female: 0. 382  ± 75%/1. 618 x 100 = 23. 6  ± 17. 7% 2. 8-year-old male: 0. 118  ± 42%/1. 618 x 100 = 7. 3  ± 3. 1% 3. 18-year-old female: 0. 418  ± 37%/1. 618 x 100 = 25. 8  ± 9. 5% 4. 18-year-old male: 0. 118  ± 42%/1. 618 x 100 = 7. 3  ± 3. 1% 5. 45-year-old male: 0. 118  ± 42%/1. 618 x 100 = 7. 3  ± 3. 1% AVERAGE: 23. 6 ±17. 7% + 7. 3  ±3. 1% + 25. 8  ±9. 5% + 7. 3  ±3. 1% + 7. 3  ±3. 1%/5= 14. 3  ± 36. 5% ANALYSIS: With this ratio, 3 of the results come out with a

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