Assessment Plan on College Algebra Research Paper

Assessment Plan on College Algebra - Research Paper Example Three categories of learning outcomes are applied in an algebra course. The outcomes are skills, attitude, and knowledge. Knowledge outcome illustrates discipline methods and processes. The students are expected to understand algebraic formulas and expressions, and then apply them to solve mathematical and scientific questions and problems. Students have adequate knowledge through the correct and effective application of the formulas and expressions. The skills outcome illustrates the approaches needed to effectively understand the algebra discipline. An effective algebra course equips the learners with adequate knowledge of skills such as; critical thinking, research, and communication (Boyer, 2011). Critical thinking enables students to analyze mathematical problems, and then illustrate the most appropriate solution for the problem. Research skills enable the student to adequately collect, analyze and present statistical information, during research projects. The communication skil ls of the students are enhanced because the ability to present and share information on statistical issues is enhanced. Attitude outcome addresses the appreciation of the algebra concepts by the students. The students must understand the importance, and the application, of algebra in the society. The algebra concepts are applicable in many work environments, for instance, engineering, and finance. The algebra is also greatly applied in research; for example, quantitative research in projects, and also in marketing research.

De Beers Case Study Example | Topics and Well Written Essays - 2250 words

De Beers - Case Study Example This $400 million employs 760 people, working day and night. De Beers is at present being faced with a quantity of new challenges that are making it essential for us to believe a change in the way that they do business. With new chaos in Western Africa, where illegal diamonds are starting to come from war torn villages, as well as other sources of diamonds are being discovered in Russia as well as Australia, it is obvious that they seriously need to start to move into the U.S. market. Antitrust law permits the imposition of a maximum fine of $10 million, or twice the gain or loss caused by a price-fixing scheme. The indictment does not specify how much the scheme cost purchasers of industrial diamonds. (http://www.nytimes.com/2004/07/10/business/worldbusiness/10diamond.htmlex=1247112000&en=20aa08705cd558b8&ei=5090&partner=rssuserland) A PEST analysis has been performed on the current situation facing De Beers. In the following section, I will focus on the most important problems identified in the PEST analysis for which we must find solutions and also on the most important positive forces that we must leverage to our advantage in order to maintain or gain market share. Please see Exhibit 1 for details on the PEST analysis and additional information on other issues we are facing and forces that might help or hinder our market share in the U.S. The most important of the problems we are faced with are due to Political issues in the United States and elsewhere. Due to war in western Africa, diamonds are beginning to flow from the war torn fields of Sierra Leone and Angola, and in Russia, mines are being controlled locally as opposed to in collaboration with De Beers. These challenges alone pose a threat to the power that De Beers currently holds over the diamond industry. Due to these challenges, we initiated a branding campaign attempting to brand De Beers diamonds to the consumers. This campaign was cantered in the U.S., where "legally, the entire De Beers group - its officers, its operations, its marketing structure - was in violation of the U.S. antitrust law" .This prohibited De Beers from directly selling in the United States. Additionally, a political issue that we need to leverage to our advantage is the U.S. foreign policy towards helping to rebuild Africa. These political issues will be further addressed in the reco mmendations section. Economically, there is an expected surge in diamond sales expected to occur in the U.S. this year. This emphasizes

To What Extent Does the Media Affect Body Image in Teens and Their Perception of Beauty Essay Example for Free

To What Extent Does the Media Affect Body Image in Teens and Their Perception of Beauty Essay There is no question that the Media has a massive impact on how we perceive ourselves, particularly when it comes to our beauty. From my own experience, I have questioned my own body due to articles in magazines promoting a slimmer body type to various audiences. We shape our opinions through what the Media tells us is right and wrong. For instance, women and young girls are judged highly on their weight and appearance where as men are judged more on their masculinity and muscularity. As the Media is a massive topic, I will focus on looking at magazines, in particular adverts, and how they portray beauty and how we then observe the Medias idea of ‘perfection’. I will also be looking at the effects of exposure to these magazines and adverts to teenagers; one particular focus will be the influences of the Media on Anorexia. â€Å"Low self-esteem contributes to a distorted body image, and the distorted body image cant be fully corrected until self-esteem issues are reconciled. If we don’t address the problem (the problem being the Media labelling a certain body type as perfect) then the issue of low self-esteem in women is never going to stop. Over 90% of people diagnosed with eating disorders are adolescent or young women, so why do young women and adolescents feel the need to go to these drastic measures to stay skinny? While the Media is not the only factor that can be contributed to the rise in Anorexia, it is a significant aspect. It’s no surprise that teenagers are obsessed with thinness and weight loss because of the way Media promotes a skinny figure to women through the constant images of celebrities’ bodies and also articles that talk about bettering our lives through our appearance. The Media promotes a skinny figure through constant articles in magazines on celebrities’ figures, for example, Star magazine has shown the same front cover advertising â€Å"45 best worst beach bodies† seven times. I believe that this is going to contribute to women having a negative body image as they constantly compare themselves to the celebrities in these magazines and deciding whether they have an â€Å"acceptable figure† due to the ones advertised as the â€Å"best†. Personally, I think it’s the mix of women’s obsession with celebrities and a low self-esteem that creates a negative body image. Approximately one in every one hundred teenage girls may develop an Eating Disorder. Body dissatisfaction is a reoccurring motif especially in women as they are constantly exposed to celebrities and advertisements from such a young age. I had to create a presentation to my peers based on my topic question earlier this year. I decided that I wanted to get real opinions on whether the content of these magazines were suitable for the magazines target audience. I gave them four popular girl magazines (Bliss, Mizz, Shout and Look), which girls ranging from 10-17+ were reading. I asked them to order the magazines from the lowest target audience to the highest, basing the order solely on the content of the magazines. Surprisingly, my peers put the magazines in the right order. However, they were still shocked by the audiences that these magazines were targeted at because the content of these magazines was not appropriate for children of that age. Bliss magazine, is initially targeted at girls aged 13-17; the class all said that â€Å"It was targeted at 16+ because of the ‘Stone’s style solutions’ that promote platform heels which aren’t appropriate for girls of 13 years. † Furthermore, Bliss magazine shows an article on ‘Pamper perfect’ showing young girls how to get the A-list look ‘without the A-list price tag. My peers decided that Bliss magazine is subtlety influencing young girls on how they can better themselves where as Look magazine, which is targeted at girls from 16-34; manipulate girls into changing their body to better themselves. This shows the diversity between magazines that are targeted at girls below 16 and those targeted at girls above 16. In both Bliss and Look magazine, they use a very slim model to advertise their clothes. Even though Bliss uses a teenage model and Look uses an adult, they both use a particular frame of woman. Mizz magazines’ target audience is from 10-14 years. Mizz’ articles, in my opinion, are suitable for the target audience because they don’t focus on celebrity lifestyle and focusing on a negative body image. Shout magazines’ seems to focus on females between 10-15 years. However, Shout magazine, targeted at females between the ages of 11-14, shows little articles involving models and looks more at celebrities and real life stories. As we live in a society, which is more obsessed with how we look, rather than what we do, it’s no wonder that women are both mentally and physically abused by the Media. This is a gut feeling of mine based on the content of agazines. From my own opinion, I see more articles congratulating celebrities on losing weight rather than their success in their career. How the Media advertises products and articles in magazines have a bigger affect on us than we initially think. On average whilst watching television, women come across around 400 to 600 adverts a day. In light of this, if in only 50% of the adverts we see thin models, then even this could have a negative affect on how we perceive our own body and also how we compare it to what the Media label as â€Å"perfect† which is usually undernourished models. By repetitively using the same figure of model, this will also stay in the sub-conscious mind of the audience. This technique of advertising is called subliminal messaging. When subliminal messages are first seen or heard, we are unable to identify what it is. In fact they may be ignored by the conscious brain and be beyond the level of conscious perception. A new study by Prof. Naomi Mandel, as sited in CBS News, has shown companies that feature normal size women, better known, as â€Å"plus-size† are less effective than those that use thin models. It also found out that overweight and normal-weight females have a lower self-esteem after seeing â€Å"plus-size† models in advertisements. I found these results quite interesting as I presumed that women who saw â€Å"plus-size† models would make them have a higher self-esteem because they have a similar body to the models in the advertisement. Additionally Jeremy Kees, a professor at Villanova University, believes that women expect to see beautiful women in advertisements, even if it makes them feel worse about themselves. In one of his studies, Kees found that even though the women felt bad about themselves after looking at the adverts, they evaluated that the brands were selling higher, and those ads which used average size models, their brands sales has decreased. Although, another source reported that women have lower levels of weight concerns after exposure to average and overweight models than after the exposure to ultra thin and even no models. This could be because women would feel accepted by society for their body size because the Media believes its okay. In my eyes, the Media always promote a very slim figure. Furthermore, a social psychologist’s research has suggested that average sized models are just as effective as thin models. But what do the public really want to see? Karl Langerfield, Head Designer of the Fashion house Chanel, said that: â€Å"the world of fashion was all to do ‘with dreams and illusions, and no one wants to see round women. † After reading both these studies, I decided to create an experiment that was heavily influenced by the experiments that the University of Sussex had conducted on self-discrepancy. One of these experiments was to see if advertisements that use models are more effective than those that don’t use any model. Also, I wanted to see if Prof. Naomi Mandel has the correct theory that advertisements are less effective with ones that use â€Å"plus-size† models or ultra-thin models. Additionally, the experiment that claims women have lower levels of weight concern after exposure to average models wasn’t conducted on teenagers and I wanted to see if teenagers find adverts with â€Å"plus-size† models more or less effective than ultra-thin models. The other experiment that was conducted on children between 5 and 6 years was to see if a specific body image does have an affect on how we perceive ourselves. They had three separate groups of girls who were all told the same story however, one group had images of Barbie, the ultra-thin doll; one group had images of Emme, the average-size doll and one group had no dolls included. Each girl was then told to fill out a self-discrepancy chart and highlighted the body they thought they had compared to the body they would like to have. The results from this showed that the discrepancy was higher in those that saw Barbie compared to the other doll. This shows a link to what heavily influences girls between what they see and their sub-conscious mind. The main objective for my experiment was to see whether adverts that use skinny models are more effective on us as a public, than those that don’t use any type of model and also to explore into the world of subliminal messaging and how it plays on the sub-conscious mind. I wanted to see if this type of advertising really does work. I carried out this experiment twice because I wanted to make sure I had clear and thorough results. I used a group of twenty students between the ages of 14 and 16 of which ten boys and ten were girls. The boys were given adverts targeted at males and the girls were given adverts targeted at females. Half of each gender was given adverts that feature models of the same sex and the other half were given adverts that featured only the products and no models. Each person that had the same booklet was all sat on a table and they would discuss the adverts. As I was walking around, I was listening to what they were asking each other about the adverts shown to them: â€Å"What is your opinion of the advert? What is the focal point for the advert? Whom is this advert targeted at? † I was surprised by the results I got from also the comments I got from both genders. All the girls that had models advertising the perfume in their adverts wanted to lose weight, and out of the 20 girls that took part, 90% overall wanted to lose weight. A lot of the girls described the models as â€Å"plain† and that â€Å"the majority of the models were skinny and blonde. This was a popular opinion with all the girls and I wondered why even though they thought the models looked plain and they weren’t envious of the models, why did all the girls want to lose weight? One girl gave an interesting point that even though Emporio Armani used Beyonce Knowles, who is African-American, to advertise their products; they thought that it was unclear of her skin colour and that they might have used a black and white image so that it would open up to a wider audience. This links back to a previous point that companies always advertise a certain frame of a model to women because this is what they believe as â€Å"perfect. Even though all the girls who didn’t have the models in their adverts had a lower discrepancy, this could be because they might have recognized the adverts from seeing them before or they could genuinely have a low self-esteem. However, what the University of Sussex had discovered was that average size models had no negative affect on body image with women. Even though I had done this experiment on boys too, I decided not to use their results as I felt they didn’t contribute to any of my product. Also, I wanted to focus on teenage girls and their perception of beauty. I was please with how the experiment was carried out and found it was a success with all the participants and the results I received were clear and reliable. However, if I was to carry this experiment out again, then I would do it with adults and also primary school children so then I could compare each set of results with one another and also I would to show how our opinions differ as we mature and also, to show who is more affected by the Medias constant advertise of celebrities and particularly the â€Å"size-0† figure. Also, I wish that I had shown them adverts that used â€Å"plus-size† models to see which one gave them a lower self-discrepancy as this would have been more relevant to the objective of my product. When I first started this topic, I began to realise how much pressure young girls are under to look good through the articles in magazines and the constant need to look at celebrities. After this, I decided that I wanted to find out if young girls and boys are actually affected by this pressure or if it is just my opinion. I created a questionnaire and gave it to secondary pupils between the ages of 11-16. I wanted to keep the questionnaires anonymous because I know these people and it could have influenced the way I interpret their answers. I don’t regret making these questionnaires however I was hoping for more detailed answers. I printed out 100 questionnaires and gave 10 to 10 tutors in my college. I wanted to give them out in tutor because they would have at least half an hour to fill out my questionnaires so they would be able to go into great detail and really think about their answers. However, I had difficulty with my questionnaires and the public doing them. Firstly, I had to print them in black and white to save ink at school; however the images I used were not clear enough in black and white so this could have affected my results. Secondly, when I received the questionnaires, there was minimal detail and also the majority of the participants were pretending to be funny in their questionnaires and didn’t provide the evidence I needed so they were invalid. On the other hand, there were questionnaires that I could use that gave detailed answers. 1% of all the results think the Media are the main cause of having a certain figure however 27% thought their friends pressured them to fit in with everyone else. However, their friends must get this idea of what is acceptable from somewhere. Could this be from the Media? In my appendix, I have included some tables, which include the results from the questionnaires I made. I found the graphs difficult to make, as I wasn’t sure how to break down the categories. Did I do it by year or by gender? The graphs were done on a trial and error basis however I felt like they were done in a correctly in the end. Another study found that 27% of the girls that they carried an experiment out on that felt the Media pressure them to have a perfect body. Even though this shows that other girls in other studies are affected by the Media, it’s not so reliable in my essay as I’m not sure of how many girls were asked, how old they were or where in the world this experiment was carried out. Eating disorders like Anorexia are caused by a physiological disorder within a person and how they view their own body. The sufferer believes that they are overweight so they take extreme actions like dieting, fasting and even starving themselves just so they feel what they believe to be ‘beautiful. ’ There are many reports; mostly around the time of London Fashion Week that fashion models have used this technique. However, it’s not only women in the fashion world who suffer with this disorder, other professions like ballet dancers and athletes show a high number of people who have/had Anorexia. Personality plays a big part in eating disorders. People who suffer with Anorexia Nervosa usually are perfectionists and overachievers’. People who suffer from Anorexia work relentlessly towards a thinner body because they feel that this will promise them beauty, success and happiness. The victims usually want to feel accepted by society however they do not feel valued by others. Anorexia and Bulimia Nervosa are most common in white people in western societies. This shows a direct link to how our society looks at behaviours and expectations of the public compared to eating disorders. Not only in the Western hemisphere is there a link towards the ethnicity of people with eating disorders, a study in Fiji showed a sudden increase in eating disorders among young women since the arrival of television in 1995, (Fearn, 1999). This also shows a strong link between the social and cultural factors. I have seen that there is a number of ways that that the Media can alter teenage girls’ perception of beauty. As I have found, magazines use the same frame of model to promote clothing and will openly slate people’s bodies if they feel they are not â€Å"good enough. Also, magazines will always show articles on how girls and women can change or correct themselves so that they are up to a standard that the Media thinks is acceptable. As humans, it has been known that we always want what we can’ have but is this just apart of our human nature? of this will make girls doubt their own body, even though I found from my own research that girls are not envious of the models in advertisements, they still wanted to lose weight and illustrated they were unhappy with themselves. This was proven through my questionnaires as 79% of the girls admitted to not being happy with their body. Although we as a public may claim to want to see women of a normal size modelling products aimed at us, fashion designers that are in charge decide what we are shown, and this could be where the problem is. Referring back to a point that Karl Langerfield, he claims that â€Å"the world of fashion was all to do ‘with dreams and illusions, and no one wants to see round women†. Even though we may openly say that we want to see designers use curvier bodies to promote their range of clothing or do we as a public secretly see want to see a skinnier frame of model? This links in with a point made earlier about my experiments. Even though all the girls admitted they weren’t jealous of the girls frame, they still wanted a lower discrepancy. So are fashion designers after all giving the public what they can’t admit to wanting? Also, Diane Von Furstenberg claimed that â€Å"To be a model, you have to be skinny. In conclusion, I have found that it’s clear that there are so many different opinions and that it’s hard to identify the general overview to this question without finding exceptions. I feel positive that I have found that the Media can affect teenagers and their perception of beauty but that it varies between person to person as my questionnaires have shown. However, if we are aware of the potential effects, then in theory, we ca n find solutions to these issues; surely that is the most important lesson we can take away from this?

Essay --

There are many drug cartels in the country of Mexico, but one of the most powerful drug trafficking organization in the world being the Sinaloa Cartel. A drug trafficking, money laundering, and organized crime group that still remains the strongest in the country and has the largest presence nationwide. It was founded in 1989 in the city of Culiacan, Sinaloa. The youngest city just up the northwest of Mexico. Not only is it known as the Sinaloa Cartel, it was also known as La Alianza de Sangre, meaning Blood Alliance. Hector Palma, a drug lord that was in charge of the cartel was arrested in the year of 1995 and passed it on to one of his well known business partner, Joaquin â€Å"El Chapo† Guzman. In that time period, he took leadership and is now currently running it. He is considered to be the second generation of drug smugglers along with many other individuals such as Rafael Quintero, Ernesto Carrillo, and Miguel Gallardo. These second generations were brought to the cartel through connections from family relations, especially Joaquin â€Å"El Chapo† Guzman. The first generation dates b...

Managing Change

In any organization change is something which is inevitable therefore it is the responsibility of the manager of any given organization to ensure that the change is managed effectively.   One major mistake managers do make is that most of their times they tend to impose the change in the organization such that every employee has to abide by it.   The point is, we have to understand that change does occur but employees have to be made to go through the change gradually. Basically a change cannot take place at once; it is something which has to come gradually.   Therefore managers should not assume that once a change is started then every employee is to use the common sense to know that the change is either taking place or has taken place. What is important before change is adopted and incorporated in daily operating procedures of an organization is the individual differences in the organization.   This will help managers improve their leadership styles especially in institutions where democracy prevails.   In any business environment the main aim is to maximize the profit and minimization of losses.   If the change is going to bring positive results then it is as good as a rest. Before any restructuring or change take place in an organization, I believe it is good to understand why the change takes place, where it is from and the target group of people it is to affect.   This is because in problem solving situation, the root cause of the problem has to be identified is when possible solutions are identified.   Individual employees operating in the organization has to be made aware of the change and things explained to them more widely. The following are some of its methods followed in individual change process according to Robert Bacal(nd).   Generally there are three phases that are followed for change to take place.   The first phase is the preparation phase which is subdivided into two stages, namely: the contact and awareness stage. The contact stage is the beginning of change process. It is the sensing or predicting that change is either taking place or has taken place.   It is the preliminary state of change process.   The awareness stage is where an individual in an organization become well informed about the change.   The change is being contemplated in this stage.   The second phase of change is the acceptance phase which is also subdivided into understanding stage and positive perception stage. The understanding stage is where the individual is to conceptualize the subject matter that is analysis of the change.   This helps one to understand its nature and why it occurs. It can only take place when a detailed research has taken place.   The positive perception stage then takes place.   This is where an individual is made to view the change positively for it will help the organization improve the results it produces. Results in this case may be products produced by a company or services provided.   For this to happen change has to be given positive judgment and perception. The last phase in change process is commitment phase, which is further subdivided into four stages namely: the installation, adoption, institutionalization and internalization stage.   The installation stage is very important because it deals with the implementation of the change.   Question like how are people made to accept the change is very important.   A change which is not effectively managed will be rejected. So this becomes a crucial stage when it comes to change process.   Installation has to do with ensuring the change works in the organization and all the resources has to be used. After implementation, the change is then adopted. In the adoption stage, change now becomes something that everyone in organization is used to.   Could be its positive effects has been seen or   it might have added some value to the organization therefore   it is worthy.   The third stage in this phase is the stage of institutionalization.   The change is now taken to have a long history and regarded to be useful to the organization. It is viewed as durable, having some value and therefore it is incorporated into the daily operating procedures of the organization.   The change is made official and unanimously accepted in the running of the organization.   The last stage is the internalization where each individual is suppose to be dedicated to change.   This is because the change now becomes something which has been tested, experimented, tried and trusted by the organization. Any change should be made clear to the whole group of employees in a business organization.   This is when the employees will have faith in their leader.   It is believed that team work is the key element for good results to be obtained.   So dealing with individuals in an organization means the leader/ manager is trying to use divide and rule method and this will demoralize employees.   So for spirit of team work to be maintained things must just be done together and discussed. The change in this case must be known to everybody so that they can react to it before implementing it or else some members will not be comfortable with the change.   Piloting should be done before the actual implementation to judge whether it will bring negative or positive impact to the organization.   The feelings and interest of employees must just be considered because they always work as a team. Sources of information also matters a lot in any organization.   For example rumors spreading will confuse and misdirect the employees.   This normally occurs when information is leaked to a click of individuals.   The information should be made official from the top most person preferably the manager.   Otherwise when it comes to large companies, top most managers tend to use mass media such as television and radio system this is because the information is targeting  Ã‚   a large number of people and very much effective when the information is to be passed very fast. In conclusion effects of change will largely depend on how effective the change was implemented and the managers’ ability to ensure that the employees take the change more positively.   Therefore, he has to know the feelings and interests of employees before change take place.   He also needs to explain in time why the change is necessary. Bibliography Luecke R. (2003) Managing Change and Transition.Havard Business School press Gianna M., Enach & Herbert W. (1998) Embracing and Managing Change in Tourism.Routledge:Taylor&Francis Group publishers Peter E. & Amanda C. (1999) Managing Change: Changing the Role of Top Public Servants. Commonwealth Secretariat publishers. Ingham, G. (2000) Managing Change: A Guide to British Economic Policy.Manchester

Imperfetto Italian Imperfect Tense

â€Å"Every Sunday, when I was a kid, my nonna cooked us a big dinner.† How do you express that sentiment in Italian? It’s something that happened in the past, but since it was something that happened often, you wouldn’t use the present perfect, or il passato prossimo. In this and similar cases, which we’ll discuss throughout this article, you would use the imperfect tense. Lucky for you, this tense, l’imperfetto, is formed by adding the same endings to all three conjugations. The only difference is the typical vowel of the infinitive. What’s more, you should know that the imperfect tense is much more frequently used in Italian than in English. It expresses the English used to and is used to describe actions or conditions that lasted an indefinite time in the past. Its also used to express a habitual action in the past and to describe time, age, and weather in the past. So if you like telling stories, it’s a critical tense to learn. Adverbial Expressions That Are Commonly Used With the Imperfect Tense: a volte - at times, sometimescontinuamente - continuouslygiorno dopo giorno - day in and day outogni tanto - once in awhilesempre - alwaysspesso spesso - again and againtutti i giorni - every day How to Conjugate Regular Verbs in the Imperfect Tense Mangiare - To eat (regular verbs with -are endings) Mangiavo - I ate Mangiavamo - We ate Mangiavi - You ate Mangiavate - You (all) ate Mangiava - He/she/it ate Mangiavano - They ate Finire - To finish (regular verbs with -ire endings) Finivo - I finished Finivamo - We finished Finivi - You finished Finivate - You (all) finished Finiva - He/she/it finished Finivano - They finished Prendere - To take, to get (regular verbs with -ere endings) Prendevo - I took Prendevamo - We took Prendevi - You took Prendevate - You (all) took Prendeva - He/she/it took Prendevano - They took Using Common, Irregular Verbs Essere - To be Ero - I was Eravamo - We were Eri - You were Eravate - You (all) were Era - He/she/it was Erano - They were Fare - To do/to make Facevo - I did Facevamo - We did Facevi - You did Facevate - You (all) did Faceva - He/she/it did Facevano - They did Dire - To say, to tell Dicevo - I said Dicevamo - We said Dicevi - You said Dicevate - You (all) said Diceva - He/she/it said Dicevano - They said Examples Using L’imperfetto: Ogni domenica, quando ero un bambino/a, mia nonna ci preparava una splendida cena.  Every Sunday, when I was a kid, my nonna cooked us a big dinner.Giocavo a calcio ogni pomeriggio.  I played soccer every afternoon.Quando ero piccolo/a, mangiavo la pasta ogni giorno. When I was a kid, I ate pasta every day.La settimana scorsa, era (c’era) un tempo bellissimo!  Last week, it was really beautiful weather!Loro credevano sempre a tutto.  They always believed everything.Volevamo andare in Italia. We wanted to go to Italy.Il cielo era sempre blu.  The sky was always blue.Ogni mattina, prendevo un bel cappuccino e un cornetto vuoto. Every morning, I got a cappuccino and a plain croissant.Nel 2000, avevo quarant’anni.  In 2000, I was forty years old.Mi ricordo quello che diceva sempre mio padre: â€Å"Guarda il ceppo†!  I remember what my dad always used to say: â€Å"Take a look at the log†! (figurative the family)

How Is Geometry Used in Architecture

Architecture could be said to begin with geometry. Since earliest times, builders relied on imitating natural forms—like the circular Stonehenge in Britain—and then applied mathematical principles to standardize and replicate the forms. The Beginnings The Greek mathematician Euclid of Alexandria is considered the first to write down all the rules related to geometry in 300 BCE. Later, in about 20 BCE, the ancient Roman architect Marcus Vitruvius penned more rules in his De Architectura, or Ten Books on Architecture. Vitruvius is responsible for all the geometry in todays built environment—at least he was the first to write down the proportions for how structures should be constructed. Renaissance Popularity It wasnt until centuries later, during the Renaissance, that interest in Vitruvius became popular. Cesare Cesariano (1475-1543) is considered the first architect to translate Vitruvius work from Latin into Italian in about 1520 CE. Decades earlier, however, the Italian Renaissance artist and architect Leonardo da Vinci (1452-1519) sketched out the Vitruvian Man in his notebook, making da Vincis the iconic image imprinted onto our consciousness. The images of the Vitruvian Man are inspired by the works and writings of Vitruvius. The man portrayed represents the human being. The circles, squares, and ellipses that surround the figures are Vitruvian calculations of mans physical geometry. Vitruvius was the first to write his observations about the human body—that the symmetry of two eyes, two arms, two legs, and two breasts must be an inspiration of the gods. Models of Proportion and Symmetry Vitruvius believed that builders should always use precise ratios when constructing temples. For without symmetry and proportion no temple can have a regular plan, Vitruvius wrote. The symmetry and proportion in design that Vitruvius recommended in  De Architectura were modeled after the human body. Vitruvius observed that all human beings are shaped according to a ratio that is astonishingly precise and uniform. For example, Vitruvius found that the human face equals one-tenth of the total body height. The foot equals one-sixth of the total body height. And so on. Scientists and philosophers later discovered that the same ratio Vitruvius saw in the human body—1 to phi (ÃŽ ¦) or 1.618—exists in every part of nature, from swimming fish to swirling planets. Sometimes called a golden ratio or divine ratio, the Vitruvian divine proportion has been called the building block of all life and the hidden code in architecture. Geometry in Our Environment Sacred geometry, or spiritual geometry, is the belief that numbers and patterns such as the divine ratio have sacred significance. Many mystical and spiritual practices begin with a fundamental belief in sacred geometry. Architects and designers may draw upon concepts of sacred geometry when they choose particular geometric forms to create pleasing, soul-satisfying spaces. The following examples of geometry in the environment frequently influence architectural design. The BodyWhen studied under the microscope, living cells reveal a highly ordered system of shapes and patterns. From the double helix shape of your DNA to the cornea of your eye, every part of your body follows the same predictable patterns. Gardens The jigsaw puzzle of life is made up of recurring shapes and numbers. Leaves, flowers, seeds, and other living things share the same spiral shapes. Pine cones and pineapples, in particular, are composed of mathematical spirals. Honeybees and other insects live structured lives that mimic these patterns. When we create a floral arrangement or walk through a labyrinth we celebrate nature’s innate forms. Stones Nature’s archetypes are reflected in the crystalline forms of gems and stones. Amazingly, the patterns found in your diamond engagement ring may resemble the formation of snowflakes and the shape of your own cells. The practice of stacking stones is a primitive, spiritual activity. The SeaSimilar shapes and numbers are found beneath the sea, from the swirl of a nautilus shell to the movement of the tides. Surface waves themselves are patterned, like waves that pulse through air. Waves have mathematical properties all their own. The HeavensNature’s patterns are echoed in the movement of planets and stars and the cycles of the moon. Perhaps this is why astrology lies at the heart of so many spiritual beliefs. MusicThe vibrations we call sound follow sacred, archetypal patterns. For this reason, you may find that certain sound sequences can stimulate the intellect, inspire creativity, and evoke a deep sense of joy. The Cosmic GridStonehenge, megalithic tombs, and other ancient sites stretch across the globe along underground electromagnetic tracks or ley lines. The energy grid formed by these lines suggests sacred shapes and ratios. TheologyBest-selling author Dan Brown has made a lot of money by using the concepts of sacred geometry to weave a spell-binding tale about conspiracy and early Christianity. Browns books are pure fiction and have been hotly criticized. But even when we dismiss The Da Vinci Code as a tall tale, we cant dismiss the importance of numbers and symbols in religious faith. Concepts of sacred geometry are expressed in the beliefs of Christians, Jews, Hindus, Muslims, and other formal religions. Geometry and Architecture From the pyramids in Egypt to the new World Trade Center tower in New York City, great architecture uses the same essential building blocks as your body and all living things. In addition, the principles of geometry are not confined to great temples and monuments. Geometry shapes all buildings, no matter how humble. Believers say that when we recognize geometric principles and build upon them, we create dwellings that comfort and inspire. Perhaps this is the idea behind the architects conscious use of divine proportion like  Le Corbusier did for the United Nations building.