Japanese Pornographic Animation Essay Example for Free

Japanese Pornographic Animation Essay Susan J. Napier’s â€Å"The Frenzy of Metamorphosis: The Body in Japanese Pornographic Animation† portrays how both female and male bodies are delineated in Japanese vivified erotic entertainment. Napier clarifies how male predominance over ladies is depicted in the distinctive energized films she has refered to, where sexual orientation explicit jobs are generally reestablished toward the finish of each film or arrangement. For instance, the female lead character in the energized film Wicked City is depicted as a superior warrior than the male lead character, however at long last she expect the customary job of maid in-trouble and mother of the youngster that would carry harmony to their city and its equal, the Black World. Napier further features the frequently hazardous and confused delineation of male-female connections in these movies. The dream behind each change a male or female character’s body experiences in the energized film subconsciously outlines hidden social foundations, just as disappointments, of the Japanese. In these movies, the female characters are regularly fabulously proportioned with gigantic bosoms and hips, and little abdomens, while the male characters are comparably incredibly explicitly enriched and licentious. Such portrayals seem to reflect substantial Western impacts. The transformation of female bodies is portrayed by Napier as â€Å"controlled† in that they are fairly intelligent of conventional jobs and observations towards females in Japanese culture. In the interim, the transformation of male bodies is portrayed as a greater amount of â€Å"demonic strength and comic dissatisfaction. † While they are incendiary to the male centric culture of Japan, male bodies are depicted in something contrary to how female bodies are depicted. Male bodies are depicted as either abnormally wicked looking or ludicrously youngster like. Napier keeps up that guys don't generally come out as the prevailing character in Japanese vivified erotic entertainment. I discover this somewhat questionable as most if not the entirety of the models featured in the perusing propose the nearness of a male figure whose job is either to overwhelm the female character or to help it. Socially, Japanese are of control-disapproved and man centric culture where each female is customarily accommodating to a male accomplice. The nearness of a male character, regardless of how funny or satanic as delineated in the film, can be credited to an endeavor to adjust the depiction of forces where the hero is a female; thus, whether the predominant job has a place with the male or female stays dangerous. The nearness of the male help character recommends that female characters can't accomplish incredible control over her foe without him. A case of this is La Blue Girl where the lead character, a female ninja, is bolstered by her male ninja sidekick who is depicted as continually craving her. Napier likewise refers to that male climaxes are delineated far not exactly male dissatisfactions in these movies since climaxes are seen as lost man centric control. Man centric control can likewise be found in the manner that female climaxes are quite often delineated in these movies, whether or not these climaxes are the aftereffect of customary lovemaking or of sexual torment. I find this is a result of socio-social variables given the adjustments in jobs of people in present day Japanese society. The Japanese male self image is by all accounts influenced by this change so much that their disappointment is reflected even in their vivified obscene movies. Consequently, Japanese enlivened erotic entertainment will in general depict female characters as youthful and non-compromising (secondary school young ladies, regularly) while male characters are either cleverly scurrilous (youthful or old voyeurs) or capably evil. A large number of the solid male characters in Japanese energized erotic entertainment are delineated as evil presences, causing them to seem compromising and eventually ground-breaking over the females. Regardless of whether the female lead characters can beat these wicked male opponents toward the finish of the film, these females are as yet depicted as generally defenseless against sexual savagery.

Luxury brands growth in India Essay Example for Free

Extravagance brands development in India Essay Absence of value extravagance space, condition and deficiency of high road or excessively premium shopping centers is a prime purpose behind limited nearness of extravagance marks in India, hence there is a desperate requirement for modernized and devoted extravagance retail territories in secured regions, for example, air terminals, as per an ongoing ASSOCHAM-KPMG joint examination. Setting up stores in high roads influences extravagance retailers productivity because of soaring rental expenses, in addition, high avenues are exceptionally jumbled, swarmed and are unacceptable because of the nonappearance of elite feel that extravagance retail requests, as per an investigation on Challenges featured by extravagance retailers in India, together directed by The Associated Chambers of Commerce and Industry of India (ASSOCHAM) and KPMG. The Indian extravagance showcase developed at a sound pace of 30% to reach $8. 5 billion out of 2013 and is probably going to keep developing at a solid pace of about 20%, and reach $14 billion by 2016 attributable to rising number of rich individuals, developing white collar class, princely youthful shoppers and other related elements. However, India right now appreciates only one-two percent share in the worldwide extravagance advertise yet it is the fifth most appealing business sector for universal retailers. Divided and broadened purchaser base in India is another noteworthy test being looked by extravagance retailers in India as high total assets individual ( HNI) shoppers are difficult to reach, noticed the ASSOCHAM-KPMG study. Extravagance brands need to deliberately structure their development intends to tap request across three classes of HNIs, to be specific the inheritors (customarily rich) who are constant spenders; the expert tip top who are recognizing spenders; a huge portion of business monsters (business visionaries, proprietors of little and medium undertakings) who have the cash however need gratefulness for fine extravagance merchandise as a result of no earlier presentation to such items, it included. There is a requirement for extravagance brands to concentrate on development in the sort and nature of items being offered and progressively receive imaginative showcasing plans to tap quickly advancing buyer social patterns, said Mr D. S. Rawat, secretary general of ASSOCHAM while discharging discoveries of the examination. Extravagance retailers need to design out of the crate advertising techniques and think of items that are customized to suit the impulses and likes of fluctuated Indian clients, said Rawat. Extravagance is not, at this point a superficial point of interest yet is currently a way of life and the worldwide brands need to quick advance and learn approaches to adjust inside the nearby condition with the goal that they can get acquainted with subtleties of the market by understanding the social character of Indian shoppers. Absence of approach support is another unmistakable test being looked by extravagance marks in India, noticed the ASSOCHAM-KPMG study. Notwithstanding solid interest energy, Indian extravagance showcase has not been seen as strategies and guidelines well disposed for the extravagance retailers, the report said. Import obligations (20-150 percent) are generally higher and this is considered as a key fear factor among the worldwide players, who may oppose them to outline forceful development plans for India, noticed the examination. Statements, for example, 100% outside direct speculation (FDI) in both single and multi-brand retail requires 30% of nearby sourcing, declared in the changed FDI approach in extravagance retail in November 2013 could be hard for the global extravagance players to conform to. The obligations are complex extending from customs obligation, counter veiling obligation (CVD), exceptional extra expense, instruction cess adding to the general expense, said Rawat. In addition, extravagance retail is additionally influenced by the arrangement of most extreme retail cost as it applies to custom obligations and to falling after the custom duties, subsequently vigorously punishing remote brands pushing their general passage costs by up to 40%. Absence of prepared staff is another all around recognized test confronting Indian extravagance retail industry which requires more noteworthy circumspection and information with respect to a sales rep, further featured the ASSOCHAM-KPMG study. Lack of gifted work for the business is a significant reason for worry as it is hard to cause the neighborhood workforce to comprehend the legacy and inheritance of the brand alongside the particular completions engaged with the assembling procedure, said Rawat. Without these essential ranges of abilities, brands have no choice however to make in their nation of starting point; absence of gifted laborers can likewise be credited to the business work where introduction and relational aptitudes structure an indispensable component for the business. Developing pervasiveness of fake extravagance merchandise and a dim market are additionally hampering the development of the business, noticed the ASSOCHAM-KPMG study. The greater part of these items have a place with portions, for example, attire, scents and frill, which are normally lower ticket things and can be handily positioned in dark channels. Extravagance players in India keep on confronting gracefully side issues, for example, lawful escape clauses relating tointellectual property rights, insufficient intends to screen different developing channels, and a developing number of online gateways, among different variables, the examination included. An aggregate, industry wide exertion is probably going to have an expansive effect in managing the issue as observed in different businesses, for example, movies and music. Mindfulness and joint effort likewise should be worked with specialists, who have encountered significant income lossesâ because of loss of assessments and obligations, on the most proficient method to manage fakes, further recommended the examination to counter the developing threat of fake extravagance items. Restorative estimates should be taken to oust the development of dim extravagance merchandise showcase in India which brings about sizeable income misfortunes for firms, said Rawat, and included that a solid legitimate structure joined with successful system of licensed innovation security would help forestall weakening of brand picture and diminished buyer trust. Measures in type of compelling protected innovation implementation, connecting escape clauses the lawful and legal structure and higher conviction rates can help control the development of phony extravagance items, said Rawat. Data gathered through optional sources, for example, web and neighborhood newspapers†¦

My 21st Birthday

My 21st Birthday This is Anna Ho, reporting live from her transition to being 21 years old. (Sidenote: a fun consequence of having a Halloween birthday is that whenever you go to the doctors office and state your birth date, the nurse/doctor/receptionist says WOW!!! YOURE A HALLOWEEN BABY?? SOS MY (sister/brother/cousin/friend/aunt/nephew/arch nemesis/husband/estranged son-in-law/daughter/stepson). Everyone seems to know one Halloween baby.) 31 October 2013 9:10am My Bed Wake up, open computer. Facebook notifications up the wazoo. 7:13pm My Floor I went out to lunch at a Japanese restaurant with Cam 13. Om nom nom: The staff got wind that it was my birthday, so this arrived after the check: After lunch, I had Pistol PE class. Mike Conti (the instructor, and author of this) gave us a talk on gun safety. After Pistol, I booked it over to Harvard Square, where Davie 12 and I went to an exhibit about using toys to communicate  basic science concepts. The exhibit took up one room, and we were the only people there I liked that, because it felt like I had my own set of toys that I could play with at my leisure. Can anyone PLEASE explain to me how this works? Another highlight: More science: And some shenanigans: 2am My Room At around 11:50pm, Sarah 17 knocked on my door to give me a tour of French House (because I need one after living here for three years). She took me to the Maisonette, then back to my room, then to the kitchen, where people were waiting in the dark As I rounded the corner, someone hopped out and stuck a hat on my head. French House sang Joyeux Anniversaire, and dark chocolate lava cake was enjoyed by all. Afterwards, Sophie 14 led me to her room, where the other 2014s were waiting with a bottle of wine. We toasted, and I had a small (LEGAL!) drink. Thank you for all the birthday wishes, everyone! 3 30 October 2013 8:40am The French House kitchen Pre-exam breakfast of champions: a piece of toast, a bowl of chocolate frozen yoghurt, and a banana. 10am 26-100 7.012 (Intro Bio) exam. It was long, and thats all I really have to say about it. 11am 4-152 21M.235 (Monteverdi to Mozart) class. We discussed the score of a Bach French suite (No. 5 in G) then listened to the piece. A suite is a collection of dances to listen to, though, not to actually dance to. The No. 5 in G has an allemande, a courante, a sarabande, a gavotte, and a gigue. (Gigue is now one of my favorite French words.) Between each movement, there is a switch in character, and the G major triad is outlined by the first note of each movement. Also, Bach is nothing but contrapuntal. Then, we moved onto a Scarlatti keyboard piece (K. 264 the K number is important because, in my music profs words, I cant tell you how many Sonatas in E there are). For our purposes, this piece represents a shift from the Baroque concept of a keyboard piece (represented by the suite) to a single-movement work. This is the beginning of what we call the sonata form of the late 18th century. Scarlattis piece was intended for courtly entertainment; in contrast, Bachs piece was intended for keyboard pedagogy. Finally, we listened to the Sonata in F Major (Prussian 1) by Bachs son Carl Philipp Emanuel (CPE Bach). The so-called Prussian sonatas were all written for Frederick the Great, who CPE worked for. We listened to a clavichord recording of the piece; at the end, the clavichordist (clavichordist?) played a lovely cadenza. Fun fact: CPEs treatise on keyboard playing was one of the first books devored by a young Hayden, while he taught himself to be a composer. 12:35pm A bench at the intersection of Building 1 and the infinite corridor. I bought a box of salmon/avocado sushi, a bottle of mighty mango Naked juice smoothie, and made camp at one of the busiest places on MIT campus. Im LaTeXing the Quantum II professors handwritten course notes, as part of my quantum rehab program. I like working when there are strangers frantically speedwalking past me; its both energing and non-distracting, because I dont know any of these people. 12:45pm Just kidding. My friend Sam 14 appeared, looking for a place to crank out 20 minutes worth of a pset. I offered him the spot next to me, so now I have company :) 12:50pm I lied about being surrounded by strangers. My friend Davie 12 just appeared, also en route to finding a place to pset. While giving me a very energetic hug, his bike helmet clattered to the ground. He actually picked me up during the hug, which is no mean feat; I hope his back is okay. 12:51pm Back to work. 2:43pm 6-120 8.033 lecture! Transcribing what Prof. Fisher is saying right now: In relativity, were going to use the principle of maximal aging. And this goes back to what we were talking about, about different kinds of time. So were sitting here in 6-120, which well call a lab frame, or Frame S. And we can measure the time it takes for an object to go from spacetime coordinates A to B. Thats the time that we would measure using this clock, watching something roll across the floor. Like if a mouse came out. There used to be a rat that lived here and came waddling out a couple of times a few years ago. I think hes dead now. Now if the rat were relativistic, and had a wristwatch on its neck, it would measure a different time. It would measure its wristwatch time. So remember, this is an absolutely cornerstone idea of relativity: there is something called wristwatch time, proper time, observer time, that is attached to whatever object youre watching move around. And that clock is always at rest with respect to that object. And so our statement of the principle of least time is that this trajectory occurssuch that the wristwatch time from A to B is minimized. 3:01pm Metrics in general relativity are called g. I have a friend whose license plate is GMuNu*that metric refers to flat spacetime. *g^( µ?) 5:26pm The floor of the French House maisonette My sister and her friend and Asra 17 are studying for an 18.701 (Algebra I*) test, with the help of Adam 15. I just got home, after an 45 min-ish Skype chat with an astronomy professor at BU. I had some questions about the astro grad school application process, and he was very helpful. I also passed along my boyfriends message that he gave an excellent talk at the recent DPS conference. *Not the kind of Algebra I youre thinking of. 6:49pm My room This evening, I made a Trader Joes trip and bought the following: a baguette, brie, a bottle of sparkling pink lemonade, and two boxes of strawberries. For a midnight birthday celebration?! you ask. No. I made the Trader Joes run because Im going to spend the next 4-5 hours trying to finish all of my fellowship applications, and I want to make a party out of it. 8:37pm The French House Maisonette I went to put my laundry in the dryer, checked my mail, and found a very sweet birthday card from my grandma. I LOVE YOU GRANDMA! :D 11:25pm The French House Maisonette Cheers, screams, bangs, smoke. The Red Sox just won the World Series, and we have a spectacular view of Fenway Park out the window across the river. Midnight The French House Maisonette I have some very punctual friends. :)

Willy Loman Existentialist Essay - 599 Words

Willy Loman an Existentialist? Can anyone control their life? Is the power of control in human beings hands to make choices and set or know the exact outcome of those choices? Personally, I dont believe that human beings are awarded with such a power as to be able to change any aspect of their lives. The purpose of my essay is to focus on the life of Willy Loman, a protagonist in a play called Death of a Salesman by Arthur Miller. Is Willy Loman an existentialist or he thinks he has no control over his life? According to my own perspective, Willy Loman is and is not an existentialist. In his life, Willy Loman desires to be a wealthy and respectful man. His blueprint of becoming successful in life is what he often says, Be liked†¦show more content†¦The other way in which Willy is an existentialist is that towards the conclusion of the play, Willy thinks of taking a responsibility of his family and therefore doing something that would benefit his entire family. Willy makes a major decision; as a mate r of fact, the biggest and the most significant decision of his life. Willy chooses to finally take control of his life and end it. This time he knows and he’s confident that the outcome of his decision will be in his favor. Ironically, Willy is excited to terminate his life, because that would give his family the twenty thousand dollar insurance that Willy had. Twenty thousand dollars would assist Biff in getting a good start in his career. Willy took control of his life and made a choice that he believes is responsible and helpful to his family, especially to Biff, therefore Willy is an existentialist. Willy Loman was and at the same time was not an existentialist. There could be many point of views whether Willy Loman was or wasn’t an existentialist. This essay demonstrates my view and perspective of Willy Loman. Works Cited existentialist. WordNet ® 3.0. Princeton University. 21 Apr. 2008. Dictionary.com http://dictionary.reference.com/browse/existentialist. Miller, Arthur. Death of a Salesman. New York: The Viking Press,Show MoreRelated Individual Choice and Failure in Arthur Millers Death of a Salesman1553 Words   |  7 Pagesfailures of a system, but from an existentialist point of view, however, the play solely represents the failures of an individual. By looking at the many distasteful characteristics of the societal system embodied by the Lomans family values and dreams, and by then arguing these points from an existentialist point of view, this essay will confirm that the play represents the failures of an individual instead of casting blame on a socially constructed system. Existentialists claim that to live is to beRead MoreNew York : A Cultural Melting Pot, And The American Dream2234 Words   |  9 Pagesaround him, and he fought to bring a realistic and existentialist point of view in the theatre. Though many of his early works failed, All My Sons (1947) was an unprecedented hit. It related the individual’s responsibility to society to advocate the greater good (Rollyson and Sterling 1). Miller’s magnum opus came in the form of Death of a Salesman (1949). The play ran for 742 performances and it still continues to be performed today. Willy Loman, the main character, chases the American Dream, but

An Analysis of Sylvia Plaths Poem, Daddy Essay - 793 Words

An Analysis of Sylvia Plaths Poem, Daddy Sylvia Plaths famous poem Daddy seems to refer quite consistently to her deceased father (and obliquely to her then estranged husband Ted Hughes) by use of many references that can clearly be associated with the background of Otto Plath, emphasizing his German heritage. These include the Polish town where Otto was born, the atrocities of the German Nazis in the Second World War (Dachau, Auschwitz, Belsen), the Luftwaffe, and even the professorial pose of Dr. Plath at the blackboard . . . / In the picture I have of you. Yet in the midst of these references to Otto Plaths specifically German origins, lines at the beginning of stanza eight mention distinctly Austrian details:†¦show more content†¦A personal association with Austria seems far more likely for Plaths inclusion of these lines, and indeed a dose and profoundly significant one exists: Plaths mother, Aurelia Schober Plath, was of Austrian descent, both of her parents having emigrated from that country (Wagner-Martin 18). Sylvia Plaths complex, emotionally charged relationship with her mother suffuses many of her poems, of course, and repeatedly in works such as Medusa and The Disquieting Muses, and throughout her novel The Bell Jar, Plath reveals her deep antipathy toward her mother--simultaneous with writing effusive, warm, affectionate letters to her Dear Mummy. In Daddy, Plaths use of Austrian references, in this otherwise so father-oriented poem, suggests that an additional focus of her wrath in it--along with Otto Plath and Ted Hughes--was indeed Aurelia. The anger that permeates the poem is so intense and comprehensive that it seems logical to suppose that all the major figures in the poets life--those who had betrayed her or failed her in some way, father, husband, and mother--should be included in it. The otherwise puzzling, seemingly gratuitous references to Austria suggest that, perhaps unconsciously, Plath made sure that every focus of her rage was indeed present in it. Reinforcing this contention is the fact that the Austrian references occur directly between twoShow MoreRelatedEssay on A Womans Struggle 1373 Words   |  6 PagesA Woman’s struggle Analysis The plague of male dominancy and female oppression has spread throughout time and cultures like a pandemic infection, targeting women. Sylvia Plath’s â€Å"Daddy† and Janice Mirikitani’s â€Å"Suicide Note,† show the struggle and pain that oppressive forces perpetrated on women. Although, both speakers are oppressed the way they end the oppression and the cause of it are very different. Patriarchy has always existed, and it affects women all over the world. For example, bannedRead MoreEssay about Sylvia Plath1185 Words   |  5 PagesSylvia Plath This line is from Sylvia Plaths poem Lady Lazarus, one of many that helped make her an icon of modern American poetry. They have an eerie, prophetic quality, seeming to foreshadow the tragic death of this young writer. Understanding Sylvia Plaths words require a closer look at both her life and a few of her works. Though critics have described her writing as governed by negative vitalism, her distinct individuality has made her a conversation piece among those familiarRead MoreBiography of Sylvia Plath1452 Words   |  6 PagesCritical Analysis Sylvia Plath, a great American author, focuses mostly on actual experiences. Plath’s poetry displays feelings and emotions. Plath had the ability to transform everyday happenings into poems or diary entries. Plath had a passion for poetry and her work was valued. She was inspired by novelists and her own skills. Her poetry was also very important to readers and critics. Sylvia Plath’s work shows change throughout her lifetime, relates to feelings and emotions, and focuses on dayRead MoreLiterary Explication: Sylvia Plaths Daddy1201 Words   |  5 Pages Conflicting Emotions of Sylvia Plath The speaker in the poem â€Å"Daddy† is someone who both fiercely hates her father but also passionately loves him. When she was younger, she compared her father to a god-like entity—always looking up to him and constantly seeking his approval. Her fierce hate towards her father stems from the deep rooted fear of him. The speaker is torn between these two polar emotions that have been constantly tormenting her and blames them on her unresolved emotions towardRead MoreHow Sylvia Plaths Life is Reflected in the Poems Daddy, Morning Song, and Lady Lazarus2237 Words   |  9 PagesHow Sylvia Plaths Life is Reflected in the Poems Daddy, Morning Song, and Lady Lazarus Sylvia Plath has had an exciting life, if I can use this word. Her father died from an undiagnosed diabetes when she was eight. At the same time, a short couplet that she wrote was published in the Boston Sunday Herald. Later, she won scholarships to study in Smith, Harvard, and finally Cambridge. There, Plath married Ted Hughes, who was a good poet, too. What amazes me in her lifeRead MoreEssay Analysis of Daddy by Sylvia Plath572 Words   |  3 PagesAnalysis of Daddy by Sylvia Plath Sylvia Plath uses her poem, Daddy, to express deep emotions toward her father’s life and death. With passionate articulation, she verbally turns over her feelings of rage, abandonment, confusion and grief. Though this work is fraught with ambiguity, a reader can infer Plath’s basic story. Her father was apparently a Nazi soldier killed in World War II while she was young. Her statements about not knowing even remotely where he was while he was in battleRead MoreThe Fight For Women s Rights1247 Words   |  5 Pageswomen feel like they are being oppressed by the opposite gender. Sylvia Plath was one of these women who felt like she was oppressed by men and even her own father, who died early in her life. Sylvia Path turned to using imagery in her poem â€Å"Daddy† such as comparing her father and men to ghastly statues, Nazis, and even vampires; meanwhile she compares herself, and to a larger extent all women to the Jews in concentration camps. Plath’s use of imagery relays her feelings of enslavement by men expertlyRead MoreMutilating Self Into Spirit: Sylvia Plaths Poems.4131 Words   |  17 PagesSylvia Plath’s poems: Translation of the self into spirit, after an ordeal of mutilation. Introduction of the poems and the essay: * â€Å"Daddy† Sylvia Plath uses her poem, â€Å"Daddy†, to express intense emotions towards her father’s life and death and her disastrous relationship with her husband. The speaker in this poem is Sylvia Plath who has lost her father at age ten, at a time when she still adored him unconditionally. Then she gradually realizes the oppressing dominance of her father, andRead MorePsychoanalytically Analyzing the Poetry of Sylvia Plath Essay1846 Words   |  8 PagesThe poetry of Sylvia Plath can be interpreted psychoanalytically. Sigmund Freud believed that the majority of all art was a controlled expression of the unconscious. However, this does not mean that the creation of art is effortless; on the contrary it requires a high degree of sophistication. Works of art like dreams have both a manifest content (what is on the surface) and latent content (the true meaning). Both dreams and art use symbolism and metaphor and thus need to be interpreted to understandRead MoreSylvia Plath th e Colossus2027 Words   |  9 PagesColossus by Sylvia Plath as an example of ideology or feminist writing. You may begin by commenting on the different definitions available for ideology in general as well as the theory of feminism. Feminism is discussed in this course as an example of modern theories and is often associated with the issue of ideology. Your discussion should refer to the discussion of these terms as well as the major elements connected to them (e.g. gender, à ©criture feminine, patriarchy, etc.). In your analysis of the

The Debate Over Ap Language and Composition Argument Essay

The Debate Over Ap Language and Composition Argument Essay Doing this will enhance your AP writing. You should be ready to work hard from the beginning. If you can't determine what the question is, return and reread the prompt. The question wasn't merely an invitation to write discursively on the field of photography. The concept that you need to become successful with no assistance from anyone else that is extremely prominent in America is likewise the cause for the significant lack of mental health professionals, with only one professional for every one-thousand individuals(6). Higher education is the point where the real problems lie. By working with different individuals, you are able to learn from one another and request support. As you are learning English, you really have a benefit. The Downside Risk of Ap Language and Composition Argument Essay Furthermore, the interface is slightly clunky. The second point, that making connections is a sort of thinking which can be taught, cannot be proven until the very first point has been sufficiently supported. Work on pacing Sometimes the toughest portion of an AP test really isn't the questions but the time constraints. There are lots of approaches that could be taken to fix an issue so attempt to brainstorm different solutions. Choosing Good Ap Language and Composition Argument Essay Analysis is understood to be the action of breaking something down into its smaller parts to be able to find a better understanding the whole. Ensure you articulate a very clear position in your paper and that you adhere to it from beginning to finish. The body paragraphs are the center of the essay. Then you're given another random piece and you make an effort to put both pieces together. Imagine you receive a random object of metal or a spring. The Hidden Facts About Ap Language and Composition Argument Essay The small note at the conclusion of the prompt about avoiding plot summary is extremely important. Additionally, by arguing for the other side of your opinion, you are going to learn which points you will need to better address in your essay. If you're attempting to refute the argument, you're discover the weakest spots there. Attempt to choose the best devices to back up your argument that you are able to. Choosing Ap Language and Composition Argument Essay Although there are just two short paragraphs, there's a good deal of room for confusion here. Naturally, you also need to remember a conclusion isn't absolutely necessary so as to be given a high score. The fact of the matter is that dishonesty will always be an alternative, even beyond the classroom. The saying ignorance is bliss isn't necessarily always correct. The Chronicles of Ap Language and Composition Argument Essay You will find out more about the subject, and you'll have more vocabulary words to enrich the essay. Nouns may be used as adjectives. Adjectives are utilised to spell out the noun. 2 or more adjectives may be used with each other to describe a noun. You'd probably be better off purchasing a well-reviewed review book with practice tests. To excel in this training course, you require good rhetorical skills particularly for the persuasive essay section. Whenever you do take practice tests, it can be of help to find another person to aid grade your free-response essays dependent on the rubric. FairTest Our tests are based by exactly the same people they benefit. Whatever They Told You About Ap Language and Composition Argument Essay Is Dead Wrong...And Here's Why Instead, you wish to analyze the essay and be ce rtain that your claim is supported. You're able to work on the prompt types that you locate the most difficult or practice outlining essays in a particular period of time, or writing all 3 essays in 120 minutes. Tie every claim you make to a bit of evidence to make sure the very best essay possible. The source material used have to be cited in the essay to be able to be considered legitimate. You should make a strong well-supported analysis instead. There is a particular essay in the prompt that you should analyze. After you memorize all the terms and their uses, you will be ready for the majority of the multiple choice questions and the rhetorical analysis essay. The evidence is a significant portion of your essay.

Considering the life and works of Andy Warhol Essay Example For Students

Considering the life and works of Andy Warhol Essay When considering the life and works of Andy Warhol, one thing is agreed upon: for good or bad, he changed the visual construction of the world we live in. By the time of his death in 1987 he was ranked on the same level with Pablo Picasso and Jackson Pollock as one of the three most important artists of this century. He was a working man, a social climber, a person who liked to build things, an acquirer of goods, and a known homosexual. These attributes all contributed to the interesting and complicated nature of his art. Andrew Warhola, was born August 6, 1928 in Pittsburg. He was the youngest son of Czechoslovakian immigrants. Andrew was born at the time of the Wall Street Crash 1929 and the Great Depression. Like millions of other families, Andrews father could not find work and his early childhood was very difficult and deprived. After several years his familys financial situation improved and he was older he attend a commercial design course at Pittsburghs Carnegie Institute of Technology. Although he was very shy and had a strong fear of failure, he did very well there. In 1949, Andrew Warhola moved to New York. After his first commission to illustrate shoes, Andrew noticed that the final a of his name was omitted in the credits and since decided to call himself Andy Warhol a name that he considered youthful. He quickly became a successful and highly paid commercial artist in the 1950s but desperately wished for fame as a fine artist. He was unsuccessful in his efforts and sold few exhibits. Andrew became depressed and believed that the fine art world had rejected his art as old fashioned and irrelevant. Andy needed new ideas to help boost his creativity. He got several ideas from a woman named Muriel Latow; a gallery owner he knew. She advised him to paint what he loved most like money or what everybody would recognize soup cans and coke bottles. Andy expanded on these ideas and his paintings of the early 60s reflected his progress as a Pop artist. He finally gained the financial success and international fame he had longed for. Although Andy was identified with Pop art and credited with its invention, this is a misunderstanding of his creative ability. Pop is much more complicated than it seems. In creating Pop art, one must create memorable although sometimes unrealistic images and awareness of the unpredictable forces in nature and society in whole. It is not simply the portrayal of popular icons but more of an expression of all that is familiar and accepted American society. Pop art also contains a serious sub-message that is not apparent at first sight. Trewin Copplestone, author of The life and works of Andy Warhol, pointed out that Pop artists were aware of this and exploited it: In Warhols later disaster paintings, for instance, he portrays illths in society, as John Ruskin described it in the 19th century, that is the downside of modern civilization that has to be set against the wealth à ¢Ã¢â€š ¬Ã¢â‚¬Å" the benefits it brings: for example death and injury that the car brings against its obvious advantages. It is this factor of focus, and not the common artifacts used, that give Pop, and particularly the work of Warhol, its significance. 3 During his working career, Andy used several different methods and media for producing his art. He was able to create the same subject in different media and by different methods. Before 1962 he used paint à ¢Ã¢â€š ¬Ã¢â‚¬Å" acrylic or oil à ¢Ã¢â€š ¬Ã¢â‚¬Å" and stencil for his subjects, included the repeated series of images as in Warhols Campbell Soup cans Copplestone 14. After 1962 he used variations of silk-screen process as in Warhols Roll of Bills Copplestone 19. In 1963, Andy began a wide range of disaster works. Under the advice of Henry Geldzahler a friend and art critic, who felt that everything wasnt so fabulous in America and that it was time to reflect that in Andys paintings. .u20418535767b2cad46640371adff774d , .u20418535767b2cad46640371adff774d .postImageUrl , .u20418535767b2cad46640371adff774d .centered-text-area { min-height: 80px; position: relative; } .u20418535767b2cad46640371adff774d , .u20418535767b2cad46640371adff774d:hover , .u20418535767b2cad46640371adff774d:visited , .u20418535767b2cad46640371adff774d:active { border:0!important; } .u20418535767b2cad46640371adff774d .clearfix:after { content: ""; display: table; clear: both; } .u20418535767b2cad46640371adff774d { display: block; transition: background-color 250ms; webkit-transition: background-color 250ms; width: 100%; opacity: 1; transition: opacity 250ms; webkit-transition: opacity 250ms; background-color: #95A5A6; } .u20418535767b2cad46640371adff774d:active , .u20418535767b2cad46640371adff774d:hover { opacity: 1; transition: opacity 250ms; webkit-transition: opacity 250ms; background-color: #2C3E50; } .u20418535767b2cad46640371adff774d .centered-text-area { width: 100%; position: relative ; } .u20418535767b2cad46640371adff774d .ctaText { border-bottom: 0 solid #fff; color: #2980B9; font-size: 16px; font-weight: bold; margin: 0; padding: 0; text-decoration: underline; } .u20418535767b2cad46640371adff774d .postTitle { color: #FFFFFF; font-size: 16px; font-weight: 600; margin: 0; padding: 0; width: 100%; } .u20418535767b2cad46640371adff774d .ctaButton { background-color: #7F8C8D!important; color: #2980B9; border: none; border-radius: 3px; box-shadow: none; font-size: 14px; font-weight: bold; line-height: 26px; moz-border-radius: 3px; text-align: center; text-decoration: none; text-shadow: none; width: 80px; min-height: 80px; background: url(https://artscolumbia.org/wp-content/plugins/intelly-related-posts/assets/images/simple-arrow.png)no-repeat; position: absolute; right: 0; top: 0; } .u20418535767b2cad46640371adff774d:hover .ctaButton { background-color: #34495E!important; } .u20418535767b2cad46640371adff774d .centered-text { display: table; height: 80px; padding-left : 18px; top: 0; } .u20418535767b2cad46640371adff774d .u20418535767b2cad46640371adff774d-content { display: table-cell; margin: 0; padding: 0; padding-right: 108px; position: relative; vertical-align: middle; width: 100%; } .u20418535767b2cad46640371adff774d:after { content: ""; display: block; clear: both; } READ: Essay on The Life of Jeannette in The Glass Castle EssayAndy took his advice and began painting images of death and chaos. His Red Race Riot is a perfect example of art, which depicts human suffering and the anger and fear felt on both sides. This anguish is emphasized by the suggestion of blood in the overall textured red tint. Other disaster works by Andy included various death images from suicides, auto wreckages, war scenes and many other vehicles of death. In 1964, Andy began silk-screening images on wooden boxes. He became well known for his boxed commodities, soapboxes and Brillo pad box sculptures. It was during this time that Geldzhaler, his friend who redirected Andy from soup cans, coke bottles, and celebrities into disaster themes, once again advised Andy to leave disasters and paint flowers. This was big change for Andy who quickly adopted the idea. Warhol and his assistant produced several hundred paintings of flowers in a variety of colors. The first exhibit sold out and the industry continued. Geldzhalers casual idea definitely paid off but it was Andys creative ability to shape this idea into powerful imagery thats behind it all. Dave Hickey writes in Andys Enterprise: Nothing Special Warhol did not change the look of the images we see. He changed the way we look at them, the importance we attach to them, and the similarities we see between them. 93 During the 1970s Andy work moved in a new direction. He began painting images of common people. He painted various subjects from his mother, to the American Indian Russell Means, to the writer Truman Capote Andy admired and was attracted to Capote but the feelings were never returned. Andy created many more paintings of those in his life. He also painted several self-portraits that I find interesting because they are all partly disguised in some way I have been unable to find one clear picture of him. Images of Warhol range from half silhouette blurred portraits to pictures from his earlier years wearing dark sunglasses or even more interesting à ¢Ã¢â€š ¬Ã¢â‚¬Å" an army camouflaged face with the jigsaw like pieces disguising his true form. By 1982, Andy had begun to lose some of his creative energy. His lack of direction was evident during this period through his $9 painting à ¢Ã¢â€š ¬Ã¢â‚¬Å" a work which depicts nine dollar signs in various shades and colors. In the year before his death, Andy made of silk-screened prints of commercial ads with some deviations from the original. It was a kind of return to his original career as a commercial artist, but with the confidence he lacked before. He had indeed crossed the final bridge by turning commerce into art by his belief that anything could be art if he said so.

A Slave Society essays

A Slave Society essays In the beginning, slavery was a very profitable commodity, but it was no more than that. Slavery was no more about human rights than the sugar trade was. It was categorized in trade with gold, iron, ivory and textiles and dismissed just as easily. However, as time passed, morals and ideals changed and communities shaped within the slave population. A new light was shed on the African-American people, a light that would change the way the world would look at them forever. The movement of Africans across the Atlantic to the Americas was the largest forced migration in world history. This brutal chapter in American history began with the Portuguese in the fifteenth century and did not end in the US until 1807. It is estimated that in the four centuries of slave trading, slave ships transported upwards of 10 million Africans to the Americas. Slave trade was by no means limited to the Portuguese though. All the nations of Western Europe participated in trade including the Dutch, Holland and even the English. The actual capturing of the slaves was left up to the Africans themselves though. As one African sold into slavery said, I must own to the shame of my own countrymen. Most Africans were enslaved though warfare in which armies would take hundreds of prisoners. Another method was smaller raids at nightfall, as well as kidnapping. When plantations expanded to the Americas in the eighteenth century, the demand for slaves increased, and the raids extende d deeper into the inner parts of Africa. While the slave trade made Europe and America stronger, it made Africa weaker. In 1700, slaved accounted for only 11 percent of the colonial population. However, during the eighteenth century slavery expanded, and by 1770 Africans in North America numbered 460,000, around 20 percent of the population. The cause of this sudden jolt in slaves brought to North America is the rising demand for certain crops, especially tobacco. Tobacco wa...

Free Essays on Minerals

Many minerals and rocks are valuable resources with direct utility in our everyday lives. We forget that these minerals and rock make our lives easier and more efficient. There are three such rocks and minerals that I can think of that play large roles. Of these rock and minerals the three consist of gold, graphite and coal. These are very important in my life because I use each one everyday and respect the rocks and minerals for their contribution to everyday life. The first mineral that plays a large role in my life as well as everyone else’s life is gold. Gold is a precious metal that is worn for personal appearance. Gold is much more than a metal it is what the world revolves around. Our nations currency is based on what is called the gold standard. Our paper money is based on the hard currency, gold, stored in Fort Knox. The naturally occurring gold-silver alloy is called electrum. Gold occurs, in chemical combination with tellurium, in the minerals calaverite and sylvanite along with silver, and in the mineral nagyagite along with lead, antimony, and sulfur. It occurs with mercury as gold amalgam. It is generally present to a small extent in iron pyrites; galena, the lead sulfide ore that usually contains silver, sometimes also contains appreciable amounts of gold. Gold also occurs in seawater to the extent of 5 to 250 parts by weight to 100 million parts of water. Although the quantity of gold present in seawater is more than 9 billion metric tons, the cost of recovering the gold would be far greater than the value of the gold that could thus be recovered (MSE, 2000). A second mineral that is very commonly used in my life is graphite. Graphite, as most people know, is what is found within pencils that make it possible to write. As a college student I use this mineral almost every day in my classes. Graphite also has other uses; it is used to produce materials such as ski poles and to enhance the strength of other products ... Free Essays on Minerals Free Essays on Minerals Many minerals and rocks are valuable resources with direct utility in our everyday lives. We forget that these minerals and rock make our lives easier and more efficient. There are three such rocks and minerals that I can think of that play large roles. Of these rock and minerals the three consist of gold, graphite and coal. These are very important in my life because I use each one everyday and respect the rocks and minerals for their contribution to everyday life. The first mineral that plays a large role in my life as well as everyone else’s life is gold. Gold is a precious metal that is worn for personal appearance. Gold is much more than a metal it is what the world revolves around. Our nations currency is based on what is called the gold standard. Our paper money is based on the hard currency, gold, stored in Fort Knox. The naturally occurring gold-silver alloy is called electrum. Gold occurs, in chemical combination with tellurium, in the minerals calaverite and sylvanite along with silver, and in the mineral nagyagite along with lead, antimony, and sulfur. It occurs with mercury as gold amalgam. It is generally present to a small extent in iron pyrites; galena, the lead sulfide ore that usually contains silver, sometimes also contains appreciable amounts of gold. Gold also occurs in seawater to the extent of 5 to 250 parts by weight to 100 million parts of water. Although the quantity of gold present in seawater is more than 9 billion metric tons, the cost of recovering the gold would be far greater than the value of the gold that could thus be recovered (MSE, 2000). A second mineral that is very commonly used in my life is graphite. Graphite, as most people know, is what is found within pencils that make it possible to write. As a college student I use this mineral almost every day in my classes. Graphite also has other uses; it is used to produce materials such as ski poles and to enhance the strength of other products ...

Capital Budgeting Research Paper Example | Topics and Well Written Essays - 1250 words

Capital Budgeting - Research Paper Example Capital budgeting is a resource allocation process that requires a balance between three factors, which include amount of resources that are to be expended, rate of utilization of those resources, and the time within which the investment starts showing some return in the form of profit. The basic aim of this report is to provide an in-depth understanding of important issues related to capital budgeting. The report also demonstrates the role of capital budgeting in the process of business development. Importance of Capital Budgeting Morgan (2006) states, â€Å"The success of a business depends on the capital budgeting decisions taken by the management†. Capital budgeting is basically a tool to evaluate, analyze, compare, and select the most appropriate project from a list of projects available for investment. Capital budgeting is one of the most important managerial tools, which helps the managers choose among different projects based on cash flows and rates of return. The mana gers choose those projects for investment, which are likely to generate considerable profits for their companies. In an interview with Mr. Darren Sammy, assistant manager finance department of Covrick Business Solutions, Sammy said that capital budgeting, if done properly, not only strengthens the financial position of the investing companies but also plays its role in strengthening the economy of a country as a whole (D. Sammy, personal communication, February 25, 2011). One can know the importance of capital budgeting by the fact that it increases a company’s credibility and profits by assisting the managers in the selection of most suitable investment opportunity for the company. Capital budgeting also helps the companies get considerable benefits from an investment over time, reduce the risks related to capital shortage, and increase the revenues. Three Important Factors There are some factors, which the companies need to consider while creating a capital budget for any s pecific project. Tatum (2011) asserts, â€Å"In order for the capital budgeting for a project to be attractive, the projections have to indicate several factors that will make up the outcome of the project†. Those factors include time needed to recoup the allocated resources, expected generation of revenues from the project, and amount of resources required to sustain the project’s momentum. It is a fact that a company, which recoups all allocated resources within a reasonable amount of time, enjoys more profits from the venture as compared to those companies which are not able to recover their investments in a short time. Capital budgeting for a project is successful if the project continues to generate profits for a long time. The graph of profitability generated from a selected project should continue to rise before leveling out, and this can only happen when the amount of resources required to sustain the project’s momentum are less than the amount of resour ces allocated to the project at the point of launch. Capital Budgeting Process Having discussed the importance of capital budgeting in the businesses and the considerable factors for budgeting, let us have a look at the capital budgeting process. The capital budgeting process helps managers select the most profitable projects from a pool of projects, time the projects’ expenditures, and include the selected projects into a

Service Learning Report Essay Example | Topics and Well Written Essays - 1000 words

Service Learning Report - Essay Example The Saudi Student Organization has been helping other Saudi Arabian students meet each other and help keep the culture alive on campus for the past ten years. We enjoy spending time together as students that represent the Saudi country and culture while spending our time getting an education at Murray in Kentucky and we also enjoy serving others. The sole purpose of our organization is to keep the culture alive on campus. While we are students learning in America, we must be true to our own cultures and upbringings. Not just in culture but in our faith. We mostly offer programs to help Saudi students connect with other Saudi students. The Saudi Student Organization also hosts National Day for Saudi Arabia. The organization that I am involved in invites all students and faculty to take part and learn more about our culture and religion. I have devoted more than 20 hours of my time into helping to guide new students and help them to fit in here at Murray because I remember how important it was to me when I came to campus to keep my culture close to my heart and while I was living in America, I did not want to forget who I was and where I came from. I feel like I owe to other students how others helped me. In regards to the Organization’s Forces for Good Diagnostic Tool, this was completed with high remarks. For Practice 1: Advocate and Serve, there were two questions. The first was, â€Å"My organization advocates for policy reform, in addition to providing direct services,† and Strongly Agree was chosen. For the second question, â€Å"My organization effectively combines service and advocacy, drawing on direct service programs to inform advocacy agendas and vice versa,† it was ranked as an Agree. For the second section, the topic was to Make Markets Work. The two questions were: â€Å"My organization changes the way local, national, or global businesses fundamentally

Priemgetallen

Priemgetallen Voorwoord Het stond vast, ons onderwerp werd priemgetallen. Onze kennis in verband met priemgetallen reikte niet verder dan de getallen die deelbaar zijn door 1 en zichzelf. En we vroegen ons af wat er nog meer over te zeggen valt. Na even te surfen op het internet bleek al snel dat er veel informatie te vinden was. Priemgetallen hebben vele wiskundigen door de geschiedenis geboeid. Zo heb je Euclides, Fermat, Mersenne, Euler. Dit waren stuk voor stuk grote wiskundigen die geboeid waren door priemgetallen en er velen jaren over nagedacht hebben. Het grote voordeel aan een onderzoekscompetentie (OZC) met twee maken, is dat je elk maar de helft moet doen. Maar met als nadeel dat je verschillende afspraken moet maken, het werk eerlijk moet verdelen en samenkomen om alles te overlopen en tot in de details uit te werken. Onze OZC is in vier hoofdstukken ingedeeld. Eerst hebben we het over de geschiedenis van de priemgetallen en over de wiskundigen die er mee bezig waren. Hoe men steeds nieuwe priem getallen blijft vinden zien we in hoofdstuk 2. Hoofdstuk 3 gaat over de eigenschappen van de priemgetallen. Zo hebben we eerst het vermoeden van Goldbach, de belangrijkste stelling bij de priemgetallen. Daarna gaan we het hebben over de soorten priemgetallen en priemgetallen met speciale eigenschappen. Tenslotte gaat hoofdstuk 4 over de toepassingen van priemgetallen, en dit blijkt vrij veel te zijn. We hopen dat het voor u een even interessante en leerrijke ontdekkingsreis door de priemgetallen zal worden als dat het voor ons was. Hoofdstuk 1 De geschiedenis van de priemgetallen Wanneer precies de priemgetallen ontstaan zijn, kan nooit met zekerheid gezegd worden. Het zou kunnen dat de Babylonià «rs de eerste ontdekkers waren. Wel staat vast dat rond 400 voor Christus, Pythagoras de priemgetallen had gedefinieerd als getallen alleen deelbaar door 1 en zichzelf. Daarmee staat hij bekend als de uitvinder van de priemgetallen. In 530 v.C. stichte hij in het zuiden van Italià « een gemeenschap die zich onder andere bezighield met wiskunde. Er was een grote interesse in natuurlijke getallen en hun eigenschappen. Natuurlijke getallen en hun verhoudingen waren volgens de gemeenschap de basis van het leven en het heelal. Dankzij hun grote interesse, ontdekten ze iets bijzonder over bepaalde getallen. Stel een getal voor als een aantal knopen. Je kan dan sommige getallen rangschikken als een rechthoek, zoals het getal 6 (een rechthoek van 2 op 3 knopen). Er zijn getallen die je onmogelijk kan rangschikken als een rechthoek, zoals het getal 5. Er werd zo het verschil gemaakt tussen de rechtlijnige en de rechthoekige getallen. Deze rechtlijnige getallen worden nu priemgetallen genoemd. Rond 300 v.C. kwam Euclides, à ©Ãƒ ©n van de grootste wiskundigen uit de oudheid. Hij schreef een 13-delig werk De Elementen, waarin onder andere een bewijs staat dat er oneindig veel priemgetallen bestaan. Bewijs: Veronderstel dat er een grootste priemgetal pn bestaat. Dan maken we een lijst van alle priemgetallen: 2, 3, 5,,pn. Definieer dan N = 2, 3, 5, , pn. N + 1 is niet deelbaar door 2 want N is dat wel. De rest is 1. N + 1 is niet deelbaar door 3 want N is dat wel. Ook hier is de rest 1. N + 1 is niet deelbaar door 5, 7,,pn. De rest is telkens 1. Als N + 1 niet deelbaar is dan moet N + 1 zelf priem zijn. Als het wel deelbaar is, dan bestaat er een priemgetal p dat N + 1 deelt maar dat niet was opgenomen in de lijst, dus moet dat priemgetal p groter zijn dan pn. Hierdoor is er dus geen grootste priemgetal en zijn de priemgetallen oneindig. In 200 v.C. werd De Zeef van Erastosthenes (zie 2.4.1) beschreven en daarna bleef het een aantal eeuwen stil rond priemgetallen. In de 16de eeuw veronderstelde Pierre Fermat dat 22n- 1 enkel priemgetallen opleverde. Indien n een priemgetal voorstelde. Marin Mersenne dacht hetzelfde over 2n 1. In 1753 toonde Goldbach aan dat geen enkele formule voldoet om alle priemgetallen te definià «ren. Vanaf de 19de eeuw werd er intensief op zoek gegaan naar grote priemgetallen en de mogelijkheden om ze toe te passen in de samenleving. Hoofdstuk 2 Het zoeken naar priemgetallen Welke getallen zijn priem? De definitie: Een priemgetal is een natuurlijk getal dat slechts 2 verschillende delers heeft. Die delers zijn 1 en het getal zelf. In het begin is het simpel. Je kan getallen à ©Ãƒ ©n voor à ©Ãƒ ©n gaan uitproberen. Zijn ze niet deelbaar door een ander getal dan 1 en zichzelf, dan is het een priemgetal. Zo zijn 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97 alle priemgetallen kleiner dan 100. Veel mensen vragen zich af waarom 1 ook niet gewoonweg een priemgetal is. Natuurlijk heeft 1 maar à ©Ãƒ ©n deler en geen twee. Dan waarom is de definitie niet gewoon een natuurlijk getal dat enkel gedeeld kan worden door 1 en zichzelf? Wel hierdoor zou de hoofdstelling van de rekenkunde (Elk natuurlijk getal valt te ontbinden in priemfactoren op juist à ©Ãƒ ©n manier) niet meer gelden. Een natuurlijk getal zou dan op oneindig veel manieren kunnen worden geschreven als een product van priemgetallen. Eà ©n voor à ©Ãƒ ©n de getallen gaan uitproberen om na te gaan of ze priem zijn is na een tijdje toch vrij vervelend. Het zou daarom wel handig zijn een patroon in een lijst van priemgetallen te herkennen. Helaas is er tot op het heden geen enkel goede formule gevonden. Euler, in de 18de eeuw, vond de formule f(x) = x ² + x + 41 en alle f(x) zijn priem. Maar het werkt enkel voor x∈(0 t/m. 39). De principià «le hoofdtheorie De principià «le hoofdtheorie houdt in dat de kans een getal x priem is, ongeveer gelijk is aan 1/ln(x), voor een x groter dan rond de 5000. Als x rond het getal 10000 ligt, dan is de kans dat het priem is ongeveer 1/9. Ligt een getal ergens bij de 1.000.000.000 dan is de kans ongeveer 1/21. Dit betekent dat de priemgetallen zeldzamer worden naarmate we kijken naar grotere getallen. Mersenne-getallen Marin Mersenne onderzocht in het begin van de 17de eeuw ook de priemgetallen en hij probeerde net zoals Fermat een formule op te stellen. Ook hij is er niet in geslaagd, maar hij heeft wel ander belangrijk werk verricht. Hij was de eerste die zich volledig toelegde op de formule Mp = 2p -1, waarin p priem is. Euler had deze formule opgesteld in De Elementen. Deze formule werkt niet altijd. Toch is al jarenlang het grootst bekende priemgetal altijd een Mersenne-priemgetal geweest. Vanaf juni 2009 zijn er 47 Mersenne-priemgetallen bekend. Het grootst bekende priemgetal is 243112609 -1. Het was het eerste bekende priemgetal met meer dan 10 miljoen cijfers! De vlugge testen De zeef van Erastosthenes De zeef van Eratosthenes is de oudste methode voor het vinden van priemgetallen. Ze is ontstaan circa 240 voor Christus. Het werkt heel simpel. Je schrijft bijvoorbeeld alle getallen op van 2 tot en met 120 Dan nemen we het eerste getal, 2, en arceren we alle veelvouden van dit getal, groter dan het getal zelf in het rood. We nemen nu het volgende, nog niet gearceerde getal, 3, en arceren alle veelvouden van 3 in het groen. De veelvouden van 4 zijn reeds gearceerd dus kunnen we deze overslaan. Daarna arceren we alle veelvouden van 5 (blauw), van 7(geel) en van 9 (groen) De resterende getallen arceren we in het paars en dit zijn de priemgetallen van 1 t/m. 120 Met deze methode kan je alle priemgetallen t/m. n achterhalen door alle veelvouden t/m. n te arceren. Dit valt ook te bewijzen: Stel dat de zeef maar van 2 t/m 100 gaat. Stel dan dat er toch een samengesteld getal x ≠¤ 100 nog niet gearceerd is. Omdat x samengesteld is, geldt x = a.b , met a ≠¤ 100 of b ≠¤ 100. (Als a en b beide groter zijn dan 100 , is a.b = x immers groter ( 100) ²=100). x Is dus een veelvoud van een getal kleiner dan 100, Al deze veelvouden hebben we gearceerd. Elk niet gearceerd getal kleiner dan 100 kan dus niet samengesteld zijn, en moet een priemgetal zijn. Het ontbinden in priemfactoren Euclides bewees eveneens in De Elementen dat elk natuurlijk getal te ontbinden valt in priemfactoren op juist à ©Ãƒ ©n manier (als we de volgorde verwaarlozen). Dit wordt ook wel de hoofdstelling van de rekenkunde genoemd. Valt een natuurlijk getal niet te ontbinden in priemfactoren, dan is het getal priem. Bijvoorbeeld met het getal 211. Je kijkt of het deelbaar is door 2,3,5,7,11 en 13. Omdat 17 > 211mag je bij 13 stoppen. Het getal 221 is niet deelbaar door deze 6 priemgetallen, dus is het zelf priem. Deze methode wordt alleen gebruikt voor getallen met maximum 25 cijfers. Fermat In de 17de eeuw stelde Pierre de Fermat dat elk getal van de vorm Fn = 22n+ 1 (met n ∈ N een priemgetal is. Echter in 1732 zei Euler dat dit onzin is. Het werkt enkel voor n = 0 t/m 4. Je hebt enkel 2 proefdelingen nodig om deze factor te vinden. Euler toonde aan dat elke deler van een Fermat-getal Fn met n > 2 de vorm 2n+2.k + 1 heeft. In het geval van F(5) is dat 128.k + 1. De getallen 129, 385 en 513 zijn niet priem dus gaan we 257 en 641 uitproberen, met succes. Waarschijnlijk zijn alleen de eerste 5 Fermat-getallen werkelijk priemgetallen. Fermats kleine stelling daarentegen is van meer nut. Het houdt in als p een priemgetal is, dan geldt voor ieder geheel getal a dat ap = a(mod p) Als het priemgetal p geen deler is van a, dan heeft ap-1/p een rest van 1. Stel dat je een bepaald getal a hebt. Als je een priemgetal p kunt vinden waarvoor ap-1/p niet als rest 1 oplevert, dan is a deelbaar door p en dus samengesteld. Bijvoorbeeld: a=4 en p=5; dan is 1024/5 = 1020 + 4. De rest is 4, dus is het getal 1024 samengesteld en niet priem. Jammer genoeg werkt de stelling niet altijd in de andere richting, maar door deze kleine stelling van Fermat kunnen we al meteen een hele hoop getallen elimineren als priemgetallen. De andere getallen kunnen daarna verder gecontroleerd worden. PRPs De hedendaagse computertests hebben hun snelheid niet alleen te danken aan de snelle hardware, maar veeleer aan de software. Men gaat eerst een aantal waarschijnlijkheidstesten uitvoeren. Ze gaan op zoek naar pseudo-priemen. De getallen die deze testen doorstaan. De simpelste test werkt met de kleine stelling van Fermat. (zie 2.4.3) Het omgekeerde van die stelling is niet altijd geldig. Als voor een gehele a en k geldt dat ak = a(mod k) dan is k niet noodzakelijk een priemgetal. Vroeger was elke k een pseudo-priemgetal. Nu is het alleen nog maar een pseudo-priemgetal als het nog meer testen doorstaat en toch geen priemgetal blijkt te zijn. Een getal k dat in een test slaagt waarin a=2 noemt met een 2-PRP (waarschijnlijk priemgetal, een vertaling van probable prime). Als de test slaagt met a=3 noemt met het een 3-PRP enzovoort. Omdat deze priemtesten veel sneller verlopen dat de exacte controles, gaat men er meerdere na elkaar uitvoeren. Men begint bij a=2, dan a=3 enzoverder. Als een getal k positief test over verschillende testen, dan is het waarschijnlijk dat het ook een priemgetal is. Bijvoorbeeld: Een 2-PRP met k=341. Het blijkt geen priemgetal te zijn want het is deelbaar door 11 en 31. Er zijn 1.091.987.405 priemgetallen kleiner dan 25.000.000.000, maar slechts 21.853 pseudo- 2-PRP priemgetallen. Dus een getal k kleiner dan 25 miljard, die in een 2-PRP-test slaagt, in 99.998% van de gevallen ook werkelijk priem is. En hoe groter k wordt, hoe groter de slaagkans wordt. SPRPs Wanneer k het getal is dat we onderzoeken of het priem is, d oneven is en s positief. Dan is in k 1 = 2s.d , k een sterk waarschijnlijk priemgetal (vertaling van strong probable prime) als aan à ©Ãƒ ©n van de volgende condities voldaan wordt op basis a. ad = 1(mod k) (ad)2r = -1(mod k) waarbij r positief is en r Ook hier zijn alle getallen k > 1 die niet in de test slagen, niet priem. En de getallen die wel slagen kunnen priem zijn. Deze waarden voor k zijn dus niet priem. Zo een SPRP-test is redelijk snel, zeker als het gecombineerd wordt met het zoeken naar de kleinste priemfactoren. Het is aangetoond dat dergelijke testen in 75% van de gevallen priemfactoren oplevert. Op zichzelf is een SPRP-test dus tamelijk zwak, maar als we enkele van deze testen combineren, maken we een krachtige test voor kleine getallen k, die priemheid aantonen. Wat wilt zeggen dat een getal zeker priem is of zeker niet. Bijvoorbeeld: Als k k priem. Als k k priem. Als k k priem. Als k k priem. Als k k priem. Als k k priem. Deze resultaten geven ons een manier om een zeer snelle priemheidstest te maken. We beginnen met het zoeken naar de kleinste priemfactoren, daarna voeren we SPRP-testen uit op basis 2, basis 3, tot wanneer een van de bovenstaande criteria is bereikt. Bijvoorbeeld, als k De klassieke testen Merkwaardig is dat de grootste priemgetallen tot nu toe gevonden, p-1 of p+1, zeer makkelijk te ontbinden zijn. Dit komt omdat dit priemgetallen zijn waarvan het gemakkelijk is om te bewijzen dat ze priem zijn. Bij deze klassieke testen kunnen we aantonen dat een getal priem is. Dit zijn dus geen waarschijnlijkheidstesten, maar bewijzen van de priemheid. Stelling 1 (Lucas-Kraitchik-Lehmer) Lucas heeft op het einde van de 19de eeuw de kleine stelling van Fermat omgevormd tot een praktische test, die later versterkt werd door Kraitchik en Lehmer. Stel n > 1. Als voor iedere priemfactor q van n-1 er een natuurlijke a bestaat zodat an-1 = 1(mod n) a(n-1)/q ≠  1(mod n) dan is n priem. Dit is zowat de basis van alle moderne priemtesten. Stelling 2 (Pocklington) Stelling 1 heeft een volledige ontbinding in priemfactoren nodig van n-1. Pocklington had daar een oplossing voor. Stel n-1 = qkr waar q priem is en r niet deelt. Als er een natuurlijk getal a bestaat zodat an-1 = 1(mod n) en de g.g.d. van(an-1q- 1,n) = 1, dan heeft iedere priemfactor q van n de vorm qkr + 1. Stel dan n-1 = FR, waarbij F > R, g.g.d. (F,R) = 1 en de ontbinding van F gekend is. Als voor iedere priemfactor q van F er een a > 1 bestaat zodat an-1=1(mod n) g.g.d. (an-1q- 1,n) = 1 dan is n priem. Er kunnen verschillende a gebruikt worden voor ieder priemgetal q. Deze formules zijn de basis van de bekendere formules, zoals die van Pepin en Proth. Pepins test Pepin heeft in 1877 een formule gevonden die Fermat-getallen (van de vorm 22n+1) op de priemheid test. Stel dat Fn het n-de Fermat-getal is met n > 1. Fn is priem als en slechts als 3(Fn-1)/2 = 1(mod Fn). Bijvoorbeeld: F2 = 222+ 1 = 17 Dan is 3(17-1)/2 = 38 =6561 = 1(mod 17) Want (6561+1)/17 = 386 Proths test Proth maakte in 1878 de formule: n =2kh +1 met 2k > h. Als er een natuurlijk getal a bestaat zodat a(n-1)/2 = -1(mod n), dan is n priem. Lucas-Lehmertest Om na te gaan of een Mersenne-getal, een priemgetal is kan je de Lucas-Lehmer test gebruiken. Als p een priemgetal (groter dan 2) is, is het Mersenne-getal 2p -1 priem, als S(p-1) deelbaar is door 2p -1, waarbij S(n+1) = S(n) ² -2 en S(1)=4. Bijvoorbeeld: Als we willen weten of M3 = 7 een priemgetal is, dan zoeken we S(2).   Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  S(2) = S(1) ²-2   Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  = 4 ²-2   Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  = 14 Dan controleren we of 14 deelbaar is door 2p -1 = 7. Dat klopt dus 7 is een priemgetal. De theorie voor de test heeft Lucas uitgevonden rond 1870. Hij heeft dan de test vereenvoudigd in 1930 tot wat hierboven uitgelegd staat. Voor heel grote Mersenne-getallen wordt het wel moeilijk de test uit te voeren. Zelfs moderne computers kunnen slecht overweg met zeer grote getallen. APR, APRT-CL In 1970 begon Williams samen met enkele anderen op een andere manier de priemheid te testen. Ze gingen nu niet meer de factoren van n-1 gebruiken, maar factoren van n2+1, n ²+n+1, n ²-n+1 en nm 1 waarbij soms m heel groot was, zoals 5040. Elk priemgetal q waarvoor q 1 een deler is van 5040 (welke n niet deelt) moet dan n5040 1 delen. Er is aangetoond dat er altijd een m is waarvoor geldt dat m q die nm 1 delen met q 1 een deler van m op zijn minst een product geven dat gelijk is aann. Zo goed als altijd ligt m rond de 100.000.000 voor een n die een 3000-tal cijfers bevat. GIMPS GIMPS (Great Internet Mersenne Prime Search) is een project waarbij men zoekt naar steeds grotere Mersenne-priemgetallen. Dankzij GIMPS kunnen we enorm grote getallen controleren op priemheid, doordat het werk wordt verdeeld onder een aantal deelnemers. Het project heeft tot op het heden 12 Mersenne-priemgetallen gevonden. Iedereen die een computer heeft en over internet beschikt kan deelnemen. Er is wel veel tijd voor nodig, à ©Ãƒ ©n priemheidstest kan gemakkelijk een hele maand duren. GIMPS is een efficià «nt systeem, het zoeken naar Mersenne-getallen gebeurt in verschillende stappen. Het aanmaken van een lijst met priemgetallen (want de formule die ze gebruiken is 2p-1 met p als priemgetal) Het zoeken naar de priemfactoren, wat op verschillende manieren kan gebeuren. Bij GIMPS zullen ze de exponent eerst omzetten naar het binair talstelsel. Bijvoorbeeld: 223 1 wordt getest en wordt daarbij gedeeld door 47. In het binair is 23 = 10111. Daarna passen ze de volgende werkwijze toe (het binair rekenen): De Pollard-methode om te ontbinden in priemfactoren. De P-1-methode werkt nogal simpel. In stadium 1 kiezen ze een vaste B1. Als q = 2kp + 1, dan zal het P-1-ontbinden in factoren deze factor q bepalen zolang alle factoren van k kleiner zijn dan B1. Dan wordt x = 3E.2.P berekend. Daarna controleren ze de g.g.d. van(x 1,2p -1) om te zien of er een factor is gevonden. In stadium 2 gebruiken ze een ander vast getal, B2. Hier zal de factor q gevonden worden als k exact à ©Ãƒ ©n factor heeft tussen B1 en B1 en alle andere factoren van k kleiner zijn dan B1. (Dit stadium maakt gebruik van zeer veel geheugen) GIMPS gebruikt deze methode om de grote factoren te vinden. Bijvoorbeeld 22944999 1 dat deelbaar is door 314584703073057080643101377. B1 en B2 worden gekozen door kansberekening. De Lucas-Lehmer test. (zie : 2.5.2.2) Om een getal te controleren zijn er heel veel vermenigvuldigingen nodig. Er worden zorgvuldig algoritmes geschreven die gebruikt worden om zeer snel te vermenigvuldigen. De kans dat zo een Lucas-Lehmer test succesvol een priemgetal ontdekt is ongeveer 1/80000. De zoektocht naar het grootste priemgetal Sommige mensen hebben er een hobby van gemaakt steeds op zoek te gaan naar het grootste priemgetal. De traditie is al gaande sinds 300 v.C. toen Euclides zijn werk De Elementen schreef. Hij merkte op dat de perfecte getallen (positieve getallen gelijk aan de som van zijn delers) nogal dicht lagen bij de priemgetallen van de vorm 2p -1 voor een priemgetal p. Vanaf toen begon de jacht op de Mersenne-priemgetallen. Grote getallen van deze vorm zijn al bestudeerd door grote wiskundigen zoals Fermat, Mersenne, Euler, Lucas, Leibniz enzovoort. Veel mensen willen de eer om hun naam bij het lijstje te voegen. De traditie om grote Mersenne-priemgetallen te vinden zal zeker blijven duren. En er valt heel wat meer met mee te bereiken. Er zijn programmas om priemgetallen te zoeken bij het testen van hardware. Dit wordt al gedaan sinds het ontstaan van de computer. Zo werden stukjes software van het GIMPS project (Zie 2.7) gebruikt door Intel om de processors Pentium II en Pentium Pro te testen alvorens ze verscheept werden. De software dat priemgetallen berekent, belast de processor meer dan andere programmas doen en duurt niet lang om uit te voeren. Als je een heel groot priemgetal invoert, moet de processor een miljoen berekeningen uitvoeren om na te gaan of het wel klopt. En hoe meer priemgetallen er gevonden worden, hoe meer de verdeling ervan kan worden bestudeerd en worden begrepen. Er is al veel onderzoek gedaan naar patronen in de verdeling van priemgetallen. Tevens is het allemaal niet voor niks. Er wordt een serieuze geldprijs van minstens $ 150.000 uitgereikt aan degene die als eerste het priemgetal vindt bestaande uit 100-miljoen cijfers. De eerste die er eentje kan vinden bestaande uit een miljard cijfers, krijgt zelfs een prijs van minstens $ 250.000. Het grootste priemgetal is dus heel bruikbaar en gewild. Hoofdstuk 3 Een priemwereld vol verrassingen Inleiding Zoals al gebleken is zijn er oneindig veel priemgetallen maar kunnen we deze nog onderverdelen in aparte groepen? Ja, er zijn zelfs zeer veel onderverdelingen met elk hun specifieke eigenschappen. Zo heb je de palindroompriemgetallen, Mersennepriemgetallen, Illegale priemgetallen, Maar eerst beginnen we met het uitleggen van enkele vermoedens in verband met priemgetallen. Enkele vermoedens Inleiding Er zijn vele stellingen in verband met priemgetallen. Deze gaan van zeer simpel tot echte breinbrekers. We vooral de meest bekende en de meest belangrijke stellingen voor de priemgetallen bespreken. En daarom beginnen we ook met de stelling die van het grootste belang was voor de priemgetallen, namelijk het vermoeden van Goldbach. Het vermoeden van Goldbach Goldbach was een Duitse wiskundige en is in 1690 geboren in Kà ¶ningsberg. Hij werd zelfs leraar bij de Tsaar in Moskou omdat hij een zeer belangrijke wiskundige was in zijn tijd. Deze job gaf hem dan ook de mogelijkheid veel te reizen zodat hij overal in contact kwam met andere belangrijke wiskundigen zoals Euler, Leibniz. Hij bleef in contact met deze geleerden door middel van brieven. Ook het begin van zijn vermoeden schreef hij in 1792 in naar Euler. In deze brief schreef hij dit vermoeden: Als een geheel getal n > 5 is dan kan dit getal geschreven worden als de som van 3 priemgetallen. Bij deze 3 priemgetallen kan herhaling optreden. Wat wel vreemd is aan het hele verhaal is dat Euler een brief terugschreef met daarin de stelling dat dit vermoeden geldt voor ieder getal n > 2 maar toch is het vermoeden enkel bekend als het vermoeden van Goldbach. Euler beschouwde de stelling van Goldbach als waar maar hierbij was de stelling nog niet bewezen. Zelfs nu is de stelling nog niet bewezen desondanks er als publiciteitsstunt 1 miljoen dollar aan te verdienen was. Maar dit betekent niet dat er geen belangrijke ontdekkingen zijn gedaan. In 1939 bewees Schnirelmann dat je elk even getal groter dan 2 geschreven kan worden als een som van ten meeste 300000 priemgetallen. In 1995 bewees Ramarà © dat een som van maximum 7 priemgetallen meer dan genoeg is. Het oude vermoeden van Goldbach Dit is het vermoeden dat Goldbach als eerst vermelde in zijn brief naar Euler: als een geheel getal n > 5 is dan kan dit geschreven worden als de som van drie priemgetallen. Dit vermoeden wordt ook wel het oneven vermoeden van Goldbach genoemd. Dit oneven vermoeden is eigenlijk een zwakkere vorm van het eigenlijke vermoeden. Want we kunnen bij n > 2 telkens het priemgetal toevoegen zodat we elk oneven getal n > 5 bekomen maar het oorspronkelijke vermoeden volgt niet uit het oneven vermoeden van Goldbach. Het oneven vermoeden staat al veel dichter bij het bewijs dan het oorspronkelijke want in 1937 bewees Vinogradov dat dit vermoeden geldt voor alle voldoende grote oneven getallen. Het probleem was wel dat Vinogradov niet wist hoe groot voldoende groot nu juist was. In 1956 kon men uiteindelijk op voldoende groot een getal plakken, namelijk groter dan 3315. De waarde die gelijk is aan voldoende groot is het getal n > 1043000 bewezen door Wang. De exacte waarde zal men pas kunnen vinden als men computers kan ontwikkelen die dit soort berekeningen aankunnen. Nog meer vermoedens We zullen vlug nog even enkele vermoedens vermelden: Voor ieder even getal 2n bestaan er oneindig veel priemgetalkoppels waarvoor het verschil tussen beide priemgetallen gelijk is aan 2n. Maar indien n = 1 dan hebben we te maken met een priemtweeling en bij n = 3 dan moet het verschil 6 zijn en is het priemgetalkoppel een koppel sexy priemgetallen. (zie 3.7.2) Ieder even nummer is een verschil van 2 priemgetallen. Priemgaten Opvallend bij priemgetallen is dat er geen logische volgorde zit in de opeenvolging. Hoe verder we gaan zoeken naar grote priemgetallen hoe moeilijkere deze te vinden zijn, want ze komen dan steeds minder voor. De gaten tussen twee priemgetallen worden steeds groter hoe verder je gaat. Deze gaten oftewel priemgaten zijn de ruimtes tussen 2 opeenvolgende priemgetallen. De grootte van deze gaten wordt dus bepaald door het verschil van de 2 opeenvolgende priemgetallen. Al een gehele tijd hebben wiskundigen een patroon proberen te ontdekken bij de opeenvolging van priemgetallen door de priemgaten te bestuderen. Priemgaten hebben geen beperking in grootte want als n ≠¥ 2 de minimale grootte is dan zijn de volgende gatallen allemaal samengesteld: (n + 1)! + 2, (n + 1)! + 3, (n + 1)! + 4, , (n+ 1)! + (n + 1) Vb. n = 2 dan zijn de eerste 3 getallen van het priemgat 8,9,10 Deze formule is niet alleen nuttig om het priemgat met grootte n te geven maar ook om het priemgat te geven met minimale grootte n. Hierdoor is de aanwezigheid van minimum n ontbindbare getallen verzekerd. Wat wel nog een probleem vormt is de mannier om de grootte van een priemgat te berekenen. Want men gebruikt het eerste priemgetal a en het tweede priemgetal b om de priemgaten te berekenen door priemgetal a af te trekken van priemgetal b. Het probleem is dat men oftewel bij de uitkomst 1 moet optellen of niet, want zonder 1 toe te voegen wordt het priemgetal a ook meegerekend met het priemgat. Illegale priemgetallen In 2001 ontdekte Phil Carmody dat de gezipte broncode C, wat men op computers gebruikt om DVDs te decoderen, overeenkomt met een priemgetal. Hij ging als volgt te werk: Eerst comprimeerde hij de C-Code met het computerprogramma Gzip. Het getal wat nu weergeven werd in het verkleinde bestand was priem. Er bestaan dus heel wat illegale priemgetallen. Hieronder volgt het allereerste illegale priemgetal, gevonden door Phil Carmody. Later zette Joerg Dietrich het priemgetal om zodat deze kon worden weergegeven in baseparen. Hij kwam een Dna-sequentie uit die 43016 basen telt. Hij kwam ook tot volgende vaststelling: het zinloos zou zijn om een wet te maken tegen het gebruik van het priemgetal want als men ooit het priemgetal in ons DNA mocht vinden dan zouden 6 miljard mensen de wet overtreden. Hier is een klein deeltje van de Dna-sequentie: Merkwaardige priemgetallen Congruente priemgetallen Een priemgetal dat een regelmatige figuur vormt noemt men een congruent priemgetal. Een regelmatige figuur oftewel een regelmatige n-hoek zoals een vierkant of een gelijkzijdige driehoek. Het middelste getal of centrum vormt dan het priemgetal omgeven door cijfers van binnen naar buiten toe. Als voorbeeld geven we volgende regelmatige figuren gevormd door een priemgetal. Vb. 1 met priemgetallen Palindroompriemgetallen Priemgetallen die je zowel naar voor als naar achter hetzelfde leest noemt men palindroompriemgetallen. Als voorbeeld kunnen we volgende priemgetallen gebruiken: 2, 11, 101, Maar ook gigantische priemgetallen zoals 14 ·10^6343-4199. Dit priemgetal telt 6343 cijfers en dit is gewoon heel de tijd 1 en 4 afgewisseld: 14 ·10^6343-4199 = 1414141414141414141 Zo heb je ook het grootste palindroompriemgetal van 3 cijfers namelijk 717. Er zijn ook priemgetallen die de decimale loop van p weergeven: 3, 31, 314159, Het 4de palindroompriemgetal bevat al 38 cijfers en het 5de al 500. Nog een zeer mooi palindroompriemgetal is het volgende: 923032900000000 00000000000006660000000000 00000000000000009230329 Het bestaan uit 666 en wordt omgeven door 32 nullen en 9230329 aan elke kant. En nog wat eigenschappen van dit palindroompriemgetal: 9230329 is exact het 666ste palindroompriemgetal 666.32 = 21312 wat een palindroompriemgetal is. 666.64 = 42624 wat ook een palindroompriemgetal is. De palindroompriemgetallen zijn nog verder ingedeeld zo heb je: De Titanic-palindroompriemgetallen gevonden door Samuel Yates: deze bevatten minimum 1000 cijfers. Samuel Yates zei dat dit een zeer lage grens is en later bleek waarom. Doordat men nu verder kon rekenen met machines werd de onderverdeling Gigantische palindroompriemgetallen gemaakt: dit zijn palindroompriemgetallen met ten minste 10 000 cijfers. De Megapalindroonpriemgetallen: deze bevatten ten minste 1 000 000 getallen en er waren er in 2003 slechts 4 gekend. Een pandigitaal palindroompriemgetal: bijvoorbeeld 1023456987896543201 Als we het getal in 2 verdelen in het midden en links en rechts het midden meetellen dan hebben we elk getal 1 keer. Een zeer bijzondere eigenschap van de palindroompriemgetallen is dat ze allen oneven zijn buiten 11 want moest men een palindroomgetal vinden dat even is dan is dit misschien wel palindroom maar zeker niet priem. Nog een palindroompriemgetaleigenschap is de palindroompriempiramide: Hier begin je met een priemgetal bij de volgende rij plak je aan beide kanten deze

The Velvet Revolution Essay -- World History

The citizens of Czechoslovakia had not known freedom in decades. During much of World War II the nation was occupied by the Nazis and later by the Red Army as it drove the Nazis back to Berlin. When they Red Army moved into an area, communist regimes were set up to govern the area, and establish satellite nations. There were numerous uprisings throughout the decade that were violently suppressed by the communist governments with help from the USSR. After Alexander Dubcek tried to grant reforms to the people of Czechoslovakia in 1968, the USSR and most members of the Warsaw Pact sent their military forces to intervene and suppress any unrest or reforms. Things grew somewhat violent and brutal, as any demonstrators were either or beaten, killed, or arrested. Dubcek himself was removed from power. While many Czech citizens were fed up with their lack of freedom and the failing economy, they had little chance to achieve change. In the mid 1980’s though things began to lighten up w hen Mikhail Gorbachev became Premier of the USSR and announced his reform programs of Glasnost and Perestroika. Gorbachev also encouraged the leaders of the satellite states to follow suit and grant their citizens more political and civil liberties. Under Gorbachev the USSR also withdrew most of its armed forces from eastern and central European countries. Many citizens and political reformers took advantage of the moment and started to push for an end to the single party political system that had been forced on them for years. 1989 was the year of many revolutions and demonstrations in eastern and central Europe. In October of 1989 police in Prague had to break up a few large demonstrations that broke out on the 71st anniversary of the establishment of Czec... ...the movement gained such widespread popular support made it possible for the demonstrators to have a great deal of leverage when negotiating with the communist party. Works Cited Ladislav Adamec, "Speech by Premier Ladislav Adamec at an extraordinary session of the CPCz CC, stating his preference for a political solution to the crisis," Making the History of 1989, Item #512, http://chnm.gmu.edu/1989/items/show/512 (accessed April 17 2012, 7:06 pm). The Civic Forum, "The Civic Forum's Exposition of its Position in Public Life with a Call for Nonviolence, Tolerance and Dialogue," Making the History of 1989, Item #503, http://chnm.gmu.edu/1989/items/show/503 (accessed April 17 2012, 7:15 pm). The Civic Forum, "List of Goals by the Civic Forum," Making the History of 1989, Item #513, http://chnm.gmu.edu/1989/items/show/513 (accessed April 17 2012, 6:56 pm).

Media: a Fictional Reality Essay

Introduction We increasingly move from one kind of reality to another. As spectacles are created with our own lives we are vastly becoming the characters we once saw on television. In media, the producing and promotion of these realities encourage people to misinterpret false depictions into reality. Advertisements When we examine media advertising we find art and technology being used to create a false reality through stories in an effort to evoke desired reactions from audiences. We see a production of characters playing physicians, housewives, used car salesmen, and everyday people with plots and quick resolutions of conflict in which the characters overcome obstacles and fulfill their desires in record time with the help of their product. For example media display products that are cosmetically altered to seem more appealing to viewers. Raw turkeys are made to look baked and delicious with food coloring, burgers are big and juicy, water drops slide down fresh vegetables, even the sizzle from cooking food turns out to be a sound effect added during editing. These sensory deceptions are supplemented by exaggerated claims, to create a false identity for the product. Commercials also include another kind of falsity in the form of digitally manipulated images. They convey a sense of life as celebration, full of people who can’t help but sing out because they love their Skittles or who emerge from swimming pools, all luminescent, with magnificent hair and wonderful lives, surrounded by bright colors, upbeat music and dancing friends, in which everything is in motion to convey a sense of what life can be if we buy the product. They invent â€Å"worlds† based on fantasy and desire. â€Å"To achieve these effects, media engage in the new production process of high-tech capitalism, which is to turn everything into an image. This process is very evident in what happens to actors — they are turned into simplified human images. Their role is to become characters in false utopias so they can act as living sales pitches for products† (Boorstin 1961). They are all false promises that make everything seem better than it is. Cities City landscapes increasingly resemble places all around the world. These false depictions serve as attractions for millions of people, as well as a pseudo reality that the media likes to make into a spectacle. For example, sin city is becoming sim city; the city of simulation. Through varies attractions people are given a misrepresented idea on how media interprets the world. â€Å"One of the city’s monuments is Luxor, a $375 million hotel and casino that is a fantasy version of ancient Egypt, presenting visitors with material images of mystery, mysticism and splendor in one of the greatest monstrosities ever built: a 36-story, pyramid-shaped hotel with a ten-story replica of the Sphinx as an entrance for valet parking. The hollow core of the pyramid is a 27-story atrium that started out with a fake river Nile at the bottom, which took visitors on a barge ride passed tableaus of ancient Egypt. Meanwhile, â€Å"inclinators† — elevators that travel diagonally, following the pitch of the pyramid — take guests to their rooms in the upper floors. † (Kens 1997) They aim at representing an ideal experience, as if you really were visiting the great monuments of Egypt, but these manipulated visions are forced onto people as true depictions of reality. â€Å"Luxor is themed, offering a story line that is intended to give the visitor’s experience a meaning and coherence. But Luxor, like many similar attractions, appears to suffer from an identity crisis: it can’t seem to keep its theme together. In place of presenting one idea or trying to show one kind of place, it has jumbled together all kinds of times and places, which are removed from any sense of context or relation to each other†. (Kens 1997) Thus, the Sphinx is the entrance to a pyramid, which contains an ancient-looking temple, which takes visitors to a dig of a fictional civilization, while a talk show goes on next door and celebrity impersonators play Michael Jackson, Madonna and the Blues Brothers, or other Vegas-style shows go on nearby in Nefertiti’s Lounge. Las Vegas thrives on having the best attractions of the world on one famous street; the Vegas strip, but they’re all attractions focused on historical allusions. Media creates a spectacle of historical information in which gets misinformed to the public. Zoos Many zoos are beginning to offer â€Å"educational† exhibits through fictional realities. Resembling scenes out of movies or Disney related themes, parks and zoos are increasingly using fictional characters and ideals to promote their parks. â€Å"They are imitations that are intended to be better than the originals. To the degree that visitors think of them as accurate representations, they will come away with an image of a rain forest as a place crowded with large animals, where one can get good vistas of peaceful surroundings full of impressive landscapes and gigantic trees. † (Eco 1990) These false depictions are being represented as an educational experience by the media and leave them with a tainted view of reality. â€Å"An increasing number of exhibits portray something that is unlike nature in another sense: under constant pressure to be entertaining, they are incorporating themed environments based on fantasy that have little to do with the natural world. In essence, these attractions, even though they are the handiwork of nonprofit institutions, have to attract an audience that will help keep the enterprise afloat financially and justify its existence. They are trying to win that audience with ever more spectacular displays and excursions into fantasy. The result is the growing numbers of those simulated ruins, suspension bridges, vines that hang over pathways and other popular fantasy elements commonly found in television and movies, which are, supposedly, the sugar that coats the pill of educational value. †(Eco 1990) The act of displaying a rainforest is for entertainment purposes but it should not tarnish the educational responsibility by providing false depictions as reality. Media provides a distorted image of rain forest by the India Jones themed movies. We come to believe that every jungle, rain forest, safari is going to have hidden civilizations, cities of gold, and ancient Mayan ruins. The reality is, that these places are not so exciting. The media raises your hopes for reality at the cost of your educational experience. â€Å"Non-Fiction† Television Newscasts are beginning to foster a type of reality that entertains a viewer as if they were watching the latest episode of Law and Order. Providing their audience with a â€Å"fictional† reality of news highly made into spectacles for entertainment rather than newsworthy purposes. â€Å"These programs are well known for reciting the daily litany of crimes, and personal and community disasters, with all the potential that has for evoking sympathy, fear and anger in audiences. † (Kens 1997) The media publishes a compelling story each with a happy ending. They are more about the storyline then the actual â€Å"factuality† and newsworthiness. Newscasts are no longer an avenue for the â€Å"need-to-know† news but rather the â€Å"want-to-know† news. It is a civil duty that we get provided with accurate information, but that sometimes gets tarnished following a new update from the Octomom. â€Å"In forms of fiction; both evoke anger, fear and sympathy in an audience and then convert these emotions into reassurance and hope. Fiction accomplishes this primarily with a happy ending. Local news does it by placing stories about danger and suffering in a program that overflows with benevolence and camaraderie. Each, in a different way, is designed to provide a satisfying emotional experience to audiences. † (Kens 2007) The experience is the most important aspect newscasts are aiming for. Kens relates newscasts as â€Å"Back to The Future†¦ the ride† because it takes viewers on a journey of images and computer generated graphics meant to serve as an entertaining attraction rather than a trusted source with direct information about the world. Conclusion â€Å"Art and technology masquerading as life. † This is medias lens on reality and how many of us perceive much of today’s world. We believe that the beautiful life portrayed in a commercial is obtainable by the simple act of buying their product. At least if we can’t look like a celebrity we can smell like one, in relation to cologne commercial. People are increasingly becoming less satisfied with their own lives and believe they can just jump into an alternative reality forever. Where there are no problems and like the actors in â€Å"Friends† seem to spend their whole lives together in a coffee shop with no relation to work or any responsibility for that matter. Being the monuments in Vegas or the story lines in â€Å"rainforests,† now days, this exposure of entertainment is increasingly becoming a pseudo reality. They are masquerading real life experiences into a huge spectacle. Media has transformed our lives and everyone in it to the characters and drama series we love to see on television. We live in fiction and are entertained by â€Å"reality. † Work Cited 1. Vick, Roger. â€Å"Story Line as Ideology. † (1989): Print. 2. Robert J. Stoller, Observing the Erotic Imagination (New Haven and London: Yale University Press, 1985) pp. 58-61. 3. Sans, Ken. â€Å"A Culture Based on Fantasy and Acting Out. † (1997): Print. 4. Sans, Ken. â€Å"Advertising and the Invention of Postmodernity. † (1997): Print. 5. Sans, Ken. â€Å"Las Vegas: Postmodern City of Casinos and Simulation. † (1997): Print. 6. Boornstin, Daniel. The Image: A Guide to Pseudo-Events in America. Vintage, 1992. 200-320. Print.

An Occurrence At Old Creek Bridge And William Faulkner s...

Short stories are rarely written in a non-linear structure. Ambrose Bierce’s â€Å"An Occurrence at Old Creek Bridge† and William Faulkner’s â€Å"A Rose for Emily† are good examples of non-linear structure. A non-linear narrative makes readers question why the author cannot present his story in a lucid form? Non-linear structure often makes stories harder to understand, but it keeps readers interested in the story. Bierce and Faulkner uses a similar strategy to present their stories by deceiving the readers to create suspense at the end of the story. Nick Melczarek explains narrative strategy in Faulkner’s â€Å"A Rose for Emily† with the help of a well-known critic and analyst Nebecker in his short article â€Å"Narrative Motivation in Faulkner’s A Rose for Emily.† Similarly, Lucy Bednar uses different voices used by Bierce to explain narrative strategy in â€Å"An Occurrence at Old Creek Bridge.† Narrative strategy no t only affects the reader’s perception of understanding the story, but also gives a deeper meaning to the story. Different author uses different narrative strategies to create deeper understanding in their stories. According to Melczarek, Faulkner uses more complicated narrative strategy to achieve psychologically complex effect of horror in his story, while Bierce uses hallucination in his story to create suspense. Bierce’s starts his story with a man who is about to be hanged to death without any description of that men. In the second section of the story Bierce describes a men