Pi Number Essays - Pi, Approximations Of, , Term Papers

Pi Number A little known verse in the bible reads "And he made a molten sea, ten cubits from the one brim to the other; it was round all about, and his height was five cubits; and a line of thirty cubits did compass it about (I Kings 7, 23)." This passage from the bible demonstrates the ancient nature of the irrational number pi. Pi in fact is mentioned in a number of verses throughout the bible. In II Chronicles 4,2, in the passage describing the building of the great temple of Solomon which was built around 950BC, pi is given as equal to three. This value is not very accurate at all and should not even be considered accurate for it's time, however it should be noted that precision was not needed for the task that was being performed and we should let the general concept of pi that the biblical characters posses impress us. Present knowledge suggests that the concept of pi first developed in 2000 BC in two separate cultures. The Babylonians used pi at a value of 25/8 while an entirely different culture, the ancient Egyptians used pi at a value of 256/81. While the biblical calculation of pi=3 most likely came from crude measurement, there is strong reason to believe, because of the relative accuracy of the values, that the Babylonians and Egyptians found pi by means of mathematical equations. In the Egyptian Rhind Papyrus, which is dated around 1650 BC, there is strong evidence supporting that the Egyptians used 4(8/9)2 =3.16 for their value of pi. At that point in history, and for the majority of modern history, pi was not seen as an irrational number as it is today. The next culture that investigated pi was the ancient Greeks. Starting in 434 BC Greeks were unraveling the mysteries of pi. The mathematician Anaxagoras made an unsuccessful attempt at finding pi, which he called squaring the circle and in 414 BC, 20 years after Anaxagoras failed in his attempt to square the circle, Aristophanes refers to the work of Anaxagoras in his comedy "The Birds". It took over 100 years for the Greeks to finally find a value for pi. In 240 BC Archimedes of Syracuse showed that 223/71*pi*22/7. Archimedes knew, what so many people today do not, that pi does not equal 22/7 and he made no claim to have discovered the exact value of pi. However if we take the average of his two bounds we obtain pi=3.1418, which was an error of about 0.0002. Archimedes found the most accurate value of pi up to that time and his value would be used exclusively until the next discovery in the world of pi. The next major finding concerning pi did not occur in the western world, but in China by Tsu Chung-chi'h who approximated pi at 355/113 in 480 AD. Next to nothing except for this work is known about Tsu Chung-chi'h's life but it is very unlikely that he had any awareness of Archimedes work. We shall now notice how during the dark ages of Europe, the lead in the research of pi is passed to the East. Aryabhata, working on his own in Persia without any outside information in 515 AD was able to approximate pi to 3 decimal places. A mathematician from Baghdad named Al'Khwarizimi worked with pi however the most accurate finding of pi to date was found even more east in Samarkand by Al-Khashi. In 1430 AD he approximated pi to 16 decimal places, the most to date. His work however, would be the last of note from the east as the European Renaissance brought about a whole new mathematical world. The first notable discovery in the approximation of pi from the European Renaissance was by Viete in 1593 AD. He expressed pi as an infinite product by using only 2's and square roots. In 1610 Ludolph van Ceulen demonstrated the new thought coming out of the Renaissance by calculating pi to 35 decimal places. Around the same time, Snell refined Archimedes's method of calculating pi, and Snell's work was used by Grienberger to calculate pi to 39 decimal places in 1630. In 1655 Wallis showed that pi/2=2/1*2/3*4/3*4/5*6/5*6/7*8/7*8/9..... The 18th centuary brought about great achievements in the calculating of pi. In 1706, Machin found pi to 100 decimal places, the first time that feat was ever achieved and in the same year, a British mathematician, William Jones first used pi for the circle ratio. In 1737, Euler first used the Greek letter pi

15 of the Best Online Writing Communities for Aspiring Authors

15 of the Best Online Writing Communities for Aspiring Authors 15 of the Best Online Writing Communities for Aspiring Authors As enjoyable and fulfilling as writing can be, the truth is that it’s often a solitary endeavor. While we might romanticize the focused artist typing away while imaginary worlds and narratives swirl inside their minds - authors know the truth: writing can get lonely. And moreover, when you’re working on a one-person project, it can be hard to remain motivated and accountable. That’s where writing communities come in.Writing communities are the perfect place to find answers to your writing questions and to discuss the ins and outs of the writing life with people who actually understand what you’re talking about.So, if you are tired of listening only to the voices in your head, take a look at our (non-exhaustive) list of top online writing communities. Which is the best writing community for you? Find out here! Top online writing communities1. Absolute Write Water CoolerWith over 68,000 members, this is a large and highly active community. Here you can find threads on every genre imaginable, as well as discussions about freelance writing, the publishing industry, pop culture, writing prompts and exercises, and much more.Perfect for: writers who are looking for a large and active community.2. AgentQuery ConnectWhile this forum will come in handy for any writer, it’s especially helpful for authors who have already completed their manuscript and are wondering what to do next. The site boasts a wealth of information on publishing topics such as querying agents, self-publishing tips, and book promotion advice.Perfect for: writers who are looking to connect with agents and learn more about the publishing industry.3. Camp NaNoWriMoIf you’ve ever wanted to go to a writer’s retreat but can’t afford it just yet, then this site might help scratch your itch. Holding online à ¢â‚¬Å"camp sessions† in April and July, Camp NaNoWriMo offers a digital space to encourage and empower writers at any point of their career. Here you can work on drafts, revisions, short stories, or any other writing project that involves word-count goals.Perfect for: writers who can’t wait until November to crack their writing goals.Do you belong to a writing community? Which one is your favorite one? Add yours in the comments below!

Article summary of Roschach Essay Example | Topics and Well Written Essays - 250 words

Article summary of Roschach - Essay Example The findings of over 125 meta-analysis and 800 multimethod assessment studies have shown that psychological assessment instruments such as the Rorschach perform as effectively as any instrument used in the entire health services industry such as â€Å"electrocardiograms, mammography, magnetic resonance imaging (MRI), dental radiographs, Papanicolaou (Pap) smears, positron emission tomography (PET) scans, and serum cholesterol level testing†. This conclusion was arrived at after analyzing a comprehensive set of 144 validity coefficients for psychological and medical tests. The results of these tests were comparable to those obtained for finding the validity of intelligence scales and the Minnesota Multi-phasic Personality Inventory (MMPI). Hence the research scholars unanimously concur on the validity of the Rorschach, stating that they find no reason why this instrument should be criticized. Moreover, when one considers the contexts in which the Rorschach is usually used, then most criticisms directed against it don’t hold good. Hence conditional validity is a key area of research going forward.

Business law- Contracts and leases Essay Example | Topics and Well Written Essays - 1000 words

Business law- Contracts and leases - Essay Example Regardless of the type of business an individual runs, it is important to have an understanding of contract law as it is the key to making sound business agreements that can be enforced legally in the event of a dispute. Normally, a contract is enforced and governed by the laws of the country where it was made. In the United States of America, a contract is governed by two types of state laws, that is, the common law and the Uniform Commercial Code (UCC) (Bagley and Dauchy, 2012). Common Law Common law is a law which governs contracts for services and contracts that are not governed by the Uniform Commercial Code. Most contracts such as employment agreements, general business agreements and leases are controlled by common law. Common law contracts can either be bilateral or unilateral. However, the contracts are valid only if the three elements of common law contract formation are met. The elements of formation are offer, acceptance and consideration (Bagley and Dauchy, 2012). The Un iform Commercial Code (UCC) The uniform commercial code (UCC) governs the contracts between merchants and the sale of goods. The law was written by the National Conference of Commissioners on Uniform State Laws (NCCUSL) and the American Law Institute (ALI). It was published in 1952 to harmonize the law of sales and other commercial transactions in the United States. Although it has not been fully enacted, some provisions of the code have been adopted by all the fifty states of the US (Fullerton, 2011). Previously, the code was divided into 9 articles; however, after a number of reviews and revisions, the code is now divided into eleven articles with each giving provisions that relate to a particular area of commercial law. Article 1, gives the definitions of terms used in commercial law and the general principles that apply to the UCC. Article 2 covers all contracts pertaining to the sale of goods. Article 2A covers all transactions pertaining to leases of goods. Article 3 covers ne gotiable instruments such as checks and promissory notes. Article 4 governs bank collections of drafts and checks. Article 4A governs the transfer of funds through banks. Article 5 governs letters of credit. Article 6 governs bulk sales. Article 7 covers domestic documents of title. Article 8 covers all transactions in investment securities and article 9 applies to security interests in real property (Bagley and Dauchy, 2012). Differences between Contracts Formed Under Common Law and Contracts Governed By the Uniform Commercial Code (UCC) Although both the common law and the UCC govern contracts, the two laws differ in various ways. The first difference is that, contracts under uniform commercial code apply to various commercial issues such as sale of goods, banking and security interests whereas common law contracts deal with the sale of real estates, employment contracts, insurance, services and sale of intangible assets (Prabhat, 2011). According to the UCC, a good is any item th at is tangible and movable. Therefore, the sale of a home is not a sale of goods since the home is immovable. Also, the sale of a right to a trademark is not a sale of goods since it is not tangible (Cornell University Law School, 2005). The second difference between the two contracts is that, contracts under UCC can be modified without additional considerations as long as they are made in good faith whereas those under common law except

Student Survival Guide Essay Example for Free

Student Survival Guide Essay To survive my academic career at University of Phoenix, many things will help me while going through the program. This Survival Guide will remind me about: the general Internet skills needed to be successful, how to use my student website and the University Library resources, how to set up and achieve my goals, how to uphold academic honesty, how to manage my time wisely, how to foster my reading comprehension and retention, and how to adapt my work habits to fit my personality. General Internet Skills. The University of Phoenix Associates Level Material: Appendix D (2012) states, there are four different forums with different purposes where discussions take place: Main, Chat Room, Course Materials and an Individual Forum. Main Forum Used for class discussion, Discussion Questions, and to reply to discussion questions Only instructor posts new threads Under Questions thread for each week, post general questions that could benefit the entire class regarding an assignment Use a professional tone Chat Room. students can create new threads or messages and reply to other messages discussion about things not related to an assignment or discussion question use a more casual tone Course Materials Forum only instructors can post in this forum syllabus, weekly assignments, and course information is posted here reading links or other materials will be posted here Individual Forum private messages between me and my instructor about my grade or specific questions about my assignment use profession communication. Keeping my audience in mind allows me to use the correct tone and wording when communicating with others in writing. When performing research for a writing assignment or for use in a forum, looking for unbiased work, a peer reviewed source, one that cannot be changed by the public, has an author, or ends in . edu or . gov are likely to be reputable and worth reading. Reading the synopsis of a webpage will help to determine if the work is politically biased or if it will pertain to the assignment. Validated resources should always be used. University of Phoenix and University Library Resources. While taking courses through University of Phoenix I am given access to my Student Website where all of my classes will be held and where I can use the school’s resources. Many different resources are available under the Library tab: Technological Tools Available University Library Library services Research/peer reviewed material Ask a librarian Useful links Reference and citation generator APA information Grammar and writing guides Center for Writing Excellence Writing and style guidelines Tutorials and guides Submit a paper for review WritePoint Plagiarism Checker. Center for Mathematics Excellence Building math confidence Live tutoring Phoenix Career Services Job Market Research Explore jobs in particular geographical areas Search jobs by type of work, employer, or degrees Career plan Career Interests Profiler Competencies Work culture preferences Reasoning aptitude Resume builder Upload current resume Create new resume Import resume from LinkedIn Career resources Exploring careers Career profile videos Executing your job search Job search tips Advice for employees looking to change careers Marketing yourself Interviewing Interview Preparation video  Resumes and Cover Letters Sample resumes and cover letters Managing your Career Employment partners More resources are available, but these are ones I can see myself using. In the Center for Writing Excellence, the most useful resources are WritePoint, Plagiarism Checker, and the resource and citation generator. The features of Phoenix Career Services will be useful when looking for a job, creating a resume, or needing career advice. Conducting research using the University Library can save time since all of the items have already been verified and are from reliable resources. Tutoring and activities to refresh my math skills prior to taking a math class are available in the Center for Mathematics Excellence. Setting and Achieving Goals The Phoenix Career Services Career Plan home page has a list of my long-term goals with due dates. To meet those goals, short-term goals must be met, and this page must be reviewed often and necessary changes made in order to keep realistic deadlines. Using the SMART goals system: Specific, Measurable, Attainable, Relevant, Time Frame; will ensure my goals are things that will be achieved. Creating exact goals with specific details, measurable progress, attainability, relevance, and a time frame will help reach my goals. (Chapter 4, Page 102, Carter, Bishop, Kravits, 2011) Obstacles may force me to reevaluate my goal deadlines to verify they are still attainable. Long-term goals can be flexible, but should never vanish completely. A degree from University of Phoenix will allow me many opportunities when looking for a job. Upholding Academic Honesty To uphold academic honesty I need to review the Student Code of Academic Integrity at least once a year or if there are changes to it. A violation of the Student Code of Academic Integrity could have severe consequences including expulsion from school, depending on the severity of the dishonest action. Plagiarism, self-plagiarism, double-dipping or dovetailing, fabrication of information, unauthorized assistance, copyright infringement, misrepresentation, and collusion are all academically dishonest. (University of Phoenix, 2011) I can avoid academic dishonesty by citing every resource I use, submitting my work to the Plagiarism Checker, and making sure my work is no more than 20% copied information. Managing Time Wisely Awareness of how much time is spent on different activities throughout the day and adjusting those activities accordingly, can allow me to effectively manage my time. Keeping a diary of activities for a couple of days every few months will allow me see how much time is spent doing certain activities, and can help me shift time from one activity to another. Caring for my family will always be my first priority. Since I am not working outside of the home, school is my second priority. Allowing myself time to de-stress and relax is important, but needs to be kept to a minimum so I am not spending hours on end playing games or reading Facebook. Fostering Reading Comprehension and Retention Using the SQ3R method in all of my academic reading assignments will enhance my reading comprehension. (Chapter 7, Page 191, Carter, Bishop, Kravits, 2011) â€Å"SQ3R is an acronym for survey, question, read, recite, and review. † (Chapter 7, Page 190, Carter, Bishop, Kravits, 2011) Surveying reading assignments allows me to look for bold words and headings which I can write my questions about. (Chapter 7, Pages 191-192, Carter, Bishop, Kravits, 2011) Finding the main idea of what I am reading, prioritizing key points, and highlighting information that stands out will help during the review phase. (Chapter 7, Page 196, Carter, Bishop, Kravits, 2011) Reciting the answers to the questions I raised will help me commit the information to memory. (Chapter 7, Page 197, Carter, Bishop, Kravits, 2011) Reviewing my questions and answers, summarizing the highlighted portions, and quizzing myself on different aspects of the material during the review phase will also be helpful. (Chapter 7, Page 198, Carter, Bishop, Kravits, 2011) Another study technique is using flashcards so I can memorize important information, especially vocabulary words or historical dates. Using study skill that work with my multiple intelligences can be helpful. Moving around while reviewing flashcards, listening to music while reading, or cutting and pasting material I have read into documents with similar ideas could all be advantageous to my studying skills. (Chapter 7, Page 204, Carter, Bishop, Kravits, 2011) When highlighting I should avoid over marking and use a regular pen or pencil instead of a highlighter. (Chapter 7, Page 205, Carter, Bishop, Kravits, 2011) Making notes in the margins will help master content. (Chapter 7, Page 206, Carter, Bishop, Kravits, 2011) Adapting Work Habits to Fit My Personality Located in the Phoenix Career Services tab on the Library page are items to survey different areas of my personality: career interests, personal competencies, work culture preferences, and reasoning aptitude. Knowledge of my personal competencies can be advantageous in all aspects of my life. I am one to follow instructions, to cooperate, and to adhere to values. University of Phoenix’s My Career Plan page defines following directions as â€Å"appropriately follows instructions from others without unnecessarily challenging authority; follows procedures and policies; keeps to schedules; arrives punctually for work and meetings; demonstrates commitment to the organization; complies with legal obligations and safety requirements of the role. â€Å" (University of Phoenix, 2013) I do not like to be late no matter what. I thrive when there are policies, procedures and schedules to follow. I do what I am asked, remain organized, and confirm compliance with any laws when necessary. Defined on University of Phoenix’s My Career Plan someone who cooperates â€Å"shows respect for the views and contributions of other team members; shows empathy; listens, supports and cares for others; consults others and shares information and expertise with them; builds team spirit and reconciles conflict; adapts to the team and fits in well. † (University of Phoenix, 2013) Working as a team where I can share information with others respectfully, support each other’s ideas and expertise, and have an environment that is well designed with all the necessary resources in order for me to do my job well are also part of my personality. (University of Phoenix, 2013) Adhering to values means I do not change what I believe in or who I am, but University of Phoenix’s My Career Plan defines adhering to values as â€Å"upholds ethics and values; demonstrates integrity; promotes and defends equal opportunities, builds diverse teams; encourages organizational and individual responsibility towards the community and the environment. † (University of Phoenix, 2013) My reasoning aptitude page says, â€Å"Your profile shows you could work well in careers that use both cognitive abilities and practical skills. You may be attracted to practical work or to analytical work, or to careers that allows you to combine practical skills and thinking. † (University of Phoenix, 2013) I love having challenges in my career, and learning new skills or trying new tasks. Conclusion This Survival Guide provides information for continued success throughout my academic career at University of Phoenix. Keeping my goals up-to-date with deadlines will ensure that I meet my long-term goals, and do not lose sight of what I have set out to accomplish. I will review my goals and this guide often as a reminder of everything available to me for my success. References Appendix D. (2013). University of Phoenix: Associate Level Material, Version 10(Unknown), , 1. Carter, C. , Bishop, J. , Kravits, S. L. (2011). Keys to Effective Learning: Study Skills and Habits for Success (6th ed. ). Boston, MA: Pearson. University of Phoenix. (2011). Student Code of Academic Integrity. Retrieved from https://ecampus. phoenix. edu/secure/aapd/studentdocuments/uophx/academic_integrity. htm University of Phoenix. (2013). Phoenix Career Services: My Career Plan: Career Competencies. Retrieved from.

Henrik Isbens A Dolls House Essay -- A Dolls House Essays

Ibsen's "A Doll's House" In Ibsen’s â€Å"A Doll’s House†, in Act Two Scene 6, Nora’s deceptive behaviour and desperation reaches its climax due to the arrival of the letter. This is because the letter contains the means she used to get hold of the money. During the time when the play took place, society frowned upon women asserting themselves. Women were supposed to play the role in which they supported their husbands, took care of their children and made sure that everything around the house was perfect. Work, politics and decisions were left to the males. Nora broke the law and decided to borrow money to pay for her husband’s treatment. She did not borrow the money in the ‘right’ way instead she forged her father’s signature. By doing this, she not only broke the law but also stepped away from the role society had placed on her, being totally dependent on her husband. In this scene, she faces the truth in the letter. The person from whom she borrowed the money, Krogstad, wants payment on the loan. He also blackmails her about influencing Helmer to give him a better job at the bank and hence increase his position in society. This causes Nora to try to keep the letter away from her husband; but what is the significance of the letter and what does it mean to Nora? Possibly, this letter catalyses how Nora acts and how she thinks and she has been deceiving Helmer for the whole of their marriage. This included all sorts of deceptions. One thing that a good audience can recogn...

Angelas Ashes

Chapter Three â€Å"He makes more tea and we have that with bread and jam so no one can say we didn't have a sweet Christmas. † McClure Page 101 Even though they went through all the despairs of the year and the embarrassment of carrying a pig head to have a happy they were still able to have a happy Christmas dinner. Chapter Four â€Å"l wanted the raisin to myself but This shows how selfless Frank is. Payday Cloche's that had standing in Even though he wants the raisin h the corner with no shoes and the mom was freezing and he was gives it to someone who will cherish shivering like a dog had been kicked it more than him. ND I always felt sad over kicked dogs so I walked over and gave Payday the raisin†¦ † McClure page 121 Chapter 5 â€Å"Sixpence will get the two of us in Since Frank doesn't want to take with outplace left Sleeves toffee. Dance he uses the money to enjoy McClure page 143 the luxuries he's not used too. Chapter 6 â€Å"His father is in a bed in the corner groaning and spitting into a bucket. † McClure page 164 It seems that in Franks day, death as more common than now especially for the people in poverty.Frank learns at an early age that death is inevitable. Chapter 7 â€Å"One of our prayers is surely powerful because, next summer Mackey himself is carried off by the GA Looping consumption†¦ † McClure Page 172 Franks life seems too surrounded by death. Ifs also ironic how Mackey wanted his siblings to die not knowing that his time was coming up slowly Chapter 8 † Patricia is gone and I'll never know what happened to the highwayman and Bess the landlord's daughter† Frank seems to be unpleased by Patrician's death.Since he so used to it, he barely flinches when Hess told McClure page 199 the news. He is more concerned on how the poem ends. Chapter 9 † She tells me give my eyes a good rib and make them look as red as I can for the worse you look at the Dispensary the more pity you get the better chance of getting the public assistance. † McClure page 232 In this chapter, since their father is using his check on beer in England, Angela has to get public assistance. She basically loses all of her dignity n the process.