In aerodynamics Bernoulli's principle is used to explain the pick up of an airplane wing in flight. (the Aerodynamic Development of the Formula One Car) wing is so constructed that air flows more quickly over its upper surface than its lower one, resulting in a reduction in pressure on the top surface when compared to the bottom. The resultant variation in pressure gives the pick up that maintains the aircraft in flight. If the wing is twisted overturned, the ensuing force is downwards. This gives details as to how racecars turn at such high speeds. The down force formed pushes the tyre into the road providing more control. In aerodynamics another vital feature is the pull or resistance acting on solid bodies moving through air. For instance, the propel force formed by the engine, must surmount the drag forces formed by the air flowing over an airplane. eorganizing the…...
Since the olden days, mathematics has been an area of study that has contributed much to diverse discoveries, inventions, and innovations of science and technology. Without mathematics, we will not experience the remarkable events of science, as well as the convenience that high technology brings to us. The academic mastery of mathematics is dominated by men, even up to these days. There are very few mathematician women who made a name in the field of mathematics. More especially in the past, social prejudices became a hindrance for women to master mathematics. At present, only three women captured success in the field of mathematics. They are Sonia Kovalevsky of Russia, Emmy Noether of Germany and U.S., and Maria Gaetana Agnesi of Italy (from Maria Agnesi and Her "Witch"). The following discussions in this paper is about Maria Gaetana Agnesi and her mathematics.
The Jansenists were condemned by the pope in 1653 and 1713. Characteristic beliefs of the school included "the idea of the total sinfulness of humanity, predestination, and the need for Christians to rely upon a faith in God which cannot be validated through human reason. Jansenism often, but it continued to have a strong following among those who tended to reject papal authority, but not strong moral beliefs" ("Jansenism," About.com, 2008).
After his final conversion, Pascal moved to the Jansenist monastery in Port Royal. He had already convinced his younger sister to move to the nunnery in the same location. It was there he penned the work that would contain his famous wager, the famous Pensees. He continued to live at the monastery until his death in 1662, worn out, it was said, "from study and overwork," although later historians think that tuberculosis stomach cancer was the likely culprit (Ball…...
Hajek, Alan. "Pascal's Wager." The Stanford Internet Encyclopedia of Philosophy. First Published Sat May 2, 1998; substantive revision Tue Feb 17, 2004. 8 Apr 2008. http://plato.stanford.edu/entries/pascal-wager/#4
" (assar, p.15) He had a wife and a young child by this time, and seemed to have a relatively stable if eccentric family and professional life. Then, the man, after a bout of mania became "frozen in a dreamlike state." (assar, p.19)
ash was treated for his dissociated states into paranoid schizophrenia with insulin therapy, drugs, shock therapy, and talk therapy, none of which seemed to help his condition. His wife at first stood by him, and then divorced him. The great mathematical genius that enabled ash to see patterns in behavior and numbers, and to construct predictable equations about human decision-making had dissolved into ravings about government agents, and nonsensical theorems.
After the failure of modern psychiatry and medicine to treat the mathematician, ash became "a phantom who haunted Princeton in the 1970s and 80s, scribbling on the blackboards and studying religious texts." (assar, p.19) Yet, while ash wandered aimlessly…...
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Nash was treated for his dissociated states into paranoid schizophrenia with insulin therapy, drugs, shock therapy, and talk therapy, none of which seemed to help his condition. His wife at first stood by him, and then divorced him. The great mathematical genius that enabled Nash to see patterns in behavior and numbers, and to construct predictable equations about human decision-making had dissolved into ravings about government agents, and nonsensical theorems.
After the failure of modern psychiatry and medicine to treat the mathematician, Nash became "a phantom who haunted Princeton in the 1970s and 80s, scribbling on the blackboards and studying religious texts." (Nassar, p.19) Yet, while Nash wandered aimlessly on the campus, this mathematician's former name, always great, suddenly "began to surface everywhere -- In economics textbooks, articles on evolutionary biology, political science treatises, mathematics journals," as his works, like that of all geniuses, became more rather than less relevant to modern life and modern thought. (Nassar, pp. 19-20).
Miraculously, by the time Nash was awarded the Nobel Prize in 1994, he had manifested a spontaneous recovery from his mental illness. Sometimes this happens with paranoid schizophrenics, although it is rare. His remission occurred without the aid of therapy or drugs, although his wife, whom he later remarried and lives with to this day, attributes his newfound enthusiasm to being in the atmosphere of campus life. Now, "at seventy-three John looks and sounds wonderfully well." Nash states that he is certain he will not suffer a relapse. "It is like a continuous process rather than just waking up from a dream." And understanding processes of the human mind in a rational and mathematical way were and are Nash's specialty. (Nassar, p. 389)
He however refused. Because of this, Polya could only return to his home country many years after the end of the war. Having taken wiss citizenship, Polya then married a wiss girl, tella Vera Weber, the daughter of a physics professor. He returned to Hungary only in 1967.
George Polya's professional life was as interesting as his personal pursuits. Before accepting an offer for an appointment in Frankfurt, Polya took time to travel to Paris in 1914, where he once again came into contact with a wide range of mathematicians.
Hurwitz influenced him greatly, and also held the chair of mathematics at the Eidgenssische Technische Hochschule Zurich. This mathematician arranged an appointment as Privatdozent for Polya at this institution, which the latter then accepted in favor of the Frankfurt appointment.
In addition to his teaching duties, Polya further pursued his passion for mathematics via his research efforts. He collaborated with zego in…...
Chinese Mathematics
In ancient China, the science of mathematics was subsumed under the larger practice of suan chu, or the "art of calculation." The Chinese are believed to be one of the first civilizations to develop and use the decimal numeral system. Their early mathematical studies have influenced science among neighboring Asian countries and beyond.
This paper examines the history of mathematical knowledge in China. It looks at the early Chinese achievements in the field of mathematics, including the decimal system, calculation of pi, the use of counting aids and the application of mathematical principles to everyday life. It also examines the influence of Indian and later, European mathematical knowledge into Chinese mathematics.
Early China
Unlike the ancient Greeks who prized knowledge for its own sake, much of the scientific studies conducted in ancient China were spurred by practical everyday needs. Because of its geographic location, China was prone to devastating floods, particularly along…...
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Works Cited
Martzloff, Jean-Claude. A History of Chinese Mathematics. New York: Springer Verlag, 1997.
Needham, Joseph. Science and Civilisation in China: Volume 3, Mathematics and the Sciences of the Heavens and the Earth. Cambridge: Cambridge University Press, 1959.
Spence, Jonathan D. To Change China: Western Advisers in China, 1620-1960. New York: Penguin Press, 200
Swetz, Frank. Was Pythagoras Chinese?: An Examination of Right Triangle Theory in Ancient China. Philadelphia: Pennsylvania State University Press, 1977.
He was miserably poor. ... He opened his book and began to explain some of his discoveries. I saw quite at once that there was something out of the way; but my knowledge did not permit me to judge whether he talked sense or nonsense. ... I asked him what he wanted. He said he wanted a pittance to live on so that he might pursue his researches" (O'Connor & Robertson, 1)
As history returns to Ramanujan's ideas and finds accuracy in most of them, Rao's response would demonstrate the degree to which the young man's internal insights had somehow transcended those of the best math minds amongst his predecessors and contemporaries. So would this be demonstrated in his trigonometric principles, such as that which is commonly referred to as the Ramanujan Conjecture. This is stated as "an assertion on the size of the tau function, which has as generating…...
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Works Cited:
Berndt, B.C. (1999). Rediscovering Ramanujan. India's National Magazine, 16.
Hoffman, M. (2002). Srinivasa Ramanujan. U.S. Naval Academy.
O'Connor, J.J. & Robertson, E.F. (1998). Srinivasa Aiyangar Ramanujan. University of St. Andrews-Scotland.
Wikipedia. (2009). Srinivasa Ramanujan. Wikimedia, Ltd. Inc.
Note the distinct similarities.
An examination of Escher's Circle Limit III can thus tell us much about distance in hyperbolic geometry. In both Escher's woodcut and the Poincare disk, the images showcased appear smaller as one's eye moves toward the edge of the circle. However, this is an illusion created by our traditional, Euclidean perceptions. Because of the way that distance is measured in a hyperbolic space, all of the objects shown in the circle are actually the same size. As we follow the backbones of the fish in Escher's representation, we can see, then, that the lines separating one fish from the next are actually all the same distance even though they appear to grow shorter. This is because, as already noted, the hyperbolic space stretches to infinity at its edges. There is no end. Therefore, the perception that the lines are getting smaller toward the edges is, in…...
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Works Cited
Corbitt, Mary Kay. "Geometry." World Book Multimedia Encyclopedia. World Book, Inc., 2003.
Dunham, Douglas. "A Tale Both Shocking and Hyperbolic." Math Horizons Apr. 2003: 22-26.
Ernst, Bruno. The Magic Mirror of M.C. Escher. NY: Barnes and Noble Books, 1994.
Granger, Tim. "Math Is Art." Teaching Children Mathematics 7.1 (Sept. 2000): 10.
Like Yardley, Agnes Meyer Driscoll was born in 1889, and her most significant contribution was also made during World War I. Driscoll worked as a cryptanalyst for the Navy, and as such broke many Japanese naval coding systems. In addition, Driscoll developed many of the early machine systems. Apart from being significantly intelligent for any person of her time and age, Driscoll was also unusual in terms of her gender. Her interests led her to technical and scientific studies during her college career, which was not typical for women of the time (NA). When she enlisted in the United tates Navy during 1918, Driscoll was assigned to the Code and ignal section of Communications, where she remained as a leader in her field until 1949.
As mentioned above, Driscoll's work also involved remerging technology in terms of machine development. These were aimed not only at creating ciphers, but also…...
Aristotle used mathematics in many of his other studies, as well. Another writer notes, "Aristotle used mathematics to try to 'see' the invisible patterns of sound that we recognize as music. Aristotle also used mathematics to try to describe the invisible structure of a dramatic performance" (Devlin 75-76). Aristotle used mathematics as a tool to enhance his other studies, and saw the value of creating and understanding theories of mathematics in everyday life and philosophy.
During his life, Aristotle also worked with theories developed by Eudoxus and others, and helped develop the theories of physics and some geometric theories, as well. Two authors quote Aristotle on mathematics. He writes, "These are in a way the converse of geometry. While geometry investigates physical lines but not qua physical, optics investigates mathematical lines, but qua physical, not qua mathematical" (O'Conner and obinson). He also commented on infinity, and did not believe that…...
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References
Devlin, Keith E. The Math Gene: How Mathematical Thinking Evolved and Why Numbers Are like Gossip. 1st ed. New York: Basic Books, 2000.
e. all loans. The same basic formulas using logarithms can be used to calculate the needed number of investments and/or the time period of investments at a given growth rate that will be needed in order to reach a target level of investments savings (Brown 2010). Both of these applications have very real implications for many individuals, whether they are trying to buy a home or planning for their retirement, as well as a n abundance of other issues related to personal banking. Logarithms are not only useful in highly technical scientific pursuits and investigations, then, but are directly applicable and necessary to situations that directly relate to and have an effect on people's daily lives.
What I found most interesting and surprising about the development of logarithms is that they are something that needed development in the first place. I suppose it is similar to having taken any invention that…...
Claude Shannon does not have the same name recognition as obert Oppenheimer, Albert Einstein, Alexander Bell, Bill Gates, or Doyle Brunson, but his work had an impact that rivaled each of these famous men. Shannon was a mathematician, an electrical engineer, and a cryptographer is famous in his field as the father of information theory. However, he also helped usher in the modern computer age, and used his mathematical knowledge to make money in Vegas playing blackjack, things that make him relevant to a modern society obsessed with computers and with gambling. In other words, Claude Shannon was a cool scientist before much of America realized that scientists could be cool.
Shannon always had tremendous promise as a scientist, and he realized that promise early in life. He was born April 30, 1916, and he spent much of his young life focused on attaining an education. He had an early interest…...
Poundstone, W. (2005). Fortune's formula: the untold story of the scientific betting system that beat the casinos and Wall Street. New York: Hill and Wang.
To protect themselves, many Americans chose to avoid working with or becoming friends with those who immigrated. A lack of trust permeated everything that the Americans did in regards to the immigrants, at least with the men. This was not always true of the women, as they often got along together and shared the trials and difficulties of raising families. However, many men who owned shops and stores would not hire an immigrant laborer (Glazer, 1998).
They believed that immigrants took jobs away from people in the U.S., and they did not want to catch any diseases that these immigrants might have brought with them. The general attitude during this time period was that immigrants were so different from Americans that they could never mesh into one society, but that attitude has obviously changed, as today America is a mix of all kinds of people (Glazer, 1998; Sowell, 1997).
Sublimation refers to this channeling of emotional intensity into creative work: to transform basic psychological or sexual urges into sublime revelations.
2. The collective unconscious is a term most commonly associated with the work of Carl Jung, a student of Freud's. Jung posited the existence of a grand database of human thought to which all persons have access. The idea that there is "nothing new under the sun" reflects the widespread belief in a collective unconscious. Common dreams, shared imagery, and similarity among world religions are extensions of the collective unconscious. The collective unconscious also serves as a wellspring of images, thoughts, sounds, and ideas that artists, musicians, and creative thinkers draw from during the creative process.
3. Archetypes are in fact part of the collective unconscious. Universal symbols or proto-ideas like "mother" or "father" are archetypal. Archetypes are what Plato referred to as the Forms. Jung deepened the theory of…...
Beautiful Mind" -- a Film
John Forbes Nash, Jr., an American Nobel Prize-winning mathematician, is such a notable individual that he is the subject of a book, a PBS documentary and a film. The film A Beautiful Mind (Crowe, et al. 2006) eliminates aspects of Nash's life and rewrites other aspects revealed in the book and documentary, possibly to make Nash a more sympathetic character for the audience. However, the film remains true to a consistent theme: in an individual's quest for satisfaction through self-fulfillment, the abnormal can also be the extraordinary.
The book and PBS documentary tell John Forbes Nash, Jr.'s story "from the outside looking in," immediately noting his abnormality in that he is a paranoid schizophrenic. The film takes a different approach, "from the inside looking out," so we experience the world as Nash experiences it and do not realize until half-way through the film that he is…...
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Works Cited
A Beautiful Mind. Directed by Ron Howard. Performed by Russell Crowe, Jennifer Connelly, Ed Harris and Paul Bettany. 2006.
Certainly! Here are some essay topic ideas for the movie "A Beautiful Mind":
1. Analyzing John Nash's character development throughout the film. 2. Exploring the theme of mental illness and its portrayal in "A Beautiful Mind." 3. Examining the impact of supporting characters on Nash's journey. 4. Discussing the representation of academia and intellectual pursuits in the movie. 5. Critically analyzing the use of visual effects and cinematic techniques to depict Nash's hallucinations. 6. Investigating the social and psychological implications of Nash's decision to conceal his mental illness. 7. Addressing the portrayal of love and relationships in the film, particularly focusing on Nash's marriage with Alicia. 8. Evaluating....
Begin with a compelling hook or question that captures the reader's attention. Define intersection theory and explain its significance in algebraic geometry. State the thesis statement, which should articulate the main argument or purpose of the essay.
II. Background and Historical Context
Provide a brief overview of the historical development of intersection theory. Discuss the contributions of key mathematicians, such as Bézout, Euler, and Poincaré. Explain the role of intersection theory in resolving classical geometric problems.
III. Fundamental Concepts
Define the basic concepts of intersection theory, such as: Intersection number Cycle Homology and cohomology....
Abstract Mathematics in Physics: A Transformative Force
Introduction
Mathematics has long played a pivotal role in the development of physics, offering a precise and abstract framework for understanding and describing the physical world. In recent decades, the influence of abstract mathematics in physics has grown exponentially, leading to groundbreaking insights and discoveries. This essay delves into the latest advancements in this area, examining specific examples that demonstrate the transformative power of abstract mathematics in modern physics.
String Theory and Calabi-Yau Manifolds
String theory is a promising candidate for a theory of everything that aims to unify all fundamental forces and particles. At its core,....
One potential essay topic could be exploring the role of abstract mathematical concepts in developing new theories and models in physics. This could involve discussing how abstract mathematical structures, such as group theory or differential geometry, have been used to describe and understand physical phenomena in innovative ways. Additionally, you could examine how the interplay between abstract mathematics and physics has led to the discovery of new principles and relationships in the natural world. Finally, you could also consider the philosophical implications of the use of abstract mathematics in physics, and how it challenges our understanding of reality and the....
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