Euclidean, Spherical, Eliptic, and Hyperbolic geometry

Euclidean, Spherical, Eliptic, and Hyperbolic geometry Free Online Research Papers Though in schools most students learn Euclidean Geometry, there are actually many different types. These different types were developed by other mathematicians who developed theories and research that may have contradicted the work of other mathematicians. This resulted in the formation of four different types of geometry. The four types are Euclidean, Spherical, Eliptic(aslo known as Riemanns geometry), and hyperbolic.(Also known as lobachevskys geometry) Euclidean Geometry which is sometimes called flat or parabolic geometry is named after the greek mathematician Euclid of Alexandria. Euclid lived in alexandria, Egypt and is credited for writing Elements which is considered to be the most successful textbook in the history of mathematics. Also, he is known for his use of logical reasoning to prove mathematical theorems which is still the backbone to mathematics. One of his most credited accomplishments was his reasearch of Euclidean Geometry which is based almost entirely on his studies. Euclidean Geometry is based on rules called postulates. It is different from other geometries because of the parralel postulate which states that through a point not on a given straight line, one and only one line can be drawn that never meets the given line. This is what seperates Euclidean geometry from other types such as Reimann geometry where no parralel lines exist. In Euclidean geometry each point is mapped on a rectangular coordinate system in Euclidean space with a unique set of real numbers. It is used to describe points in space or on a plane to express geometric relations. Spherical geometry contradicts Euclidean geometry in two ways. Spherical geometry states that there are no parralels to a given line through an external point and the sum of angles and triangles is greater than 180 degrees. An understanding of this geometry can be made by considering geometry on the surface of a sphere where the shortest distance between two points is an arc of a great circle reather than a straight line. This is what seperates spherical geometry from Euclidean geometry. Because spherical geometry is based on great circles, all circles meet in two points on a spherical plane meaning that no two circles can be parralel. Also, In spherical geometry triangles and other angles exist where great circles meet. The triangles are formed where three great circles meet, using a portion of the equator and two meridians of longitude whos endpoints connect to one of the poles. Because the two angles at the equator would each measure 90 degrees the sum of all three would exceed 180 degrees. Reimann geometry, which is based on the studies of german mathematician Bernhard Reimann is extremely similar to spherical geometry. Bernhard Reimann is considered to be the most influential mathematician of the mid nineteenth century. His study of geometry, called Riemann geometry or Eliptic Geometry is much like spherical geometry in the statement that there are no parralels to a given line through an external point. Reimann geometry is also known as elliptic geometry because like an elipse, a line in a plane in Reimann geometry has no point at infinity where parralels could intersect. Very opposite the studies of Reimann, is Lobachevskys geometry. Lobachevsky was a russian mathematician who is not only responsible for Hyperbolic geometry but also is credited fordeveloping a method for the approximation of roots of algebraic equations. Lobachevskys Geometry is also known as hyperbolic geometry. It is called hyperbolic geometry because just like a hyperbola has to asymptotes, a line on a hyperbolic plane has two points at infinity. Hyperbolic geometry explores the theorum that the sum of the angles of a triangle is less than 180 degrees which contradicts Reimann, spherical, and euclidean geometry. Euclidean states that the sum of the angles of a traingle always add up to 180 and Reimann and spherical geometries both state that the sum of the angles of a triangle exceeds 180 degrees. The best way to understand the hyperbolic plane is by using the image of a saddle-like or saddle-shaped surface. hyperbolic geometry states that two rays extending in either direction from a point, and not meeting a line are considered to be distinct parralels to that line. Another result of Lobachevskys geometry is the statement that there is a finite upper limit on the area of a triangle, corresponding to a traingle whose sides are parralel and all of whose angles are zero. All four of these types of geometry were developed by brilliant mathematicians and have sufficent proof that none is more correct than the other. All of been very influencial to the world of modern math and math of their own times. They are all huge contributions to the world around and are all widley used throughout the world. Research Papers on Euclidean, Spherical, Eliptic, and Hyperbolic geometryThe Hockey GameThree Concepts of PsychodynamicAssess the importance of Nationalism 1815-1850 EuropeTrailblazing by Eric AndersonMarketing of Lifeboy Soap A Unilever ProductMind TravelEffects of Television Violence on ChildrenStandardized TestingResearch Process Part OneOpen Architechture a white paper

The Scarlet Letter Essays (409 words) - Film, Free Essays

The Scarlet Letter Essays (409 words) - Film, Free Essays The Scarlet Letter The Scarlet Letter Death, deceit, beauty, and love: These are some of the many themes of Hawthorns The Scarlet Letter. The most visible theme in this novel of the four is love. They say that love can last forever, and this book is written proof. The protagonist, Hester Prynne, is a lovely lady who has committed one of the worst crimes a woman can, adultery. Her husband had sent her over to the new world from Europe. He had asked her to wait for him there until he finished some business. She had waited for two years. When it seemed that he would never come, she gave into temptation. After resurfacing incognito, her husband discovers the identity of the unnamed man that she had relations with. After all of her husband's attempts to destroy their love, they decided on leaving the country. That way they would not have to bear the shame that the town had grown to pay unto them. Even after her newly found love, Arthur Dimmesdale, had passed away her love for him still thrived. The punishment for her crime was she must wear a scarlet A on her bosom for the remainder of her life. Her daughter, Pearl, had stared at it, wondering what it was many times. She had grown accustomed to seeing her mother wearing it. The townspeople had all ridiculed her for her crime, but still commended her on her sewing skills. These skills displayed every day in plain site on Her chest. One event that truly explains the theme of this book is the part in the forest when Pearl sees her mother for the first time as her true self. She saw her as she used to be without the scarlet letter on her chest. Pearl's reaction was that of non-recognition. She would not even approach her mother because she did not recognize her. It was not until her mother put her hair up and the letter back on that she would come back. Though she loved her mother she had grown accustomed to seeing the letter everyday. If you grow up seeing something everyday and then all of a sudden it is gone it can be very traumatizing. Though at first Pearl was afraid of Arthur, she grew to love him in the end. The best part of this book is the theme of everlasting love. The rest of it is actually quite boring. If you like love stories this is a good one to read. There love and hardships end in tragedy just like real life.

Annotated bibliography Example | Topics and Well Written Essays - 500 words - 1

Annotated Bibliography Example Students were then allocated to either ethnically diverse or all Anglo groups. There were around 135 subjects. Individual and group responses were tabulated using Prisoner’s Dilemma task in which participants could either compete or help the other party. It was hypothesized that groups carrying collectivist cultural traditions will be more co-operative compared to the one carrying individualist cultural traditions. The results confirmed the hypothesis. The reasons cited by 82% of the subjects confirmed that they were expecting the other party to cooperate. Further analysis showed that ethnically diverse groups made more co-operative choices than the groups that composed solely of Anglos. The study emphasizes and addresses on one cultural dimension and one behavioral dimension in a collectivist setting. More research needs to be done using cultural differences on the individualism-collectivist dimension. The study helps explain the reader the impact of cultural differences on decision making in an organization when working in groups. It can help him when he is working in a culturally diverse group as he will know what to expect from other group members. It can also contribute to different models on leadership and group work and help reader gain a broader understanding of the organizational demographics. Hoftsede’s framework provides methodological, theoretical and practical contributions in the cultural domain. Its popularity has raised a lot of eyebrows and attracted considerable debate. Thus it became necessary to conduct further research to overcome its limitations. This study, seeks to address those limitations. The general belief that cultural influences reward preference is found in this study. The applicability of Hoftsede’s framework is tested through cross cultural comparison of reward preferences in four countries. The study used data collected from four different countries, comprising of 1000

Competition Essay Example | Topics and Well Written Essays - 250 words

Competition - Essay Example Competition can serve as a driving force that motivates children to work harder. In a school setting, competition can be a driving force towards better performance. When children recognize that they have rivals at a similar level, they face the compulsion of moving beyond their comfort zone. If there were no rivals, children would remain in their comfort zone without any additional efforts. For this reason, teachers should promote healthy competition within the school setting. In sports, competition can help children improve their talent and become more successful. When children are aware that there is always a winner in sports, they are more likely to nurture their talent. In addition, competition in sports makes children more excited a factor that makes them look forward to participating. Many children who have won in sports recognize the value of hard work and are willing to exert more efforts in other sectors of their lives. In different games, children require competition so that they may find the find the games exciting. Competition in games introduces children to the realities of life, which is defined by different levels of competition. Games that do not encourage competition are less thrilling for children. Many children prefer games that have a winner so that they can have more fun. Introducing children to competition helps them learn how to address losing, which is a common aspect of life. For this reason, healthy competition should be promoted in different aspects of children’s

Definition of Racism Essay Example | Topics and Well Written Essays - 750 words

Definition of Racism - Essay Example The influence of environmental factors such as the family, school, and religion which all played a part in molding the characteristics and traits of a person are downplayed; the characteristics of a person have already been determined by his/her race. Connotative Meaning The definition of racism above connotes that a specific race will have a specific set of qualities and characteristics which make it different from other races. That difference can be interpreted as superiority or inferiority depending on the person who looks at it. Some races, then, are simply superior to other races; they possess the genes that establish the superiority of their race even before they were born. Racism in this sense is a work of nature rather than a construction of culture and society. The belief that certain races are better than other races is another connotation of racism. It is a belief system that people hold about different races that influences how they see their own race and its relation to other races. This definition shows that races fall on a hierarchy; it could be a hierarchy of class, intelligence, or political power that guides people’s beliefs about their own and other people’s races. ... Racism can also lead people to discriminate against other races. This refers to the behavioral manifestation of racism. While other people keep racist ideas in their minds, others would act out those ideas and display racist behaviors. When people hold a belief of superiority or inferiority of other races, this could result to a discriminating or a hostile behavior towards people belonging to other races. Since a person believes that his/her race is better than others, he/she would tend to treat people belonging to a specific race unfairly and unjustly. The next connotation of racism that I’ll be tackling is about the distorted belief system that people hold against other races. First, there is no verifiable evidence which supports the idea that race predetermines the traits and characteristics of the people possessing it. There are just too many factors that influence people’s traits and characteristics. Attributing those traits and characteristics to race alone seems illogical. Second, there isn’t a single race that excels or performs best in a specific area such as business, sports, or politics, for instance. Successful people in those areas mentioned may come from different races (e.g. African-American Kobe Bryant and Argentinean Manu Ginobili for basketball). Racial differences are always present but these differences, however, are cultural in nature. A person’s accomplishment and achievement are only partially influenced by the culture he/she belongs to. Family, religion, education will have bigger influence than race in how a person grows and matures. It doesn’t follow, then, that differences in race will create superiority in a particular race. This notion of difference and otherness is another connotation of

Motorcycle Inustry Essay Example for Free

Motorcycle Inustry Essay Hero Honda launched CBZ 156cc motorcycle . Bajaj launched Kawasaki, Boxer AT CT . Royal enfield launched machismo A350 and lightning 535 . Kinetic engineering ltd launched Brat and kinetic challenger . 2000: There was a entry of new companies like TVS , Yamaha , (Lohia Motors) . Hero Honda launched Joy, Passion , and a remodeled Street. Bajaj launched KB Eliminator , KB Caliber Chroma , KB Aspire and KB Acer . LML came up with Adreno and Energy . Escorts Yamaha launched Crux and TVS Group launched Fiero . 2001: Bajaj launched the Pulsar range . TVS launched Victor 110cc . Yamaha upgraded the Crux version with Crux R. Kinetic engineering launched the GF125 and GF150. Background note:- Indian two wheeler market is divided into three major segments :- India is the 2nd largest user and 3rd largest manufacturer of two wheelers in the world. Bajaj Auto laid the foundation of the Indian two wheelers industry in 1948 by trading in imported Vespa scooters. Change in the Trend: Scooters dominated the Indian market till 1990. Thus till 1990 Bajaj was the undisputed leader in scooter market followed by LML Kinetic . After the Liberalisation , privatization and globalization , many companies entered into joint ventures and technical collaborations with foreign companies lke Honda , Suzuki , Yamaha etc. Due to introduction of 100-cc motorcycles an intersegment shift began to start which resulted in the decline in the sales of the motorcycles. Due to delayed launch of new and advanced scooter models , four stroke scooters prone to skidding risk and vibrations etc the demand for motorcycled went up. This demand was mainly driven by rural and semi-urban comsumers. In 2000 , the motorcycle market was characterized by the presence of sub segments based on price :- The Motorcycle Story:- In 1980’s factors namely high running and maintenance cost , perception that motorcycle is more suitable for rural roads , high price of motorcycle in comparison with mopeds or scooters and the availability of fairly new models of scooter led to a sharp decline in the growth of motorcycle segment. De-licensing in the motorcycle industry in mid-1980’s came to their rescue , and hence there was a healthy growth in the sales figure. In 1990 , motorcycle industry witnessed recession because of rising fuel prices , high input cost and reduced purchasing power due to significant rise in general price level and liquidity crisis in comsumer financing. In 1992 companies suffered big time . Entry of new players in the motorcycle market led to losses or fall in profits. In 1993, launch of 100-cc motorcycles led to a inter-segment shift began to take place and motorcycles sales began to grow as a result of flag in the recession. In 1999 , there was a big shift from demand of scooters to the demand of Motorcycles. This shift was mainly attributed tpo the change in customer’s preference towards fuel-efficient and appealing models, delay in launch of new scooters etc. PESTLE ANALYSIS :- Pestle analysis is a tool that can aid the organization in making strategies which will help them understand the external environment in which they operate now and will operate in the future. PESTLE FLOWCHART PESTLE Political/Legal:- 1. Restrictive policy of the govt. towards the car industry in the pre liberalization era . This indirectly helped the motorcycle industry to develop . 2. Delicensing of the automobile sector in mid 1980’s . This led to the entry of foreign players in the automobile industry 3. Break up of the joint venture between -Escorts Yamaha -TVS Suzuki -Hero Motors Honda Motors Due to these break ups Indian Companies were forced to invest in R D for manufacturing indigenously develop models Economical:- 1. High running and maintenance cost . High price of motorcycles in comparison with scooters or mopeds. Due to this companies had to reduce either the quality or had to increase the price of the motorcycles and this resulted in fall in the sales 2. Rise in fuel price high input , reduced purchasing power. This led to increase in the price level and gradually recession. Sociocultural:- 1. Rise in demand for personal transport. This created a demand for two wheelers in the industry 2. Inefficiency of public transportation system made people dissatisfied with it and they demanded some vehicle that could be economical and cater to their needs. 3. Perception that motorcycle were more suitable for the rural roads Availability of fairly new models of scooters. This led to sharp decline in growth of motorcycles . Technological:- 1. Due to Launch of 100-cc motorcycles there was a Intersegment shift and growth of sales figures of motorcycles. 2. Factors like delayed launch of advance scooter models fear of four stroke scooters being prone to increased skidding risks and vibration contributed in the decline in the demand of scooters.

HUMAN BEINGS AND NATURE DURING THE REVOLUTION OF THE MIND Essay

HUMAN BEINGS AND NATURE DURING THE REVOLUTION OF THE MIND "Enlightenment is man's release from his self-incurred tutelage. Tutelage is man's inability to make use of his understanding without direction from another. Self-incurred is this tutelage when its cause lies not in lack of reason but in lack of resolution and courage to use it without direction from another. Dare to Know! Have courage to use your own reason!- that is the motto of enlightenment." -Immanuel Kant, 1784 (1) From the sixteenth through the eighteenth centuries, a drastically new way of thinking developed in Western Civilization, a way of thinking that has shaped and defined the modern world. This new mode of thought evolved within two movements, the Scientific Revolution and the Enlightenment. These movements led Western Civilization to a departure from reverence for traditional authority, from a fatalistic view of the world, and from a blending of the spiritual and the secular, allowing the emergence of the individualistic, scientific, progress-oriented attitude that fuels the Western world today. The thinking of the leaders of the Scientific Revolution and the Enlightenment built upon and revolutionized that of Medieval and classical intellectuals. It introduced a belief that human beings could learn to control and conquer nature, defining their lives in new ways and leaving a fear of the supernatural behind. Departure from Traditional Authority The most obvious form in which this new way of thinking deviated from the norm was its rebellion against traditional authority, particularly the powerful authority of the Church. The rebellion against traditional authority, particularly the powerful authority of the Church. The astronomer Nicolaus Co... ...vilization, ed. Perry M. Rogers (Upper Saddle River, NJ: Prentice Hall, 1997): p. 23-24. 19. Marquis de Condorcet, "The Progress of the Human Mind," in Aspects of Western Civilization, ed. Perry M. Rogers (Upper Saddle River, NJ: Prentice Hall, 1997): p. 25-26. 20. William Harvey, "I Learn and Teach From the Fabric of Nature," from On the Circulation of the Blood, in Aspects of Western Civilization, ed. Perry M. Rogers (Upper Saddle River, NJ: Prentice Hall, 1997): p. 20-21. 21. Voltaire, "If God Did Not Exist, He Would Have To Be Invented," in Aspects of Western Civilization, ed. Perry M. Rogers (Upper Saddle River, NJ: Prentice Hall, 1997): p. 35-36. 22. Immanuel Kant, "What Is Enlightenment?" in Aspects of Western Civilization, ed. Perry M. Rogers (Upper Saddle River, NJ: Prentice Hall, 1997): p. 32.