Archimedes theory of a circle ABCD and a triangle K

Archimedes theory of a circle ABCD and a triangle K Archimedes compared the area enclosed by a circle to a right triangle whose base has the length of the circle’s circumference and whose height equals the circle’s radius. If the area of the circle is not equal to that of the triangle, then it must be either greater or less. He then eliminates each of these by contradiction, leaving equality as the only possibility. Archimedes’ proof consists of constructing a circle ABCD and a triangle K. Archimedes starts by inscribing a square in the circle and bisects the segments of arc AB, BC, CD, DE subtended by the sides of the square. Afterwards he proceeds to inscribe another polygon on the bisected points. He repeats this process until the difference in area between the circle and the inscribed polygon is smaller than the difference between the area of the circle and the area of the triangle. The polygon is then greater than the triangle K. Archimedes then proceeds to explain that a line from the center of the polygon to the bisection of one of its sides is shorter than the radius of the circle, and its circumference is smaller than the circumference of the circle. This disproves the statement that the polygon is greater than the triangle, since the legs of the triangle are made up of the radius and circumference of the circle. The triangle K cannot be both smaller and larger than the polygon, and thus cannot be smaller than the circle. After Archimedes proved that that the triangle cannot be smaller than the circle, he continues to prove that the triangle cannot be larger than the circle, either. This is accomplished by first assuming the triangle K to be larger than the circle ABCD. Then, a square is circumscribed around the circle so that lines drawn from the center of the circle will go through the points A, B, C, and D and bisect the corners of the square, one of which Archimedes labels T. Archimedes then connects the sides of the square with a tangent line and labels the points at which the line meets the square G and F. He goes on to say that because TG GA GH, the triangle formed by FTG is larger than half the area of the difference in area between the square and the circle. Archimedes uses the fact that continual bisecting of the arc of a circle will produce a polygon with this characteristic to assert that continuing this method will ultimately produce a polygon around the circle such that the difference in area between the polygon and the circle is less than the difference in area between the triangle K and the circle. The polygon is thus less in area than the triangle K The length of a line from the center of the circle to a side of the polygon is equal to the radius of the circle. However, the perimeter of the polygon is larger in length than the circumference of the circle, and since the circumference of the circle is equal to the length of the longer leg of the triangle, the polygon must be larger in area than the triangle K. Again, the triangle cannot be both larger and smaller than the polygon, so the triangle cannot be larger than the circle. Archimedes accomplished to prove his theory by using contradiction. After he proved that the triangle with legs equal to the radius and circumference of a given circle is not greater or less in area than that circle he concludes that the two must be equal in area.

Gay rights Essay Example | Topics and Well Written Essays - 500 words

Gay rights - Essay Example The main difference most probably is the treatment of the society towards the issue specifically since through the course of the movement’s history it had evolved in stages of prohibition, being trivial, being hated and being accepted and even legal (Andryszewski, 2000). Prior to openly promoting and fighting for gay rights, the gay people are also active promoting and fighting for other related civil issues. It can then be considered that their own situations inspired them (Clendinen & Nagourney, 2013). Based on another author, there are already initiatives toward gay civil rights fifty years before it had been given attention in the United States. The Scientific Humanitarian Committee which is considered as the forerunner of the rights of gay people was established in Germany with the visions of actively promoting gay civil rights, abolition of laws against gay people and information dissemination and education regarding gay people. It was then suppressed and halted during the period of the Nazis. In 1950, the Mattachine Society started the move in the United States although in 1924 the Society for Human Rights was established by Henry Gerber and in 1940 the Veterans Benevolent Association was established in New York City (Marcus, 2009). One of the most evident rise of the gay rights movement occurred in the middle of 1960s through the Stonewall event following the trend for the black civil right movement. The said group focused on ceasing the homosexual discrimination. It can be considered that during that year, there had been an epiphany and the gay population cannot wait to stand their ground and achieve their own rights. In the 70s, different institutions and mainstream organizations supported the fight by being against all forms of discriminations targeting the gay men and lesbians. Through the year 1969-70, gay liberation or â€Å"gay pride† became a highly popular and talked about social concept with active appearances in all forms of

Choose one topic in the attachment Essay Example | Topics and Well Written Essays - 1500 words

Choose one topic in the attachment - Essay Example The saying on regret mentioned above is the best way to sum up or describe the plot and story of this movie. In this movie, every person is related or their story is linked and connected with the other person. Therefore, every scene and story of every individual in the movie consists of complex situations which get along very well with each other. "Magnolia" is a film of sadness and loss, of lifelong bitterness, of children harmed and adults destroying themselves. (Magnolia Movie Review & Film Summary (1999) | Roger Ebert) It is said that Magnolia is not one of those movies which could be understood by every viewer. Even when Magnolia was released worldwide in 1999, there were many viewers and those who reviewed the movie, their responses were quite conventional regarding it. They believe that it is a representation of emotional vulnerability. Therefore, due to these reasons, this movie can be looked through various aspects, perspectives, and prism as it includes a religious world an d dimension. After releasing the first trailer of this movie, it demonstrates that the movie about love which is either lost, gained, given, or withheld according to different situations. Basically, the religious aspect which is given in this movie shows the action of trapping the conflicted sinners and miscreants due to their wrongdoings in past relationships of reprobating. As it is clearly shown that this movie does not really have a plot but it conveys a very strong message as well as some great views and points. As this movie is about the lives and doings of 9 to 11 individuals, it is really hard to have a specific plot on which a movie had to be directed but the least a good movie can do is to motivate and spread out a strong message to its viewers. Not only the movie brings forward the shortcomings and fear but also sexual and emotional abuse. It is said that the people and viewers who call this movie exemplary are â€Å"actively dodging the social gravity, the psychological resonance, and the emotional poignancy of the conflicts mined in the film’s sensitive writing and talented ensemble acting. Most of the Magnolia’s characters have hit a crisis point at the start of the story. (Lane, 2) Anderson’s (the director) only philosophy was that bigger is better which was proven right with the help of this movie. However there are certain points in the movie where the director has shown inability to create a good film. It would be one thing if Magnolia offered multiple points of view, but Anderson is really only concerned with his own: a heavy-handed, self-pitying indictment of bad parenting and its sorry effects. Anderson expands his timeworn theme with a motif about chance and destiny (MAGNOLIA) As this movie is basically based on 9 to 11 people’s lives who are faced with regrets, his biggest failure in this movie is technical failing. As from every person to the stories and scenes, everything is linked and correlated. Therefore , switching the stories and making right decision at the right time is a difficult task. Therefore, the narration and writing of this movie is very complex. He has not perfected it yet that the way he crosscuts and switches from one scene to another which eventually is not the match of temporal relationships. For instance, there was a scene where a couple breaks up at one second, and the next moment the whole movie is switched Stanley who was the genius boy, deciding to put a stop at playing the tawdry game show. Even

The Changing of American Workplace Assignment Example | Topics and Well Written Essays - 2000 words

The Changing of American Workplace - Assignment Example The Changing of American Workplace There are various factors which may affect the workplace and working environment in a radical manner. One of the important factors is balancing family and work life. Balancing family and work life signifies that an individual should be engaged as well as satisfied with his or her responsibilities in relation to work life and family life. Employees are required to develop a balance amid work life and their personal life so that they are able to perform their activities in a relaxed way with zeal and dedication. Furthermore, the instability in personal and professional life has been affecting the working environment as well as personal life. It has been ascertained that there lays numerous factors such as workload pressure, demographic changes in relation to dual-income family and the sandwich generation and changes in workforce composition which dramatically influence both personal as well as professional life. This paper intends to discuss the various factors in relation to work-life balance which are accountable for affecting environment and workplace environment. Additionally, the discussion will also emphasize on asserting certain recommendations towards facilitating social as well as economic benefits. Work-life balance plays an important role in the life of every individual. Moreover, this aspect is also seemed to be adversely affecting the workplace and working environment. There are few major components on which the balances for work and life are dependent. These components are as follows: Time Balance An individual is required to devote equal time for personal and professional life. In this respect, time should be managed in an effective manner with the objective of creating a better balance amid work and life so that an individual is able to play his or her role proficiently. Time is to be managed in a flexible way so that individuals are capable to co-ordinate their activities efficiently (European Agency for Safety and Health at Work, 2013). Involvement Balance Individuals are required to be involved psychologically in both family life as well as work life. In this regard, individuals should be mentally involved with activities in order to accomplish the required objectives successfully. Subsequently, employees with better psychological involvement are likely to deliver or execute their activities in accordance with the objectives and goals of an organization (European Agency for Safety and Health at Work, 2013). Satisfaction Balance Individuals are required to have a balance in their satisfaction level both in their roles as well as activities which are performed in their professional and personal life. The appropriate balance in their professional as well as personal life, employees will attain increased level of satisfaction from their work and personal life accomplishments (European Agency for Safety and Health at Work, 2013). These are the three major components which are essential for employees in order to manage and balance their work as well as personal life. On the basis of these three elements a work-life balance can be ascertained. The working environment and workplace are significantly influenced with certain social changes. The social chan ges are the major factors which are accountable for an increased concern in relation to balancing professional and personal life in an effective manner. The ultimate factor which is primarily accountable for the social changes in the working environ

Africa’s Physical Geography

Africa’s Physical Geography Africas Physical Geography Africa is a continent rich in beauty, culture, and wealth. It has several diverse and singularly captivating landscapes including vast savannah and desert, lush rainforest, and sun-kissed beaches. There is potential for great wealth and prosperity, due to the resources in this luminous continent. North and South Africa are split into almost two equal parts by the equator, and the climate and physical features in both the north and the south repeat themselves. For example, the Sahara and Kalahari deserts, the Cape region and the Mediterranean, and the Karoo and the Maghreb. It is incredibly hot in most places, and insanely bright. Although it is so diverse, Africa is mainly made up of rolling flat plateaus. There is not a great variety of physical features, though those that are there can be quite remarkable. Compared to other continents, there are few broad coastal plains. It is an enormous mass of land, connecting at the Isthmus of Suez to Asia and almost to Europe at Gibraltar. Africa is the only continent which lies in all four hemispheres, lying on the equator at zero degrees latitude and Prime Meridian at zero degrees longitude. It has no deep indentations and very few well defined peninsulas. Africa is surrounded by major bodies of water such as the Mediterranean Sea in the north, the Red Sea in the northeast, the Atlantic Ocean in the west, and the Indian Ocean in the southeast. The coast, stretching 18,900 miles is largely level. There are few islands, Madagascar being the largest and the thirteen Canary islands being the largest group. The major landforms of Africa include the Nile River System, Atlas Mountains, Great Rift Valley, Sahel, Congo River Basin, Kalahari Desert, and the Sahara Desert. The Nile River is the longest river in the world with a length of 4,160 miles. It runs north, rising from the highlands of the southeast, and then draining into the Mediterranean Sea. It is made up of multifarious dams, rapids, streams, swamps, rivers, rapids, and tributaries. The major rivers making up the Nile are the Albert Nile, Blue Nile, White Nile, and the Victoria Nile. The great Nile River is a lifeline for the inhabitants on its banks. It provides nourishment for crops which are both food and a means of business. The Atlas Mountains are located in Northern Africa and stretch from southwestern Morocco across the coast of the Mediterranean, to the extreme east of Tunisia. These mountains are made up of several smaller mountain ranges namely, the High Atlas, Middle Atlas, and Maritime Atlas. The highest in the entire range is Mt. Toubkal located in western Morocco at a height of 13,671 feet. The Great Rift Valley is a dramatic depression in the surface of the earth which extends from an area near the Red Sea in Jordan in the Middle East, to the country of Mozambique in Africa, which is a length of about approximately 4,000 miles. The Great Rift Valley is essentially a series of depressions caused by volcanic activity thousands of years ago, which also created what is now called the Ethiopian Highlands. Some of the highest peaks in the continent are found in the Great Rift Valley including Mount Kilimanjaro, Mount Kenya, and Mount Margherita. The Sahel is a great expanse of land running across north and central Africa, across the extreme southern Sahara. The Sahel is the transition between the desert conditions of the north and the tropical conditions of the south. The region receives very little rainfall, about six to eight inches annually, and vegetation is relatively sparse. The Congo River Basin dominates the landscape of the Democratic Republic of Congo and a large portion of neighboring Congo. It also stretches into Angola, the Central Republic of Africa, Cameroon, and Zambia. This fertile basin contains about twenty percent of the worlds rainforest. The Congo River Basin is about 1,400,000 square miles in size. The Congo River is the second longest river in Africa and is made up of multiple tributaries, streams, and rivers that help intertwine the people in the cities along the banks of these waterways. The Kalahari is the major desert of southern Africa. It extends about 100,000 square miles and covers much of Botswana, the southwestern region of South Africa, and all of western Namibia. Dry river beds and shrubs crisscross along the desert plateau. A few small mountain ranges are located in the Kalahari Desert: the Karas and the Huns. The Kalahari Gemsbok Wildlife National Park in southern Africa near the border of Namibia hosts large herds of animals. The Sahara Desert covers about one-third of Africa, making it the largest desert in Africa and is around 3,500,000 square miles in total size. Elevations range from one hundred feet below sea level to mountains which exceed 11,000 feet (the Ahaggar and Tibetsi mountains). The Libyan, Western desert of Egypt, and Nubian deserts are regional deserts located just west of the Nile. The area receives almost absolutely no rainfall, although a few rivers flow from the Atlas Mountains underground which assist in irrigating alienated oases. The water of the Nile helps fertilize the eastern parts of the landscape. These landforms occupy a large section of the land, and the climate, resources, and vegetation of these are similar to those of the countries they stretch through. The people are largely reliant on the natural resources the earth yields in their country. Agriculture makes up a huge part of the economies of several countries. Each country has its own unique characteristics and although each separate one cannot be listed here, it is accurate to say that Africa is a diverse country which could be rich due to the resources the breathtaking country yields, and which the inhabitants can manipulate to their profit. Bibliography: http://www.worldatlas.com/webimage/countrys/aflnd.htm

Essay --

Out of the many experiments being conducted, I have the pleasure of introducing a layered density column to the class. Density is defined as mass divided by volume or the amount of stuff in a certain amount of space. Composed of many different household products (vegetable oil, rubbing alcohol, and even water), density columns present different layers through the masses of each liquid. These columns can contain as many products the experimenter desires. The liquids chosen that have a higher density tend to weigh more, unlike those that weigh less and float to the top if poured into the column. Along with the liquids chosen objects can be placed into the column, and then we would be able to see how each layer has an effect on the objects. For my lab experiment, I will be using 7 products throughout my demonstration. I could use as many products that I want, however 7 is a common amount to start with. Every product will be measured according to the amount that the cup can hold. To conduct my experiment, I will be pouring the products into 2 ounce cups and will construct the column th...

Nursing Homes Essay

For many of us we have a place that we go to, to rest, relax, and sleep a place that’s filled with memories, laughter, tears, and family a place we call home. Then we have the people such as the elderly that is forced or persuaded to believe that their place of comfort where they shared in memories with their family and love ones in their home is no longer suitable to meet their demanding needs due the illness and capabilities. So, their love ones take them on a tour to this place that tries to imitate a familiar place, but are far from feeling like home. What is this place you may ask?! A nursing home that is â€Å"a home away from home†, really? In my opinion Nursing homes do not benefit the ones that it’s design to help, rehabilitate, and care for but to strip the elderly of their dignity, sense of belonging, and respect. Many elderly people are at times helpless and really depending heavily on the individual who was hired to help them with day-to-day activiti es that we may take for granted. We wake up every day get out of bed, go to the restroom, and dress ourselves without any assistance, but the elderly do not have the opportunity to do the same day-to-day activities without waiting tirelessly on the people who seem to have forgotten that the elderly are humans. I have personally experience the careless and unthinkable acts of the people who work at the nursing home from ignoring the elderly who is screaming desperately from the depths of their soul to the top of their lungs for help! Yet the workers walk on by as if the sounds of help are sounds of sweet humming birds singing. As we freely walk to the restroom and cleanse ourselves the elderly waits upon the answer of their call button that seems to go unanswered until the elderly has no choice, but to release all that they were holding onto themselves and their beds. A lot of families think that they are doing their elderly love ones a good deed by sending them to a place that portrays to be a loving and caring because the family feel that they are unable to provide the round the clock care that their love one’s now need. But little do they know the place that they are sending their love one’s is not the place that appears to be, in my experience you have to ensure that your love one is receiving the care that the nursing homes promise to deliver by making daily visits to show the workers that this particular resident has a family that care and visit daily. When the workers see that the residents have family that comes daily the worker tends to answer pages and stay on top of what their job consist  upon. However, if you are a family that don’t visit your love one daily but just on holidays your elderly love one is more at risk of neglect then the motto of most nursing homes â€Å"We want those special members of your family to become equally special members of ours. We want to relieve the anxiety and frustration you may be experiencing by providing a nursing home community of constant support, attention and personalized care. Above all, we want to serve each person entrusted to us with compassion, dignity, purpose and respect.†