Apollonius Of Perga :: essays research papers fc

Apollonius of Perga Apollonius was a great mathematician, known by his contempories as " The Great Geometer, " whose treatise Conics is one of the greatest scientific works from the ancient world. Most of his other treatise were lost, although their titles and a general indication of their contents were passed on by later writers, especially Pappus of Alexandria. As a youth Apollonius studied in Alexandria ( under the pupils of Euclid, according to Pappus ) and subsequently taught at the university there. He visited Pergamum, capital of a Hellenistic kingdom in western Anatolia, where a university and library similar to those in Alexandria had recently been built. While at Pergamum he met Eudemus and Attaluus, and he wrote the first edition of Conics. He addressed the prefaces of the first three books of the final edition to Eudemus and the remaining volumes to Attalus, whom some scholars identify as King Attalus I of Pergamum. It is clear from Apollonius' allusion to Euclid, Conon of Samos, and Nicoteles of Cyrene that he made the fullest use of his predecessors' works. Book 1-4 contain a systematic account of the essential principles of conics, which for the most part had been previously set forth by Euclid, Aristaeus and Menaechmus. A number of theorems in Book 3 and the greater part of Book 4 are new, however, and he introduced the terms parabola, eelipse, and hyperbola. Books 5-7 are clearly original. His genius takes its highest flight in Book 5, in which he considers normals as minimum and maximum straight lines drawn from given points to the curve ( independently of tangent properties ), discusses how many normals can be drawn from particular points, finds their feet by construction, and gives propositions determining the center of curvature at any points and leading at once to the Cartesian equation of the evolute of any conic. The first four books of the Conics survive in the original Grrek and the next three in Arabic translation. Book 8 is lost. The only other extant work of Apollonius is Cutting Off of a Ratio ( or On Proportional Section ), in an Arabic translation. Pappus mentions five additional works, Cutting off an Area ( or On Spatial Section ) , On Determinate Section, Tangencies, and Plane Loci. Tangencies embraced the following general problem : given three things, each of which may be a point, straight line, or circle, construct a circle tangent to the three. Sometimes known as the problem of Apollonius, the most difficult case arises when the three given things are circles. Of the other works of Apollonius referred to by ancient writers, one, On

Individual Analysis of Working in a Group Situation

In this paper I will describe and analyze my experience working in a group situation, writing a paper on the movie 12 Angry Men. I will address therapeutic communication techniques used in our group situation. I will address any conflicts that arose in our group. Utilizing Tuckman’s group process theory, I will also address the effectiveness of our group process. Individual Analysis of Working in a Group Situation Learning how to work effectively in a group situation is key to success in many professions as well as in social situations. Groups vary from each other based on the individuals that make up each group, all of us belong to various groups at one time or another. The roles that we fulfill vary from group to group, and may even vary within the same group over time. The purpose of this paper is to analyze the communication process and the interaction of my group during the completion of an assignment. The group consisted of four members. Our task was to prepare an analysis paper on the movie 12 Angry Men. Because this was only a four-member group focused on a single specific task, there was a high level of cohesiveness and no conflict. Our group would be considered a secondary group because the relationship was impersonal and goal-oriented (Arnold & Boggs, 2011). Every member of a group plays a certain functional role within the group. Some functional roles relate to the task aspect of the group, while others promote social interaction. These functions are manifested in the behaviors of individual members and affect group dynamics. Task functions include such behaviors as; identifying tasks, coordinating, clarifying and summarizing. Maintenance functions include such behaviors as harmonizing, gatekeeping, encouraging and compromising. All of the members of our group were task specialists (Arnold & Boggs, 2011). According to Arnold and Boggs (2011), when task specialists dominate a group, members become dissatisfied and collaboration is diminished. However, this was not the case with our group. Due to the fact that our group was very task oriented and we collaborated well with each other everyone was satisfied with the experience. Our group was able to effectively function without a designated leader. As a group, we had many strengths. I believe one of our biggest strengths was our effective communication. When we met in person all the members of our group used therapeutic communication such as active listening, paraphrasing, and summarizing. We were all very respectful of each other and maintained eye contact and receptive nonverbal communication. There were several times during the movie that we paused the movie to discuss the jurors’ ages, professions, or the dynamics between the different jurors. Normally it wouldn’t be acceptable to repeatedly pause a movie for discussion, but it was widely accepted among our group and did not cause any conflicts. Another form of communication that our group used was the internet. It enabled us to receive papers via email attachment, and then download, print, edit, and return the changes at our own leisure. The only drawback with using the internet for communication is the lack of acknowledgement. In the future I will make sure that I ask the recipient to acknowledge that they have received my communication. Groups do not always start off fully-formed and functioning. Bruce Tuckman's model of the developmental sequence in small groups suggests that groups grow through clearly defined stages, from their creation as groups of individuals, to cohesive, task-focused teams. There are five stages of Tuckman’s theory, forming, storming, norming, performing, and adjourning. During the forming stage of Tuckman's theory, group members meeting each other for the first time are primarily concerned with overcoming their discomfort with one another. In this phase, the group members are engaged in establishing boundaries and group norms for communication (Arnold & Boggs, 2011). In contrast to Tuckman’s description, our group did not introduce themselves or share their backgrounds or reasons for coming to the croup, since we have been together in class for a few weeks and had already been acquainted. Our group did not pass through all of Tuckman’s stages of group development. Specifically, we omitted the storming stage and passed from forming to norming. Tuckman's storming phase focuses on the interpersonal conflicts that erupt among the members as they compete with one another for leadership roles. According to Tuckman, the interpersonal conflicts that typically include personal criticisms undermine the group's ability to accomplish the task (Arnold & Boggs, 2011). There was no real conflict in our group, since there was no clear leader in our group and all of the members were very task oriented. According to Tuckman, during the norming phase the group has one goal and all group members take responsibility and work toward the success of the group's goals (Arnold & Boggs, 2011). Our group was able to arrive at this level of cohesiveness at the beginning of the first meeting. Our group agreed to watch the movie once by ourselves and then meet and watch the movie together, and once we had view the film we would decide as a group which questions to assign to each of the members. Tuckman’s preforming phase happened on our second meeting, when our group watched the movie. After viewing the movie we discussed each question and collaboratively decided who would be most knowledgeable about each of the different areas. After dividing up the different areas of the paper we decided on a date that we would email our individual sections to Katie. The final phase of Tuckman’s theory is the adjourning phase. Our group reached this phase after we completed our final paper with the satisfaction of all of the group members. I left the group with a real feeling of satisfaction at having achieved what I set out to do. Throughout this group process has been helpful in a number of ways. I have learned how to communicate more effectively and I have also learned to step outside of my comfort zone. I have also leaned to be more conscious of my body language, because it is more effective than what you say. This group project has helped me learn how to convey my thoughts, feelings, opinions and ideas to my group in an effective manner. . I will be able to apply what I have learned to my work and also to future group projects at school. Groups are a fundamental structure for accomplishing a wide variety of tasks. An effective group has many traits or characteristics that combine to ensure that it is able to reach its goals and objectives in a manner that is conducive to a high level of performance. Most groups go through five separate stages before achieving effective collaboration. Bruce Tuckman described these stages as forming, storming, norming, performing, and adjourning. Several factors affect group performance: composition, size, norms, and cohesiveness. In working with groups it is important to be aware of the many factors that affect group performance and understand the individual as well as the group issues.

The Legacy of the Qin Dynasty

The Legacy of the Qin Dynasty The Qin Dynasty, pronounced like chin, emerged in 221 BCE. Qin Shihuang, the king of the Qin state at the time, conquered the many feudal territories vying for influence during the bloody Warring States period. He then united them all under one rule, thus putting an end to the notoriously violent chapter in Chinese history that lasted for 200 years. Qin Shihuang was only 38 years old when he came into power. He created the title Emperor (  Ã§Å¡â€¡Ã¥ ¸ ,  Ã‚  hungdà ¬) for himself, and thus is known as  the first emperor of China. While his dynasty only lasted 15 years, the shortest dynastic rule in Chinese history, the impact of the Qin Emperor on China cannot be understated. Although highly controversial, Qin Dynasty policies were very influential in uniting China and maintaining power. The Qin Emperor was famously obsessed with immortality and even spent years trying to find an elixir to eternal life. Though he ultimately died, it would seem that Qin’s quest to live forever was ultimately granted – his practices and policies were carried into the subsequent Han Dynasty and continue to flourish in present-day China.   Here are just a few remnants of Qin’s legacy.   Central Rule The dynasty adhered to Legalist principles, which is a Chinese philosophy that followed strict compliance with  the rule of law. This belief allowed Qin to rule the population from a centralized power structure and proved to be a very effective way to govern. Such a policy, however, did not allow for dissent. Anyone who protested Qins power was quickly and brutally silenced or killed off.   Written Script   Qin instituted a uniform written language. Before then, different regions in China had different languages, dialects, and writing systems. Imposing a universal written language allowed for better communication and implementation of policies. For example, a singular script allowed scholars to share information with a greater number of people. It also led to the sharing of culture that was previously only experienced by a few. Additionally, a single language allowed later dynasties to communicate with nomadic tribes and pass along information on how to negotiate or fight with them. Roads The construction of roads allowed for greater connections between provinces and major cities. The dynasty also standardized the length of axles in carts so that they could all ride on the newly-built roads. Weights and Measures The dynasty standardized all weights and measures, which led to more efficient commerce. This conversion also allowed subsequent dynasties to develop a taxation system. Coinage In another effort to unify the empire, the Qin Dynasty standardized the Chinese currency. Doing so led to greater commerce across more regions.   The Great Wall The Qin Dynasty was responsible for the construction of the Great Wall of China. The Great Wall marked national boundaries and acted as a defensive infrastructure to protect against invading nomadic tribes from the north. However, later dynasties were more expansionist and built beyond Qin’s original wall. Today, the Great Wall of China is easily one of Chinas most iconic pieces of architecture. Terracotta Warriors   Another architectural feat that draws tourists to China is the enormous tomb in present-day Xian filled with terracotta warriors. This is also a part of Qin Shihuangs legacy. When Qin Shihuang died, he was buried in a tomb accompanied by an army of hundreds of thousands of terracotta soldiers that were supposed to protect him in his afterlife. The tomb was uncovered by farmers  digging for a well in 1974.   Strong Personality One other lasting impact of the Qin Dynasty is the influence of a leader’s personality in China. Qin Shihuang’s relied on his top-down method of ruling, and, on the whole, people conformed to his rule because of the power of his personality. Many subjects followed Qin because he showed them something larger than their local kingdomsa visionary idea of a cohesive nation-state. While this is a very effective way to rule, once the leader dies, so can his dynasty. After Qin Shihuang’s death in 210 BCE, his son, and later his grandson, took power, but both were short-lived. The Qin Dynasty came to a close in 206 BCE, just four years after Qin Shihuang’s death. Almost immediately following his death, the same warring states that he unified sprang up again and China was again under numerous leaders until it was unified under the  Han Dynasty. The Han would last over 400 years, but much of its practices were started in the Qin Dynasty. Similarities in charismatic cult personalities can be seen in subsequent leaders in Chinese history, such as Chairman Mao Zedong. In fact, Mao actually likened himself to Emperor Qin.   Representation in Pop Culture Qin was  popularized in Eastern and Western media in Chinese Director Zhang Yimou’s 2002 film Hero. While some criticized the movie for advocating totalitarianism, movie-goers went to see it in droves. A hit in China and Hong Kong, when it opened to North American audiences in 2004, it was the number one movie and grossed $18 million in its opening weekend – a rarity for a foreign film.