Biography of John Napier, Scottish Mathematician

John Napier (1550-April 4, 1617) was a Scottish mathematician and theological writer who developed the concept of  logarithms and the decimal point as a mathematical calculation method. He also had an influence in the world of physics and astronomy. Fast Facts: John Napier Known For: Developing and introducing the concept of logarithms, Napiers Bones and the decimal point.Born: 1550 at Merchiston Castle, near  Edinburgh, ScotlandDied: April 4, 1617, at Merchiston CastleSpouse(s): Elizabeth Stirling (m. 1572-1579), Agnes ChisholmChildren: 12 (2 with Stirling, 10 with Chisholm)Notable Quote: Seeing there is nothing that is so troublesome to mathematical practice.... than the multiplications, divisions, square and cubical extractions of great numbers, which besides the tedious expense of time are... subject to many slippery errors, I began, therefore, to consider [how] I might remove those hindrances. Early Life Napier was born in Edinburgh, Scotland, into the Scottish nobility. Since his father was Sir Archibald Napier of Merchiston Castle, and his mother, Janet Bothwell, was the daughter of a member of Parliament, John Napier became the laird (property owner) of Merchiston. Napiers father was only 16 when his son, John, was born. As was the practice for members of the nobility, Napier did not enter school until he was 13. He did not stay in school very long, however. It is believed that he dropped out and traveled in  Europe to continue his studies. Little is known about these years, where or when he may have studied. In 1571, Napier turned 21 and returned to Scotland. The following year he married Elizabeth Stirling, daughter of Scottish mathematician James Stirling (1692-1770), and bat a castle at Gartnes in 1574. The couple had two children before Elizabeth died in 1579. Napier later married Agnes Chisholm, with whom he had ten children. On the death of his father in 1608, Napier and his family moved into Merchiston Castle, where he lived the rest of his life. Napiers father had been deeply interested and involved in religious matters, and Napier himself was no different. Because of his inherited wealth, he needed no professional position. He kept himself very busy by being involved with the political and religious controversies of his time. For the most part, religion and politics in Scotland at this time pitted Catholics against Protestants. Napier was anti-Catholic, as evidenced by his 1593 book against Catholicism and the papacy (office of the pope) entitled A Plaine Discovery of the Whole Revelation of St. John. This attack was so popular that it was translated into several languages and saw many editions. Napier always felt that if he attained any fame at all in his life, it would be because of that book. Becoming an Inventor As a person of high energy and curiosity, Napier paid much attention to his landholdings and tried to improve the workings of his estate. Around the Edinburgh area, he became widely known as Marvellous Merchiston for the many ingenious mechanisms he built to improve his crops and cattle. He experimented with fertilizers to enrich his land, invented an apparatus to remove water from flooded coal pits, and bat devices to better survey and measure land. He also wrote about plans to bad elaborate devices that would deflect any Spanish invasion of the British Isles. In addition, he described military devices that were similar to todays submarine, machine gun, and army tank. He never attempted to build any of the military instruments, however. Napier had a great interest in astronomy. which led to his contribution to mathematics. John was not just a stargazer; he was involved in research that required lengthy and time-consuming calculations of very large numbers. Once the idea came to him that there might be a better and simpler way to perform large number calculations, Napier focused on the issue and spent twenty years perfecting his idea. The result of this work is what we now call  logarithms. The Father of Logarithms and the Decimal Point Napier realized that all numbers can be expressed in what is now called exponential form, meaning 8 can be written as 23, 16 as 24  and so on. What makes logarithms so useful is the fact that the operations of multiplication and division are reduced to simple addition and subtraction. When very large numbers are expressed as a logarithm, multiplication becomes the addition of  exponents. Example: 102  times 105  can be calculated as 10  25  or 107. This is easier than 100 times 100,000. Napier first made this discovery known in 1614 in his book called A Description of the Wonderful Canon of Logarithms. The author briefly described and explained his inventions, but more importantly, he included his first set of logarithmic tables. These tables were a stroke of genius and a big hit with astronomers and scientists. It is said that English mathematician Henry Briggs was so influenced by the tables that he traveled to Scotland just to meet the inventor. This lead to a cooperative improvement including the development of  Base 10. Napier was also responsible for advancing the notion of the decimal fraction by introducing the use of the decimal point. His suggestion that a simple point could be used to separate the whole number and fractional parts of a number soon became accepted practice throughout Great Britain. Edited by Anne Marie Helmenstine, Ph.D.

Confidentiality Confidentiality And Confidentiality

Understanding Confidentiality Brooke S Bentley Liberty University Abstract Confidentiality is one of the most important, complicated and expected parts of counseling. Counselors and clients view confidentiality as an unspoken given, it is sometimes not discussed but expected. Counselors should always explain to a client reasons in which they may be required to break confidentiality. Confidentiality laws can vary from state to state so a counselor should always be aware and up to date on those laws depending on which state they are practicing in. Some states, like South Carolina, have adopted the ACA Code of Ethics as their own code. Counselors are deemed mandated reporters, which means they are required by law to report certain†¦show more content†¦Another type of duty a counselor should be aware of is the duty to protect, which is when the counselor is not only protecting a potential victim but the public, this may also require going to the police. There is no one set of rules regarding duty to warn or duty to protect for all states. Some s tates have adopted one exception, both or neither. Some states, like Florida, have adopted a law that allows the counselor the option of choosing to warn but not required to do so (Sommers, 2008). Although duty to warn can change from state to state, mandatory reporting is the same in most every state. Mandatory reporting is the responsibility a counselor has to protect those that can not protect themselves, for instance children and the elderly. The vignette presentation explains other situations in which confidentiality can be broken including; suing someone for compensation, malpractice suits against counselors, some custody battles are a few or when there is no expectation of confidentiality (Sommers, 2008). Discovery ACA Code of Ethics Confidentiality should not be a complicated subject for a counselor, simply keep your clients information to yourself, however it is anything but that simple. A client seeking counseling will have a high expectation of privacy regarding the personal information they choose to share in sessions. It is and should always

River Road Community Free Essays

We re all going to have to learn how to walk again. After a nuclear holocaust devastates the country of the United States, the people of the River Road Community have to work through adversity and strive for the survival of every family. Households have to do without the things they would usually have taken for granted. We will write a custom essay sample on River Road Community or any similar topic only for you Order Now They have to bond together to fight the trials of learning to walk. Frank s quote demonstrates his understanding of the task ahead of them as they start to learn to live again. They would have to begin by crawling before they can once more stand-up on both feet. Frank s quote is manifested throughout the story by the observed changes in the lifestyle of the community, the ways in which the diminishment of supplies are dealt with, and how the loss of community members forces others to take on new roles. After the nuclear holocaust, the lifestyle of the River Road community changed drastically. Before The Day, many residents of the community were wastrels. These rejects of society lived each day to eat, drink, and sleep. They lacked the drive to succeed in everyday life. After the bomb drop, everything changed. These blots on modern society crawled out of their shells in order to contribute something to a struggling society. They worked hard on construction and other things that would help the community. This strenuous work gave these once slobs a new outlook on life as well as the regular exercise they lacked. But, this sudden increase in work was not the only variable playing a role on them. After the bomb, anarchy broke out among community and surrounding towns. Highwaymen robbed the innocent, and people were taken advantage of. They had to start over. Randy gained leadership for the community. The next part was to gain control. He and other community members formulated a plan in which to regain control. Once it was obtained, laws were made that would govern the growing community. The government had started all over again. Another lifestyle serve was in the economy. The US currency no longer had value. With no gold to back up the paper money, it was worthless (except as toilet paper). Instead, the River Road community relied on the barter system. Trades were made for the items that were needed. If one person needed a spoon, they could trade some honey for it. Because of the nuclear holocaust, the lifestyle of the River Road community changed. Another way in which the community had to learn how to walk again, arose from the lack of supplies. Before The Day, many residents live on a diet of beer and nuts. After the bomb incident, many of the foods found in the pre-bombed world were no longer available. During chapter 666, the food supply runs terribly low. Helen and Lib create a new salad using leaves and other greenery found around the house. This new salad would never have been attempted had it not been for the lack of food due to the holocaust. The nutritional value of this green salad, compared to the beer and nuts, shows a positive improvement in nutritional content of their diet. Another loss came as a result of the loss of running water after the nuclear holocaust. Not long after the water was cut off the tub supplies and other rations of water, which had been stored up, were running out. The community had to limit its use of water and cut back on things that on a pre-bomb day would have seemed natural (like flushing the toilet or taking a bath). The community adapted the Artesian water to use as their source for water. This water was not as nice as the purified water they had previously had, but it was water none-the-less. The harnessing of this water required the help of many. LALALAALA. Also, when medical supplies ran low, things had to be improvised. With just the aid of a billiard table, steak knives, darning needles, hair curlers, and nylon line, Dan operated on Ben Franklin, removing his appendix. This is just one example where things had to be invented due to a lack of supplies. They also decided to use hypnotism as a form of anesthesia. Dan could speak a few sentences, and they would fall into malleable trance. He would then be able to operate without the patient feeling the procedure. Another example of the River Road community having to learn to walk again would be with food preservation. Without the use of refrigerators and other systems for keeping food fresh, there was a great need for salt. The salt could be used to preserve most meats. An animal could be slaughtered, and part eaten for a meal. The remaining portions of the animal could be salted and kept for a while. Towards the end of July, Randy noticed the salt supplies running dangerously low. He and many other members of the community had to set sail in search of a source for salt. They did return triumphantly with many bags of salt. These are all ways in which the community has adapted to a loss of supplies and had to work through the adversity and learn to walk again. The last way in which the River Road community had to learn to walk again was how the loss of community members forces the others to take on new jobs. When the towns were bombed, many skilled people were lost. Jobs needed to be filled and the residents of the River Road community rose to the challenge. Helen served as the barber for the group, cutting everyone s hair. Randy was the leader. He took control of the group and returned order to an anarchical society. Dan took over as the full time doctor, and Lib took over most of the cooking. Many Frank s quote, we re all going to have to learn how to walk again†¦, is manifested throughout the story by the observed changes in the lifestyle of the community, the ways in which the diminishment of supplies are dealt with, and how the loss of community members forces others to take on new roles. The great disaster affected everyone, and everyone pulled together to strive through the hard times. The community, crippled by the nuclear blast, regained strength and managed to walk again. The road there was filled with hardship and pain, but the path made them stronger. The River Road Community survived the nuclear holocaust, even though they had to learn how to walk all over again. How to cite River Road Community, Essay examples

A Memorable Experience in Photography Essay Example For Students

A Memorable Experience in Photography Essay To experience photography, one must have a certain style of photographs to really appreciate or admire. Photographs are picturesque images and views that really catch the interest of the photographer. For me to experience and admire photography, it took me only one photographer to really appreciate the power it has his name is Robert Capa. Robert grew up in Hungary he experienced the political unrest and turmoil.He lived under the oppression of Horthy and knew the kind of anarchy that constitutes war(Images of War 8). Roberts work represented 3 categories:1. Images of battle.2. Images of the effects of war. 3. Images of calamity(Photographs,Introduction). His work also had a swift understanding and sympathy for the people who suffer from being caught in war. This type of suffering made itimpossible for him to ignore the events which affected their lives(Images of War 9). Roberts belief on photography is If your pictures are not good enough, your not close enough(Photographs Foreword).Roberts breakthrough in the field of photography came during the Spanish Civil War. His most famous picture was a snapshot of a courageous man in the act of falling(Capa18). His own special talents and course of world happenings, led him into a role as a professional photographer of war(Images of War20). To really admire and understand Capa, you must have a fascination for dramatic and emotional pictures of war. There probably has been thousands who admire the work he does. Well you can include me in that group of thousands. Capa puts into perspective in just one photograph, something my grandfather will never forget. The Bombing of Pearl Harbor. The phot ograph that brings back these memories is taken somewhere in Europe during World War II. Its a photograph that has the air full of scores of Japanese warplanes. They are flying over war stricken farmland. As an American citizen, this photograph brings a lot of emotions through me and would have brought greater emotions to my grandfather. I used this photograph because it brings back the memory of my grandfather telling me the story of how he survived that tragic day. On December 7, 1941, my grandfather was stationed at Pearl Harbor as a airplane mechanic. It was still early in the morning and he was still sleeping. Then out of nowhere he heard numerous explosions and then the sirens went off._ _He rushed out of bed and ran upstairs to see what was happening. In the sky he saw scores of Japanese airplanes flying and bombing the area. Some of the airplanes would risk their own lives to do more damage to the ships and the harbor. My grandfather said it was just unbelievable what was happening. You had to of been here to have a clear picture of the destroyed surroundings. Numerous airplanes and ships were being destroyed and hundreds were being wounded or killed. My grandfather said he was so scared he did not know what to do. After it was all over he just sat their in midst of all the destruction and cried. After he got his emotions together, he helped in cleaning up one of the most disastrous events in United States history. This experience has been a emotional one for me. In my eyes my grandfather was a hero and Robert Capa helps me recollect that image in that one picture. This picture was not directly related to the event, but it brings back the memories of the day my grandfather told me the story. I never really was interested in photography, but now I realize the beauty and power it can have on your emotions. .ua5f41ffba507db857e3c586476d0a99c , .ua5f41ffba507db857e3c586476d0a99c .postImageUrl , .ua5f41ffba507db857e3c586476d0a99c .centered-text-area { min-height: 80px; position: relative; } .ua5f41ffba507db857e3c586476d0a99c , .ua5f41ffba507db857e3c586476d0a99c:hover , .ua5f41ffba507db857e3c586476d0a99c:visited , .ua5f41ffba507db857e3c586476d0a99c:active { border:0!important; } .ua5f41ffba507db857e3c586476d0a99c .clearfix:after { content: ""; display: table; clear: both; } .ua5f41ffba507db857e3c586476d0a99c { display: block; transition: background-color 250ms; webkit-transition: background-color 250ms; width: 100%; opacity: 1; transition: opacity 250ms; webkit-transition: opacity 250ms; background-color: #95A5A6; } .ua5f41ffba507db857e3c586476d0a99c:active , .ua5f41ffba507db857e3c586476d0a99c:hover { opacity: 1; transition: opacity 250ms; webkit-transition: opacity 250ms; background-color: #2C3E50; } .ua5f41ffba507db857e3c586476d0a99c .centered-text-area { width: 100%; position: relative ; } .ua5f41ffba507db857e3c586476d0a99c .ctaText { border-bottom: 0 solid #fff; color: #2980B9; font-size: 16px; font-weight: bold; margin: 0; padding: 0; text-decoration: underline; } .ua5f41ffba507db857e3c586476d0a99c .postTitle { color: #FFFFFF; font-size: 16px; font-weight: 600; margin: 0; padding: 0; width: 100%; } .ua5f41ffba507db857e3c586476d0a99c .ctaButton { background-color: #7F8C8D!important; color: #2980B9; border: none; border-radius: 3px; box-shadow: none; font-size: 14px; font-weight: bold; line-height: 26px; moz-border-radius: 3px; text-align: center; text-decoration: none; text-shadow: none; width: 80px; min-height: 80px; background: url(https://artscolumbia.org/wp-content/plugins/intelly-related-posts/assets/images/simple-arrow.png)no-repeat; position: absolute; right: 0; top: 0; } .ua5f41ffba507db857e3c586476d0a99c:hover .ctaButton { background-color: #34495E!important; } .ua5f41ffba507db857e3c586476d0a99c .centered-text { display: table; height: 80px; padding-left : 18px; top: 0; } .ua5f41ffba507db857e3c586476d0a99c .ua5f41ffba507db857e3c586476d0a99c-content { display: table-cell; margin: 0; padding: 0; padding-right: 108px; position: relative; vertical-align: middle; width: 100%; } .ua5f41ffba507db857e3c586476d0a99c:after { content: ""; display: block; clear: both; } READ: Pearl Harbor - Brief Look EssayWorks Cited Capa, Robert. New York: Grossman, 1974. Capa, Robert. Images Of War New York: Paragraphic Books, 1974.Capa, Robert. PhotographsEds. Cornell Capa and Richard Whelan. New York: Alfred A. Knopf Inc, 1985.