Biography and the main scientific achievements of Archimedes
The history of the discovery of Archimedes formula to calculate areas and volumes of spheres, cylinders and other plane and solid geometric figures. The Archimedes screw - a machine to transport water from low-lying sources in the irrigation ditches.
| Рубрика | Математика |
| Вид | реферат |
| Язык | английский |
| Дата добавления | 20.12.2014 |
| Размер файла | 10,1 K |
Отправить свою хорошую работу в базу знаний просто. Используйте форму, расположенную ниже
Студенты, аспиранты, молодые ученые, использующие базу знаний в своей учебе и работе, будут вам очень благодарны.
Размещено на http://www.allbest.ru
Размещено на http://www.allbest.ru
Contents
When we think of the great scientists and mathematicians of the ancient world, who could forget Archimedes.
In the hearts and minds of scientists Archimedes occupies the same respectable position as Newton and Gauss. In his ancient Greek days he was known as the "the wise one," "the master" and "the great geometer". His works such as the "Death Ray" gained him popularity and fame that lasts till this day. He was one of the last great Greek mathematicians.
1. Biography
Archimedes was born c. 287 BC in the seaport city of Syracuse, Sicily. A biography of Archimedes was written by his friend Heracleides but this work has been lost. It is unknown, for instance, whether he ever married or had children. During his youth, Archimedes may have studied in Alexandria, Egypt, where Conon of Samos and Eratosthenes of Cyrene were contemporaries. He referred to Conon of Samos as his friend, while two of his works (The Method of Mechanical Theorems and the Cattle Problem) have introductions addressed to Eratosthenes . Archimedes died c. 212 BC during the Second Punic War.
2. Tomb of Archimedes
The tomb of Archimedes is famous for it depicts his famous diagram, a sphere in a cylinder of the exact height and diameter. Archimedes had earlier proved that the volume and surface area of the sphere would be two thirds that of the cylinder. In 75 B.C., 137 years after the death of Archimedes, it was Cicero who was responsible for giving respect and attention to Archimedes' tomb, which had been long neglected. Cicero had heard about the tomb of Archimedes, but it took him a long time to find it, as the local populace were unable to help. Ultimately he found it at the Agrigentine gate in Syracuse, covered in bushes. He cleaned up the tomb and gave it its due respect.
3. Discoveries in math
Some of the mathematical problems Archimedes solved concerned areas and volumes of geometric figures. He had to devise a better number system and a new way to determine the formula for the areas and volumes of spheres, cylinders, parabolas, and other plane and solid figures.
I'd like to tell about some of his famous discoveries.
Circles and spheres.
Archimedes showed that the surface of a sphere is four times that of a great circle, that the volume of a sphere is two-thirds the volume of a circumscribed cylinder, and that the surface of a sphere is two-thirds the surface of a circumscribed cylinder including its bases.
The Great Pyramid at Giza, constructed c. 2589-2566 BC, was built with a perimeter of about 1760 cubits and a height of about 280 cubits; the ratio 1760/280 ? 6.2857 is approximately equal to 2р ? 6.2832. Based on this ratio, some Egyptologists concluded that the pyramid builders had knowledge of р and deliberately designed the pyramid to incorporate the proportions of a circle. Others maintain that the suggested relationship to р is merely a coincidence, because there is no evidence that the pyramid builders had any knowledge of р, and because the dimensions of the pyramid are based on other factors.
The earliest written approximations of р are found in Egypt and Babylon, both within 1 percent of the true value. In Babylon, a clay tablet dated 1900-1600 BC has a geometrical statement that treats р as 25/8 = 3.1250. In Egypt, the Rhind Papyrus, dated around 1650 BC, but copied from a document dated to 1850 BC has a formula for the area of a circle that treats рas (16/9)2 ? 3.1605.
In India around 600 BC, the Shulba Sutras р as (9785/5568)2 ? 3.088. In 150 BC, or perhaps earlier, Indian sources treat р as ? 3.1622.
Two verses in the Hebrew Bible (written between the 8th and 3rd centuries BC) describe a ceremonial pool in the Temple of Solomon with a diameter of ten cubits and a circumference of thirty cubits; the verses imply р is about three if the pool is circular. Rabbi Nehemiah explained the discrepancy as being due to the thickness of the vessel. His early work of geometry, Mishnat ha-Middot, was written around 150 AD and takes the value of р to be three and one seventh.
In his measurements of circles, Archimedes showed that the exact value of pi (р) was between the numbers 310/71 and 31/7. He found this by approximating a circle by a regular polygon having 96 sides. This was the most accurate approximation of pi at that time.
Integration.
One of the methods he used to find the areas, volumes and surface areas of many bodies was an early form of integration. This was considered his greatest mathematical invention, leading to the field of Calculus.
To determine the area of sections bounded by geometric figures such as parabolas and ellipses, Archimedes broke the sections into an infinite number of rectangles and added the areas together.
Number system.
Unhappy with the unwieldy Greek number system, Archimedes proposed a number system capable of expressing extremely large numbers. Using that system, he calculated the number of grains of sand that would fill the known universe. In modern notation, that number is 8x1063.
Discoveries in physics.
Center of gravity.
He then applied his calculations and methods of geometry to physical objects, discovering fundamental theorems concerning the center of gravity of plane figures and solids.
Pump.
Archimedes' screw, also called the Archimedean screw or screwpump, is a machine historically used for transferring water from a low-lying body of water into irrigation ditches. The screw pump is commonly attributed to Archimedes on the occasion of his visit to Egypt, but this tradition may reflect only that the apparatus was unknown to the Greeks before Hellenistic times and introduced in his lifetime by unknown Greek engineers, although some writers have suggested the device may have been in use in Assyria some 350 years earlier. This type of water pump is still used in many parts of the world today.
Summary
archimedes geometric solid
I chose this theme because Archimedes is widely regarded as one of the greatest mathematicians ever - perhaps the most influential of them all. If that were not enough, he is also regarded as the father of mathematical physics and engineering, having created many widely used machines and construction principles. No other scientist or inventor has produced as many essential breakthroughs in both theory and practice.
Размещено на Allbest.ru
...Подобные документы
Characteristics of the main two-dimensional, three-dimensional and n-dimensional geometric shapes, their use in mathematics, physics and other. Properties of two-dimensional geometric shapes arranged on the plane: polygon, triangle, quadrilateral, circle.
топик [251,8 K], добавлен 21.12.2013Biography and description of the major scientific achievements of I. Newton, M. Faraday, T. Edison, B. Franklin and T. Jefferson. The history of the discovery of the differential calculuses, of the nature of white light, and of the law of gravitation.
контрольная работа [20,4 K], добавлен 08.11.2010The main characteristic features of Ancient and Medieval history of Ireland. The main events, dates and influential people of Early history of Ireland. The history of Christianity development. The great Norman and Viking invasions and achievements.
курсовая работа [34,6 K], добавлен 10.04.2013Biography. Physics in Rome. Nobel Prize and The Manhattan Project. Post-War Work. Personal life. Fermi's golden rule. Discovery of fermium. Facts. History. Binary compaunds. Basic factsIsotope. Notable characteristics.
курсовая работа [53,9 K], добавлен 19.12.2007Familiarity with the biography and the main activities of Louis Pasteur. General characteristics of the most famous and widespread discovery of the famous chemist. Louis Pasteur as French scientist, the founder of modern microbiology and immunology.
презентация [3,2 M], добавлен 03.06.2015Viruses as a special form of life, their role in Microbiology. Russian scientist DI Ivanov - discoverer of the tobacco mosaic virus and the founders of virology. History of discovery. Biography of the scientist and his major works. History of Virology.
презентация [2,3 M], добавлен 22.05.2014Modern development of tragedy, the main futures of the hero. A short biography and features a creative way of Arthur Miller, assessment of his literary achievements and heritage. Tragedy of Miller in "The crucible", features images of the main character.
курсовая работа [32,3 K], добавлен 08.07.2016Body Water Compartments. The main general physico-chemical laws. Disorders of water and electrolyte balance. Methods bodies of water in the body, and clinical manifestations. Planning and implementation of treatment fluid and electrolyte disorders.
презентация [1,1 M], добавлен 11.09.2014Machine Translation: The First 40 Years, 1949-1989, in 1990s. Machine Translation Quality. Machine Translation and Internet. Machine and Human Translation. Now it is time to analyze what has happened in the 50 years since machine translation began.
курсовая работа [66,9 K], добавлен 26.05.2005Biography of life of Peter Great, his childhood and late years. The reasons and preconditions of reforms of Peter in different spheres of the state. The characteristic of reforms, their value for history of Russia. Estimation of efficiency of reforms.
курсовая работа [40,4 K], добавлен 14.12.2011Users and uses of financial information. Range of areas of the accounting and finance. Financial activities and their management. Securities and stock exchanges. Parts of the balance sheet: assets and liabilities. Main external sources of finance.
контрольная работа [20,7 K], добавлен 20.05.2010Research of causes of explosion of the plane in the city of Lokerbi (flight 103 Pan Am) on December 21, 1988 in Scotland which carried away for itself lives of 259 people. 11 years of searches of the guilty terrorists who have enclosed a bomb the plane.
курсовая работа [22,9 K], добавлен 11.11.2013Water - the beauty of nature. Description of several ways to determine if good water you drink or not. The study of the quality of bottled water producing in Ukraine. The definition of bottled water given by the International Bottled Water Association.
презентация [2,0 M], добавлен 21.05.2013Analysis of specific features of plane Il-76. Basic technical descriptions and destiny of Il-76. Ilyushin as a designer of plane Il-76. Reasons of popularity of IL 76 all over the world, the tests of the military plane, features of emergency equipment.
отчет по практике [105,1 K], добавлен 26.05.2012The physiological, hygienic and epidemiological value of water. Diseases associated with water factor. Measures to prevent transmission of infectious diseases through the water. Influence of biological factors on survival of microorganisms in water.
презентация [762,9 K], добавлен 17.05.2016Theory of economics was created and is developed by the economists of different schools. Main article: History of Economics. Areas of study. Techniques. Language and reasoning. Development of economic thought. The system of economic relations.
реферат [22,6 K], добавлен 12.05.2008Oxford is the oldest English-speaking university in the world and the largest research center in Oxford more than a hundred libraries and museums, its publisher. The main areas of training students. Admission to the university. Its history and structure.
презентация [1,6 M], добавлен 28.11.2012The clandestine tradition in Australian historiography. Russell Ward's Concise History of Australia. Abolishing the Catholics, Macintyre's selection of sources. Macintyre's historical method, abolishes Langism. Fundamental flaws in Macintyre's account.
реферат [170,7 K], добавлен 24.06.2010History, basic stages and directions of development of the first aircraft, its operating principle and internal structure. The study of this subject the Wright brothers, assessment of their contribution to the development of aircraft, its evolution.
презентация [1,8 M], добавлен 05.03.2015The interpretations of cybernetics. The term "cybernetics" has been associated with many stimulating conferences, yet cybernetics has not thrived as an organized scientific field within American universities. Questions about the history of cybernetics.
реферат [58,5 K], добавлен 24.06.2010
