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 |
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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.
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