Archimedes is undisputedly one of the greatest mathematicians and scientists produced by ancient Greek civilization. His outstanding contributions in many scientific fields have won him the favor of his contemporaries. He was highly respected and used his wisdom to subvert human history. Mechanics: Archimedes' achievements in mechanics are the most outstanding. 1. On the basis of summarizing the Egyptian experience of using levers to lift heavy objects, Archimedes systematically studied the center of gravity of objects and the principle of levers. He proposed a method to accurately determine the center of gravity of an object, pointing out that the object can be balanced by supporting it at the center; at the same time, in the process of studying machinery, he discovered and systematically proved Archimedes' principle (i.e., the lever law ), laying the foundation for statics. In addition, Archimedes designed and manufactured many machines using this principle. 2. In the process of studying floating bodies, he discovered the law of buoyancy, which is also the famous Archimedes' law. Its formula is: F float = G liquid displacement = ρ liquid gV liquid displacement. Geometry: Archimedes' mathematical achievement lies in the fact that he not only inherited and developed the ancient Greek scientific method of studying abstract mathematics, but also connected the research of mathematics with practical applications. 1. Archimedes determined the calculation methods for the areas of parabolic arcs, spirals, circles, and the surface areas and volumes of various complex geometric bodies such as ellipsoids and paraboloids. In the process of deriving these formulas, he created the "exhaustion method", which is similar to the method of gradually approximating limits in modern calculus. 2. He was the first person to scientifically study pi. He proposed to calculate pi by using the method of increasing the number of sides of polygons inscribed and circumscribed in a circle and gradually approaching their areas. He found that the range of pi is: 223/71lt; πlt; 22/7. 3. Faced with the complicated numerical representation methods of ancient Greece, Archimedes also pioneered the method of remembering large numbers, breaking through the limitation that counting with Greek letters could not exceed 10,000 at that time, and used it to solve many mathematical problems. 4. Proposed the famous Archimedes' axioms, expressed in modern mathematical language. Archimedes' principle means that for any natural number (excluding 0) a, b, if ab. In terms of astronomy: 1. He invented water propulsion A planetarium, and used it to simulate the movement of the sun, planets and moon and perform solar and lunar eclipses; 2. He believed that the earth was spherical and revolved around the sun. This view was better than Copernicus's "heliocentric earth" "Dong theory" dates back 1,800 years. Due to the conditions at the time, he did not conduct in-depth and systematic research on this issue. Emphasis on practice: Archimedes is obviously different from the scientists of the Athenian period, that is, he not only valued the rigor and accuracy of science, requiring precise and logical proof of every problem; he also attached great importance to the development of scientific knowledge. practical application. He attached great importance to experimentation and made various instruments and machinery by himself. He designed and manufactured many mechanisms and machines throughout his life. In addition to the lever system, it is worth mentioning that there are lifting pulleys, water pumps, the use of sunlight to burn enemy ships, and military trebuchets. The water pump known as the "Archimedes' spiral" is still used in Egypt and other places.