In the late ancient Greece, another great scientist Archimedes appeared. He correctly obtained the formulas for calculating the volume and surface area of spheres and cylinders, and put forward the methods for calculating the area enclosed by parabolas and the arcuate area. The most famous method is to find the area surrounded by archimedean spiral (ρ = α× θ), which is named after Archimedes. Conic curve method is used to solve the univariate cubic equation and get the correct answer. Archimedes was also the founder of calculus. When calculating the volume of spheres, cylinders and more complex solids, he used the method of gradual approximation to find the limit, thus laying the foundation for modern calculus calculation. The most interesting thing is Archimedes' discovery about volume: once, the son of Archimedes' neighbor Janley went to Archimedes' small yard to play. Jenny is very naughty and a very lovely child. Zhanli raised his red face and said, "Uncle Archimedes, can I use your column as a pillar of the church?" "yes." Archimedes said. After little Janley erected the post, he was going to add a ball to it according to the model of the post in front of the church. He found a cylinder, because its diameter is exactly equal to the diameter and height of the cylinder, the ball plopped into the cylinder and could not be poured out. So, Li Zhan called Archimedes. Archimedes saw this situation and thought: the height and diameter of the cylinder are equal, and the newly embedded spherical surface is not the inscribed spherical surface of the cylinder. But how do we determine the relationship between a sphere and a cylinder? At this time, Xiao Li Zhan brought a basin of water and said, "Excuse me, Uncle Archimedes, let me wash the ball with water, which will be cleaner." When Archimedes' eyes lit up, he hugged little Janley and said lovingly, "Thank you, little Janley, you helped solve a big problem." Archimedes poured water into the cylinder and put the inner ball in it; Take the ball out again and measure the remaining water; Then fill the cylinder with water and measure how much water the cylinder can hold. After this kind of trial and error, he found an amazing miracle: the volume of the inner ball is exactly equal to two-thirds of the capacity of the outer cylinder. He was ecstatic and remembered this extraordinary discovery: the ratio of a cylinder to its inscribed sphere, or the relationship between them, was 3: 2. He is proud of this extraordinary discovery. He told future generations to carve a cylindrical pattern engraved with a sphere on his tombstone as an epitaph. Archimedes' amazing intelligence attracted people's attention and admiration. Friends call him "alpha", which is a first-class mathematician (alpha-alpha, the first letter of the Greek alphabet). Archimedes, as an "alpha", deserves it. Therefore, the 20th century mathematical historian E.T. Bell said, "Archimedes must be included in any list of the three greatest mathematicians of all time." The other two mathematicians are usually Newton and Gauss. However, compared with their great achievements and background of the times, and their far-reaching influence on the present and future generations, Archimedes should be the first to be respected. "We say that Archimedes' mathematical achievement lies in that he not only inherited and carried forward the scientific method of studying abstract mathematics in ancient Greece, but also linked the research and practical application of mathematics, which is of great significance in the history of scientific development and has a far-reaching impact on later generations. Archimedes is undoubtedly one of the greatest mathematicians and scientists produced by ancient Greek civilization. His outstanding contributions in many scientific fields earned him the high respect of his contemporaries. Mechanics: Archimedes made the most outstanding achievements in mechanics. He systematically and strictly proved the lever law and laid the foundation of statics. Archimedes systematically studied the center of gravity and lever principle of an object on the basis of summarizing the experience of predecessors, put forward a method to accurately determine the center of gravity of an object, and pointed out that supporting it in the center of the object can keep the object in balance. In the process of studying machinery, he discovered the law of lever and used this principle to design and manufacture many machines. He discovered the law of buoyancy in the process of studying floating bodies, which is also known as Archimedes principle. Geometry: Archimedes' calculation method for determining the area of parabola bow, helix and circle, and the surface area and volume of ellipsoid, paraboloid and other complex geometric bodies. In the process of deriving these formulas, he founded the "exhaustive method", which is what we call the method of gradually approaching the limit today, and is therefore recognized as the originator of calculus calculation. He calculated pi more accurately by increasing the number of sides and approximating the areas of inscribed polygons and circumscribed polygons. Facing the tedious numerical representation in ancient Greece, Archimedes also pioneered the method of memorizing large numbers, which broke through the restriction that Greek letters could not exceed 10 thousand at that time and solved many mathematical problems with it. Astronomy: Archimedes also made outstanding achievements in astronomy. In addition to the planetary instruments mentioned above, he also thinks that the earth is spherical and revolves around the sun, which is earlier than Copernicus' "Heliocentrism" 1800 years. Limited by the conditions at that time, he did not make a thorough and systematic study on this issue. But it is remarkable to put forward such an opinion as early as the third century BC. Writings: There are more than 10 mathematical works handed down by Archimedes, most of which are Greek manuscripts. His works focus on quadrature problems, mainly the area of curved edges and the volume of curved cubes. His style is deeply influenced by Euclid's Elements of Geometry. First, he established some definitions and assumptions, and then proved them in turn. As a mathematician, he wrote about spheres and cylinders, the measurement of circles, the quadrature of parabolas, spirals, cones and spheres, and the calculation of sand. As a mechanic, he wrote many mechanical works, such as On the Balance of Numbers, On Floating Bodies and On Lever and Principle. Among them, On the Ball and Column is his masterpiece, including many great achievements. Starting from several definitions and axioms, he deduced more than 50 propositions about the area and volume of spheres and cylinders. The balance of plane figure or its center of gravity, starting from several basic assumptions, demonstrates the mechanical principle with strict geometric methods and finds out the centers of gravity of several plane figures. The sand counter designs a method that can represent any large number, which corrects the wrong view that sand is uncountable, and even if it can be counted, it can't be represented by arithmetic symbols. On the floating body, the buoyancy of the object is discussed and the stability of the rotating projectile in the fluid is studied. Archimedes also put forward a "herd problem", which contains eight unknowns. Finally, it comes down to a quadratic indefinite equation. The number of its solutions is amazing, * * * more than 200,000 digits! In addition, there is a very important work, which is a letter to Eratosthenes, the content of which is to explore ways to solve mechanical problems. This is a scroll of parchment manuscript discovered by Danish linguist J.L. Heiberg in 1906. Originally written in Greek, it was later erased and rewritten in religious words. Fortunately, the original handwriting was not wiped clean. After careful identification, it was confirmed to be Archimedes' work. Some of them have seen it in other places, and some people think it has disappeared in the past. Later, it was published internationally in the name of Archimedes Law. This paper mainly talks about the method of finding problems according to mechanical principles. He regards an area or volume as something with weight, divides it into many very small strips or pieces, then balances these "elements" with the known area or volume, finds the center of gravity and fulcrum, and can use the lever law to calculate the required area or volume. He regards this method as a tentative work before strict proof, and will prove it by reducing to absurdity after getting the result.