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.
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 of mathematics with practical application. 1, Archimedes' calculation method for determining the area of parabola bow, helix and circle, and the surface area and volume of complex geometric bodies such as ellipsoid and paraboloid. In the process of deriving these formulas, he founded the "exhaustive method", which is similar to the method of gradually finding the limit in modern calculus. He is the first person to study pi scientifically. He proposed to calculate pi by increasing the number of sides and approaching the areas of inscribed polygons and circumscribed polygons. He calculated the range of pi: 223/7 1
Among them, On the Ball and the Cylinder is his masterpiece, which contains many great achievements. Starting from several definitions and axioms, he deduced more than 50 propositions about the area and volume of spheres and cylinders. Archimedes is a great mathematician and mechanic and enjoys the reputation of "the father of mechanics". The reason is that he discovered the lever principle through a lot of experiments, and then deduced many lever propositions by geometric methods and gave strict proofs, including the famous Archimedes principle (lever principle). He has made brilliant achievements in mathematics, especially in geometry. His mathematical thought contains the idea of calculus, but what he lacks is the concept of limit, but the essence of his thought extends to the field of infinitesimal analysis, which is maturing in the17th century, and predicts the birth of calculus.