1906, Danish mathematician Heiberg discovered a copy of Archimedes' letter to erato Sese and some other works of Archimedes. Through research, it is found that these letters and transcripts contain the idea of calculus. What he lacks is the concept of no 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. ?
Archimedes was born in Syracuse, Sicily, at the southern tip of the Italian peninsula in 287 BC. Father is a mathematician and astronomer. Archimedes had a good family upbringing since childhood. 1 1 years old, was sent to study in Alexandria, the cultural center of Greece. In this famous city known as the "Capital of Wisdom", Archimedes Job collected books and learned a lot of knowledge, and became a protege of Euclid students erato Sese and Cannon, studying geometric elements.
Sand Calculation is a book devoted to the study of calculation methods and theories. Archimedes wanted to calculate the number of grains of sand in a big sphere full of the universe. He used a very strange imagination, established a new counting method of order of magnitude, determined a new unit, and put forward a model to represent any large number, which is closely related to logarithmic operation. ?
"Measurement of a circle" uses 96 circumscribed and inscribed polygons of a circle to obtain pi.
He also proved that the area of a circle is equal to the area of a regular triangle with a circumference as the base and a high radius; An exhaustive method was used. "Ball and cylinder", skillfully using the exhaustive method to prove that the surface area of the ball is equal to 4 times the area of the great circle of the ball; The volume of a ball is four times that of a cone. The base of this cone is equal to the great circle of the ball, which is higher than the radius of the ball. Archimedes also pointed out that if there is an inscribed sphere in an equilateral cylinder, the total area of the cylinder and its volume are the surface area and volume of the sphere respectively. In this book, he also put forward the famous "Archimedes axiom"
"Parabolic quadrature method" studies the quadrature problem of curves and figures, and draws a conclusion by exhaustive method: "The area of any arch (i.e. parabola) surrounded by the sections of straight lines and right-angled cones is four-thirds of the area of a triangle with the same base height." He also verified this conclusion again by mechanical weight method, and successfully combined mathematics with mechanics.
On Spiral is Archimedes' outstanding contribution to mathematics. He made clear the definition of spiral and the calculation method of spiral area. In the same book, Archimedes also derived the geometric method of summation of geometric series and arithmetic series.
"On Cones and Spheres" is about determining the volumes of cones formed by parabolas and hyperbolas rotating around their axes and spheres formed by ellipses rotating around their major and minor axes.
1906, Danish mathematician Heiberg discovered a copy of Archimedes' letter to erato Sese and some other works of Archimedes. Through research, it is found that these letters and transcripts contain the idea of calculus. What he lacks is the concept of no 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. Because of his outstanding contribution, American E.T. Bell commented on Archimedes in Mathematical Figures: Any open list of the three greatest mathematicians of all time will definitely include Archimedes, while the other two are usually Newton and Gauss. However, compared with his brilliant achievements and background of the times, or his far-reaching influence on contemporary and future generations, Archimedes should be the first to be respected.