Famous scholars believe that abstract noun concepts are different from their original entities, and they put forward that "it is impossible to be square if the moment is not right;" If the rules are not correct, it will not be a circle, and the circle can be infinitely divided. Mohism believes that names come from things, and names can reflect things from different sides and depths. Mohist school gave some mathematical definitions, such as circle, square, flat, straight, secondary and end.
Mohism disagrees with the proposition that the circle can be infinitely divided, and puts forward the proposition of "non-half" to refute: if a line segment is infinitely divided into two halves, there will be a "non-half" that can no longer be divided, and this "non-half" is a point.
The famous scholar's proposition discusses that a finite length can be divided into an infinite sequence, while the Mohist proposition points out the changes and results of this infinite division. The discussion on the definition and proposition of mathematics by famous scholars and Mohists is of great significance to the development of China's ancient mathematical theory.
Sima Qian mentioned that the Han Dynasty abolished the Qin criminal law in Historical Records of the Han Dynasty. Breaking a circle contains a simple idea of infinitesimal division, which is roughly summarized by Sima Qian from the practice of turning a square into a circle and a straight line into a curved shape when a craftsman processes a circular object.
These propositions about "division" have a far-reaching influence on the idea of infinitesimal division in mathematics later. China's ancient mathematical classic "Nine Chapters Arithmetic" wrote in the first chapter "Square Field" that "product step of semi-circle radius" is the formula we are familiar with now.
In order to prove this formula, Liu Hui, a mathematician in Wei and Jin Dynasties, wrote nine chapters of arithmetic notes, and wrote more than 1800 words after this formula. This note is the famous "cyclotomy" in the history of mathematics.
Liu Hui reprocessed the data cut into 192 polygons with "difference power". Through simple operation, he can get a high-precision result of 3072 polygons, and the extra calculation is almost negligible. This is a wonderful embodiment of infinitesimal division in ancient mathematics.
Liu Hui introduced infinitesimal division into mathematical proof for the first time in human history and became an immortal chapter in the history of human civilization.