Since the 1980s, the following ancient Chinese mathematical books of the Qin-Han period have been discovered: Zhangjiashan Han bamboo book "Suanshu-shu", Yuelu Academy's Qin bamboo book "Shu" (Yuelu Shu, for short), Peking University's Qin bamboo books (Beida Qinjian, for short), and Suihudi Han bamboo book "Suanshu." This paper discusses Chinese mathematics during the Qin-Han period, focusing on the Beida Qinjian, whose report books with photographs of bamboo slips were published in 2023.
1. The Gougu method
Both the Beida Qinjian and the Yuelu Shu contain problems for finding the fractions 15+15/31 that approximate the square root of 240, but they calculate them in different manners. In addition, both the Beida Qinjian and the Yuelu Shu contain the other problems using the Gougu method. By examining their solutions, we will confirm that the Gougu method has been already used in the Qin Dynasty.
2. The chants
The "Litian" problem of the Beida Qinjian contains the chants for memorizing the constant 375 as (124+1) times 3, which were deciphered by the author and published in 2015 in Japanese and in 2018 in English. The Yuelu Shu also has the problem which includes some phrases of the nine-times-nine table as chants in the text of the method. Thus, we can see that in the Qin Dynasty, oral practices were an important means for officials to learn how to solve problems.
3. Other findings in the Yuelu Shu from the study of the Beida Qinjian of the same period will also be shown.

In ancient Chinese mathematics texts concerning areas and volumes, problems usually are given parameters for applying algorithms or formulas to get the answers. Take Chapter 5 of Jiuzhang suanshu for example. It is devoted basically to computing volumes in various shapes. The methods for solving Problem 5.11 (on yuantai, a truncated cone) and 5.13 (on yuanzhui, cone) respectively would self-explain quite clearly. However, ancient Chinese mathematics never paid attention to the geometrical properties that interconnect the two solids, say yuantai and yuanzhui until Zhang Qiujian. There follows Yang Hui of Song dynasty and Wu Jing of Ming dynasty were also interested in the problem-solving. In this talk I will try to make sense of the format which might also attract the attention of those who are concerned about educational issues.

The Jiuzhang Suanshu appeared around the 1st century B.C. formed the ancient Chinese mathematical tradition. In the Tang Dynasty (618~906), mathematician Li Chunfeng (602~670), under the imperial order and with the help of 20 scholars, edited and annotated Ten Mathematical Classics written by predecessors which were used as textbooks for imperial mathematics education. Chinese mathematics developed to a new height, a large number of mathematical works appeared, and some important mathematical achievements were obtained, in the Song and Yuan Dynasties (960~1368). East Asian countries shared this cultural tradition of mathematics. In the Sui and Tang Dynasties (581~906), Japan and the Korean Peninsula began to introduce the Ten Mathematical Classics from China. In the 17th century, Chinese mathematics played a very important role in laying the foundation of Korea and Japan. Among the mathematics works of Song and Yuan Dynasties, Chinese mathematician Zhu Shijie’s Suanxue Qimeng (Enlightenment in Mathematics, in 1299) played an important role in the early development of mathematics in Korea and had a far-reaching influence.
The following questions will be discussed in this presentation:
The spread history of the Suanxue Qimeng in Korea;
The studies by Korean mathematicians on the Suanxue Qimeng;
How the Suanxue Qimeng shaping the Korean mathematics;
The place of Suanxue Qimeng in the history of mathematics in Korea;
The influence of the Korean mathematician’s studies of the Suanxue Qimeng to Chinese mathematics.
Through the discussion of the case of Suanxue Qimeng, we try to show how East Asian countries share the same mathematical tradition.