First, mathematics:

1, Chapter 9 Arithmetic

This is an important mathematical work in ancient China, which was written around the first century. Including 246 application problems and algorithms, involving many mathematical fields, such as algebra, geometry, equation theory and so on. Nine Chapters Arithmetic marks the peak of the development of ancient mathematics in China.

2. Pi

Ancient mathematicians in China began to study pi very early, and Zu Chongzhi, a mathematician in the Northern and Southern Dynasties, was accurate to seven decimal places for the first time, one thousand years earlier than Europeans.

3. Decimal counting method

The decimal counting method was adopted in ancient mathematics in China, which was more advanced than the hexadecimal or decimal counting method used in other ancient civilizations.

Second, astronomy:

1, armillary sphere:

Zhang Heng, a scientist in Han Dynasty, invented the armillary sphere, which is a hydraulically driven armillary sphere that can automatically display the stars and time. The invention of the armillary sphere had an important influence on the later development of astronomy.

2. Twenty-four solar terms:

The ancient calendar of China divided a year into 24 solar terms, and each solar term represented a specific position of the sun on the ecliptic, which provided important guidance for agricultural production.

3. The astronomical research of Stone God:

Shi Shen was one of the earliest astronomers in the Warring States Period in China. He recorded a large number of astronomical data through long-term observation of astronomical phenomena, which provided important information for later astronomical research.

The Significance of China s Achievements in Ancient Mathematics and Astronomy in the Development of Science and Culture;

1. These achievements mark the advanced level of ancient science in China.

For example, the invention of the nine-chapter arithmetic and decimal counting method shows the developed degree of ancient mathematics in China, and these achievements are ahead of the civilizations in many other regions. The formulation of the armillary sphere and the twenty-four solar terms shows China's in-depth research and accurate observation in the field of astronomy in ancient times.

2. These achievements had a far-reaching impact on the development of ancient culture in China.

For example, the research results of astronomy have influenced ancient religions, philosophy and literature, and people have learned about the order and mysterious power of the universe by observing astronomical phenomena. At the same time, the development of mathematics has also had an impact on the cultural level, such as its application in education, commerce, handicrafts and so on.

3. These achievements also laid a foundation for the inheritance and development of ancient science and culture in China.

For example, later scientists and scholars conducted in-depth research on the basis of "Nine Chapters of Arithmetic" and "Huntianyi", and constantly promoted the progress of science and culture. At the same time, these achievements have also stimulated people's curiosity about nature and the universe, and promoted the development of scientific exploration and innovative spirit.