A Comparative Study On Geometry In Ancient China And India

The development of geometry in ancient China and India together with their intercommunication have been concerned in researches of the history of mathematics. It is an important topic to investigate characteristics of geometry in these two countries. However, the comparative study on this topic has not been systematically done. This paper analyzes the differences and similarities of geometry between ancient China and India. The main results and viewpoints of this dissertation are as follows:1. The paper investigates the development and level of traditional geometry in ancient China and India. The development of mathematical ideas of traditional Indian geometry is made clear. The origination of traditional Indian geometry is considered of having theoretical foundation. The level of traditional Indian geometry is almost the same as that of Chinese. In certain specific field, traditional Chinese and Indian geometry is not inferior much to Western.2. Geometrical knowledge before the 12th century in China and India is studied thoroughly and systematically. The origination and application of Gougu Theorem (usually called Pythagoras Theorem) are discussed comprehensively. Pythagoras Theorem plays important role in both countries. Not only do its applications make Chinese measurement theory reach a high level but that the surd theory flourishes in China and India at the same time because of its applications. Many similar characteristics in geometry of ancient China and India show the important influences of historical culture, geographical location and philosophical tradition in the two countries.3. The area and volume of geometrical figure in ancient China and India before the 12th century are compared in multiple aspects for the first time. Firstly, the area and volume of geometrical figure in early cultural relics and historical literatures in China and India are compared. It comes to a conclusion that the development of geometry in ancient China and India is simultaneous and the levels are parallel. Chinese mathematics was once transmitted into India verbally. Especially, the surface area and volume of the sphere are compared in the two countries which indicates the different mode of thought on the problem. Finally, the constructive characteristic of geometry in the two countries is compared. Their geometries have similar structure and are both based on several key theorems.4. The Indian trigonometry and the relationship between the sides of rectangular triangle of China are compared. The nationalization of Indian trigonometry in China is discussed, and the reason that Indian trigonometry has not effect much on Chinese mathematics and astronomy is analyzed as well. As a conclusion, the first tangent function table was created independently by Yixingand had not been influenced by Indian trigonometry.5. This paper explicates the content of traditional Indian geometry and clarifies some scholar' ideas that Chinese mathematics had never been transmitted into India. The communication and cultural interaction between ancient China and India are mutual and promote the geometric development of both countries.