Sea mirror of Circle measurements (Ceyuan haijing) and The development of nine inscribed circles (Jiu yong yan dai)

Chun Chor Litwin CHENG

Research output: Contribution to conferencePaper

Abstract

The book “Sea mirror of Circle measurements《測圓海鏡》” (Ceyuan haijing) investigate cases of circles inscribed in a right angle triangle. This paper discuss the development of the mathematics content written by the scholar Yang Zhao Jun (楊兆鋆) in the Qing dynasty on the content of Ceyuan haijing in his book “Development of nine inscribed circles (九容演代) [Jiu yong yan dai]. This book investigated the problems of inscribed circles based on algebraic knowledge known at Qing dynasty and construct equation leading to solve the diameter of the circle. Yang categorized the problems into 6 groups and he worked with 600 problems and only 160 of them were recorded. This paper with to draw some conclusion on the method Yang used in devising the equation, which include the using of the Gou-Gu Theorem (Pythagoras theorem), mathematics expression result from cross-ratio table, and the technique of interchange of triangles and event. Copyright © 2013 MIT Departmental Seminar.
Original languageEnglish
Publication statusPublished - Nov 2013

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Incircle or inscribed circle
Mirror
Circle
Triangle
Pythagorean theorem
Cross ratio
Right angle
Table
Theorem

Citation

Cheng, C. C. L. (2013, November). Sea mirror of Circle measurements (Ceyuan haijing) and The development of nine inscribed circles (Jiu yong yan dai). Paper presented at the MIT Departmental Seminar, The Hong Kong Institute of Education, China.