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Geometry in "Jiuzhang Suanshu" and Liu's commentaries
Author
Phan, Wai Mun
Supervisor
Soon, Spario
Abstract
"The Nine Chapters on the Mathematical Art", (九章算术, Jiuzhang suanshu) is a compilation of works on mathematics from the Zhou, Qin to Han Dynasties (c 11th century BC - 200 AD). Presented in the format of problems, answers and algorithms (术, shu), the book contains 246 problems on mathematics, which were encountered in everyday life then. The mathematics involved range from arithmetic, algebra to geometry. Based on the nature of the mathematics involved, the works were sorted into nine chapters and compiled into a book, that is, "The Nine Chapters".
Through the decades, many mathematicians had written commentaries on the book. The more significant commentaries was that written by Liu Hui in 263 AD. Through his commentaries we were able to see more of the concepts behind the mathematics presented in "The Nine Chapters".
The focus of this academic exercise will be on the area of geometry reflected in Chapter 1, 4, 5 and 9 of "The Nine Chapters". Mensuration problems related to areas and volumes of various structures commonly seen in those days were discussed. Algorithms for the determination of sides of right-angled triangles and their applications were also included.
In the first part of this exercise a brief account on the background and contents of "The Nine Chapters" will be given. This is followed by discussions, on the geometric aspects of the book. Next, based on Liu Hui's commentaries, we will attempt to look into the principles that were possibly used to derive the algorithms for the mensuration problems presented. Finally, we shall look at Liu Hui's discoveries on some of the inaccuracies of the works.
Through the decades, many mathematicians had written commentaries on the book. The more significant commentaries was that written by Liu Hui in 263 AD. Through his commentaries we were able to see more of the concepts behind the mathematics presented in "The Nine Chapters".
The focus of this academic exercise will be on the area of geometry reflected in Chapter 1, 4, 5 and 9 of "The Nine Chapters". Mensuration problems related to areas and volumes of various structures commonly seen in those days were discussed. Algorithms for the determination of sides of right-angled triangles and their applications were also included.
In the first part of this exercise a brief account on the background and contents of "The Nine Chapters" will be given. This is followed by discussions, on the geometric aspects of the book. Next, based on Liu Hui's commentaries, we will attempt to look into the principles that were possibly used to derive the algorithms for the mensuration problems presented. Finally, we shall look at Liu Hui's discoveries on some of the inaccuracies of the works.
Date Issued
1997
Call Number
QA443.5 Pha
Date Submitted
1997