## The Sea Island Mathematical Manual

Surveying and Mathematics in Ancient China

### Frank J. Swetz

# The Sea Island Mathematical Manual

Surveying and Mathematics in Ancient China

### Frank J. Swetz

*The Haidao Suanjing*or

*Sea Island Mathematical Manual*, is one of the "Ten Classics" of traditional Chinese mathematics, and its contents demonstrate the high standards of theoretical and mathematical sophistication present in early Chinese surveying theory. The

*Haidao*composed in A.D. 263 by Liu Hui, established the mathematical procedures for much of East Asian surveying activity for the next one thousand years. The contents of the

*Haidao*also testify to the ability of the Chinese to systematize mathematics and hint at the use of proof in Chinese mathematics, a concept usually associated with Greek mathematical thought.

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*The Haidao Suanjing*or

*Sea Island Mathematical Manual*, is one of the "Ten Classics" of traditional Chinese mathematics, and its contents demonstrate the high standards of theoretical and mathematical sophistication present in early Chinese surveying theory. The

*Haidao*composed in A.D. 263 by Liu Hui, established the mathematical procedures for much of East Asian surveying activity for the next one thousand years. The contents of the

*Haidao*also testify to the ability of the Chinese to systematize mathematics and hint at the use of proof in Chinese mathematics, a concept usually associated with Greek mathematical thought.

Frank Swetz provides an annotated translation of the *Haidao* and an analysis of its surveying problems. In particular, he details surveying techniques and undertakes a mathematical exposition of the Chinese *chong cha* solution procedures. The *Haidao* is a testimony to the ingenuity and skill of China's early surveyors and its author, Liu Hui. This study complements and extends the findings of Swetz's previous book, *Was Pythagoras Chinese?* *An Examination of Right Triangle Theory in Ancient China.*

Frank J. Swetz is a Professor of Mathematics and Education at the Pennsylvania State University, Harrisburg. He is the author of, among other books, *Capitalism and Arithmetic* (1987), *Was Pythagoras Chinese?* (Penn State, 1977), and *Mathematics Education in China *(1974).

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