The Sea Island Mathematical Manual: Surveying and Mathematics in Ancient China

by 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.

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.

88 pages, Paperback

First published January 1, 1992

About the author

For most of my life, I have taught mathematics. This task has spanned audiences from young preschool children to graduate teachers and involved cultural and social settings from the inner city schools of New York to those of several developing countries of Southeast Asia. In all these ventures, I have been troubled by the perceived difficulties people associate with the learning and teaching of mathematics. My solution to this situation has been to try to “humanize” the learning of mathematics, that is, to more closely associate it with its historic and cultural origins and its purposes. In my books, I attempt to reveal these often unknown but fascinating aspects of the subject and to promote a clearer understanding of mathematics as a human endeavor, its uses and potentials.