Research Catalog

Title

The sea island mathematical manual : surveying and mathematics in ancient China / Frank J. Swetz.

Author

Swetz, Frank J., 1937-

Publication

University Park, Pa. : Pennsylvania State University Press, ©1992.

Items in the Library & Off-site

Details

Additional Authors

Liu, Hui, active 3rd century-4th century.

Description

xi, 73 p. : ill.; 24 cm.

Summary

An annotated translation and analysis of the Haidao Suanjing, a Chinese mathematical classic composed by Liu Hui in A.D. 263. All ancient societies practiced the art of land surveying. In fact, tradition tells us that geometry--land measure--had its origins in such surveying. However, an examination of early Western literature reveals few records concerning the practical uses of geometry and mathematics in the tasks of surveying. Recent research into the content and origins of early Chinese mathematics is beginning to reveal the existence of strong traditions and interest in the methodologies and applications of land survey. It is from these Chinese sources that a clearer picture of how people adapted mathematics and geometry to the needs of surveying emerges. 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 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 analysis of the Haidao's 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.

Subject

• Liu, Hui
• Geschichte 263
• Surveying > China > History
• Mathematics, Chinese > History
• Mathematics, Chinese
• Surveying
• Geometrie
• Quelle
• Mathématiques chinoises > Histoire
• Topographie > Chine > Histoire
• China

Genre/Form

History.

Note

• An annotated translation and discussion of Liu Hui's Haidao Suanjing (Sea island mathematical manual), written in 263 A.D.

Bibliography (note)

• Includes bibliographical references (p. [67]-70) and index.

Contents

1. Perspectives. The Importance of Surveying to the Chinese Empire. Surveying Tools of the Ancient Chinese. The Haidao Suanjing and Its Tradition in Chinese Surveying Literature. Liu Hui, His Work, and His Times -- 2. The Haidao Suanjing. Research on the Haidao. The Problems of the Haidao Suanjing -- 3. Analysis and Discussion of the Haidao's Contents. The Haidao as an Extension of the Jiuzhang. A Surveying Thesis? The Origins and Concept of the Chong Cha Procedure. Mathematical Significance and Controversies. The Methodology Behind Liu's Proofs. Verification of the Sea Island Manual Formulas -- 4. Conclusions. A Mathematical Testimony. Chinese Surveying Accomplishments: A Comparative Retrospection.

ISBN

• 0271007958
• 9780271007953
• 0271007990
• 9780271007991

LCCN

91013002

OCLC

• ocm23584159
• 23584159
• SCSB-9572250

Owning Institutions

Princeton University Library