Screen LibraryFleeting footsteps : tracing the conception of arithmetic and algebra in ancient China /
The Hindu-Arabic numeral system (1, 2, 3, ...) is one of mankind's greatest achievements and one of its most commonly used inventions. How did it originate? Those who have written about the numeral system have hypothesized that it originated in India; however, there is little evidence to suppor...
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| Published: |
World Scientific Pub. Co.,
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| Publisher Address: | Singapore ; River Edge, N.J. : |
| Publication Dates: | 1992. |
| Literature type: | eBook |
| Language: | English |
| Subjects: | |
| Online Access: |
www.worldscientific.com/worldscibooks/10.1142/1784#t=toc |
| Summary: |
The Hindu-Arabic numeral system (1, 2, 3, ...) is one of mankind's greatest achievements and one of its most commonly used inventions. How did it originate? Those who have written about the numeral system have hypothesized that it originated in India; however, there is little evidence to support this claim. This book provides considerable evidence to show that the Hindu-Arabic numeral system, in spite of its commonly accepted name, has its origins in the Chinese rod numeral system. This system was in use in China from antiquity till the 16th and 17th century. It was used by officials, astronomers, traders and others to perform addition, subtraction, multiplication, division and other arithmetric operations, and also used by mathematicians to develop arithmetic and algebra. Sun Zi Suanjing (The Mathematical Classic of Sun Zi) written around 400 AD is the earliest existing work to have a description of the rod numerals and their operations. With this treatise as a central reference, the first part of the book discusses the development of arithmetric and the beginnings of algebra in ancient China and, on the basis of this knowledge, advances the thesis that the Hindu-Arabic numeral system has its origins in the rod numeral system. Part Two gives a complete translation of Sun Zi Suanjing. |
| Item Description: | Part two is the translation of Sun Zi suanjing. |
| Carrier Form: | 1 online resource (xvi,199pages) : illustrations |
| Bibliography: | Includes bibliographical references (pages 187-193) and index. |
| ISBN: | 9789814537032 |
| CLC: | O112 |
| Contents: | 1. The Sun Zi Suanjing (The mathematical classic of Sun Zi). 1.1. The text in perspective. 1.2. Author and date. 1.3. Existing versions. 1.4. The translation -- 2. Numbers and numerals. 2.1. Why the need for a detailed study of numbers and numerals? 2.2. The written numbers. 2.3. The rod numerals -- 3. The fundamental operations of arithmetic. 3.1. Were the operations simple? 3.2. Manipulating rod digits. 3.3. Multiplication. 3.4. Division. 3.5. Addition and subtraction. 3.6. The multiplication table. 3.7. Conclusion -- 4. The common fraction. 4.1. Concept, notation and rules. 4.2. The reduction of a fraction. 4.3. The addition and subtraction of fractions. 4.4. The averaging of fractions. 4.5. Other rules. 4.6. The subject in general -- 5. On extracting roots of numbers. 5.1. The background. 5.2. The method in Sun Zi suanjing. 5.3. An analysis of the method. 5.4. Significance of the method. 5.5. Conclusion -- 6. Tables of measures. 6.1. Introduction. 6.2. Measures of length. 6.3. Measures of weight. 6.4. Measures of capacity. 6.5. A common set of decimal fractional units. 6.6. Densities -- 7. The various problems. 7.1. The problems in Sun Zi suanjing. 7.2. Rule of Three. 7.3. Geometrical configurations. 7.4. Partnership and sharing. 7.5. The remainder problem. 7.6. Rule of false position. 7.7. Fang cheng method. 7.8. Miscellaneous problems. 7.9. Listing the early mathematical methods -- 8. Socioeconomic aspects in Sun Zi's China. 8.1. The period. 8.2. Buddhism. 8.3. Wei qi and the nobility. 8.4. Taxation. 8.5. The barter trade -- 9. Did the Hindu-Arabic numeral system have its origins in the rod numeral system? 9.1. The background leading to such an investigation. 9.2. The rod numeral system and the Hindu-Arabic numeral system have the same concept. 9.3. On the significance of the concept of an invention. 9.4. No other numeral systems of antiquity share the same concept as the rod numeral system. 9.5. On the hypothesis that the Hindu-Arabic numeral system has an Indian origin. 9.6. evidence of a Chinese origin. 9.7. Other identical conventions. 9.8. On the question of transmission. 9.9. Conclusion -- Translation of Sun Zi Suanjing. Preface -- ch. 1. -- ch. 2. -- ch. 3. |