Fleeting Footsteps: Tracing The Conception Of Arithmetic And Algebra In Ancient ChinaWorld Scientific, Oct 7, 1992 - 238 pages 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. |
Contents
The Sun Zi Suanjing The Mathematical Classic of Sun Zi | 3 |
Numbers and Numerals | 11 |
The Fundamental Operations of Arithmetic | 29 |
The Common Fraction | 53 |
On Extracting Roots of Numbers | 65 |
Tables of Measures | 83 |
The Various Problems | 89 |
Socioeconomic Aspects in Sun Zis China | 127 |
Did the HinduArabic Numeral System have its Origins in the Rod Numeral System? | 133 |
Preface | 151 |
Chapter 1 | 153 |
Chapter 2 | 163 |
Chapter 3 | 173 |
187 | |
195 | |
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13th century amount ancient Chinese Answer arithmetic becomes the divisor Brahmi numerals century Chang'an China coarse rice computation concept counting board counting rods deficit deng shu denominators digit dividend shi dynasty equations Find the number follows fractions give greatest common divisor Han dynasty Hindu-Arabic numeral system Jiu zhang suanshu large numbers left column length Li Chunfeng liang Liu Hui lower numeral lower position Luoyang mathematical meral method middle position millet multiplication and division number of persons number word obtain the number operations Prob problem procedure proportional value Qian quotient remainder right column rod numeral system Sect shang sheng shi zhi ſº square root Step subtraction Sun Zi suanjing thousands tion top grade cereal top position translation units upper numeral upper position vertical rods wan wan written numerals Yang Hui ying ying bu Zhu Shijie Zi's