By Lam Lay Yong, Ang Tian Se
The Hindu–Arabic numeral method (1, 2, 3,...) is one in every of mankind’s maximum achievements and considered one of its most typically used innovations. How did it originate? those that have written in regards to the numeral method have hypothesized that it originated in India; even if, there's little proof to aid this declare.
This booklet presents significant facts to teach that the Hindu–Arabic numeral procedure, regardless of its normally authorized identify, has its origins within the chinese language rod numeral process. the program was once popular in China from antiquity until eventually the sixteenth century. It used to be utilized by officers, astronomers, investors and others to accomplish addition, subtraction, multiplication, department and different mathematics operations, and in addition utilized by mathematicians to improve mathematics and algebra. in line with the program, various mathematical treatises have been written.
Sun Zi suanjing (The Mathematical vintage of sunlight Zi), written round four hundred advert, is the earliest present paintings to have an outline of the rod numerals and their operations. With this treatise as a valuable reference, the 1st a part of the e-book discusses the advance of mathematics and the beginnings of algebra in historic China and, at the foundation of this information, advances the thesis that the Hindu–Arabic numeral procedure has its origins within the rod numeral approach. half provides an entire translation of solar Zi suanjing.
In this revised variation, Lam Lay Yong has incorporated an edited textual content of her plenary lecture entitled "Ancient chinese language arithmetic and Its impact on international Mathematics", which was once introduced on the overseas Congress of Mathematicians, Beijing 2002, after she got the distinguished Kenneth O. may possibly Medal conferred through the foreign fee at the historical past of arithmetic. this could function an invaluable and easy-to-comprehend advent to the publication.
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Extra info for Fleeting Footsteps: Tracing the Concepti: Tracing the Conception of Arithmetic and Algebra in Ancient China
Sample text
It is therefore highly likely that some of them adapted this Chinese numeral system into a written system to suit their own requirements. Between 1200 to 1600, the peoples of Europe began to realise the enormous advantages of the new numeral system. They discarded their own numeral systems in favour of the new one. The methods of performing the four fundamental operations of arithmetic especially multiplication and division were laboriously learned and practised at university level. The next question you would ask me is: inspite of all these exposures to Chinese influences, could not our universal numeral system have been an independent invention?
The second group were the mathematicians which was a much smaller group. The development of mathematics through the rods reached its peak in the 13th and 14th centuries. p65 9 12/31/03, 11:44 AM 10 Fleeting Footsteps to shorten their manipulations from the 8th century onwards. However, they could not satisfy the demands of an advancing civilisation for quicker calculations. This led to the invention of the abacus. By the 15th century, the abacus was already widely used in China. In the next century, a number of mathematical texts using abacus calculations as the main means of computation were written; among them, the most influential was Cheng Dawei’s Suanfa tongzong (Systematic treatise on arithmetic) (1592).
He showed in detail how to solve an equation of this form: -x4 + 763200 x2 40642560000 = 0 . The display of the rod numerals in the different stages of calculations took up twenty one panels in his book. I like to show you a diagram which is familiar to all of you. p65 8 12/31/03, 11:44 AM Ancient Chinese Mathematics and Its Influence on World Mathematics 9 This Chinese representation of what we call “Pascal Triangle” is from Xiang jie suanfa (A detailed analysis of the methods of computations) (1261).