Cheng Dawei (1533–1606), also known as
Da Wei Cheng or
Ch'eng Ta-wei, is a Chinese mathematician known mainly as the author of
Suanfa Tongzong (
General Source of Computational Methods). He has been described as "the most illustrious Chinese arithmetician."
Almost all that is known about his life is contained in a passage written in the Preface of the book by one of his descendants when the book was being reprinted:
:In his youth my ancestor Cheng Da Wei was academically gifted, but although he was well versed in scholarly matters, he continued to carry out his profession as a sincere Local Agent, without becoming a scholar. He never lagged behind either on the classics or on ancient writings with old style characters, but was particularly gifted in arithmetic. In the prime of his life he visited the fairs of Wu and Chu. When he came across books that talked about "square fields" or "grain with the husk removed" ... he never looked at the price before purchasing them. He questioned respectable old men who were experienced in the practice of arithmetic and gradually and indefatigably formed his own collection of difficult problems.
Cheng Dawei was not a professional mathematician. From the description cited above, one could deduce that he must have traveled widely. Also must have been well off since he purchased books without asking the price. Again we can see that he was an avid collector of books on mathematics. This is borne out by the contents of his work General Source of Computational Methods which is essentially a compilation of problems from earlier works.
Read more...: General Source of Computational Methods Cheng Dawei Abacus Museum
General Source of Computational Methods
The General Source of Computational Methods was first published in 1592. It is essentially a general arithmetic for the abacus. Though there is nothing particularly original about this book, it was republished several times and became widely popular. Beyond the limited circle of mathematicians, it must have reached a vast popular audience. Its popularity must have continued to modern times as can be seen from a remark by a contemporary historian of Chinese mathematics: "Nowadays, various editions of the book can still be found in China and old people still recite the versified formulas and talk about the difficult problems in it."
The book contains 595 problems divided into 12 chapters. According to Jean Claude Martzloff, historian of Chinese mathematics, "... unlike the authors of the venerable classic, Cheng Dawei was not afraid of superfluity or verbosity. His book is an encyclopaedic hotch-potch of ideas which contains everything from A to Z relating to the Chinese mystique of numbers (magic squares, ... generation of the eight trigrams, musical tubes), how computation should be taught and studied, the meaning of technical arithmetical terms, computation on the abacus with its tables which must be learnt by heart, the history of Chinese mathematics, mathematical recreations and mathematical curiosities of all types."
The book provided a poem to solve a remainder problem.
三人同行七十稀， (Divide it by 3 and multiply the remainder by 70.)
五树梅花廿一枝； (Divide it by 5 and multiply the remainder by 21.)
七子团圆正半月， (Divide it by 7 and multiply the remainder by 15.)
除百零五便得知。 (Adjust the sum by subtracting or adding multiple of 105, LCM of 3, 5 and 7.)
Cheng Dawei Abacus Museum
In the Huangshan City in southern Anhui province in, there is a museum for abacuses named after Cheng Dawei. There are more than 1,000 abacuses and 3,000 copies of related materials displayed in the showcases. These abacuses are made of gold, silver, ivory, jade, stone, hard wood respectively with different shapes.
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程大位（1533年 - 1606年），字
汝思，號
賓渠，直隸休寧縣率口人（今安徽省黃山市屯溪）。
Read more...: 生平 程大位幻圓 參考書目 外部鏈接
生平
嘉靖十二年四月初十（1533年5月3日）出生於商人家庭，因商業上的需要，對數學很有興趣，不惜重金購求算書，日後繼承父業，「週遊吳楚之壚」，六十歲時著書《算法統宗》17卷，載595個數學問題，被推崇為中國「珠算鼻祖」。萬曆三十四年（1606年）卒。其故居至今仍坐落於屯溪區率口渠東側，佔地540平方米。
程大位在他所著的《算法統宗》中，對于這種解一般「孫子問題」的方法，還編出了四句歌訣，名曰《孫子歌》：
三人同行七十稀，
五樹梅花廿一枝；
七子團圓正半月，
除百零五便得知。
歌中的「廿」，讀音與「念」音相同。「廿」即二十的意思。
這一歌訣的「詩意」，我們可以不去理會，只需注意它的數字就行了。歌訣中的每一句話，都指出了一步解題方法：
三（3）人同行七十（70）稀」——是說除以3所得的餘數，要用「70」去乘它；
五（5）樹梅花廿一（21）枝」——是說除以5所得的餘數，要用「21」去乘它；
七（7）子團圓正半月（15）」——「半月」是一個月30天的一半，即15日，這是說，除以 7所得的餘數，要用「 15」去乘它；
除百零五（105）便得知」——這是說要把上面所乘得的三個數相加，加得的和如果大于105，便應減去105，或者減去105的倍數。這也就是《孫子算經》上的「一百六（106）以上，以一百五（105）減之」。這樣得出的差，便是所要求的這個最小的未知數了。
程大位幻圓
File:Suanfatongzong-792-792.jpg
File:Suanfatongzong-793-793.jpg
File:Suanfatongzong-795-795.jpg
參考書目
• 《程氏宗譜》
外部鏈接
• 算數の歌～光由が捨てたもの 『キッズレーダー』から
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