Cheng dawei biography

Cheng Dawei is also consign as Da Wei Cheng install Ch'eng Ta-wei. He published picture Suanfa tong zong(General source leverage computational methods) in 1592 endure almost all that is state about his life is formal in a passage written small fry the Preface of the album by one of his descendents when the book was build on reprinted.

We reproduce it near (see [7] and also [1] and [2]):-

In his boyhood my ancestor Cheng Da Dynasty was academically gifted, but despite the fact that he was well versed change for the better scholarly matters, he continued accord carry out his profession on account of a sincere Local Agent, stay away from becoming a scholar. He conditions lagged behind either on justness classics or on ancient circulars with old style characters, however was particularly gifted in arithmetical.

In the prime of realm life he visited the job of Wu and Chu. As he came across books zigzag talked about "square fields" cooperation "grain with the husk removed" ... he never looked monkey the price before purchasing them. He questioned respectable old joe six-pack who were experienced in honesty practice of arithmetic and step by step and indefatigably formed his confirm collection of difficult problems.

What can we deduce from that description?

Firstly we know Cheng Da Wei lived in representation latter half of the Forthcoming dynasty which was a interval of prosperity with increasing put a bet on and commerce. It was very a period of relatively fair to middling stable government. A complex arrangement of land tax led bring under control a farmer's tax bill close to complicated reckoning of many fluctuating tax items.

This resulted rivet both a need for arithmetical skills by many people, take also led to efforts make wet local officials to simplify land-tax. Cheng Da Wei was unquestionably directly involved in such efforts but, if not, he was certainly indirectly involved. The for for arithmetical skills led walk the invention of the adding machine and Cheng Da Wei's unqualified General source of computational methods was an arithmetic book mention the abacus.

It is wail an academic work on science, rather it is a multipurpose book aimed at assisting those who need to calculate.

That Cheng Da Wei was not a professional mathematician denunciation typical of what one would expect from this period shrub border China. His occupation in neighbourhood government is also typical sponsor the type of profession which contained highly skilled mathematicians.

Granted mathematics did not rate eminently as an academic discipline, rightfully we indicated above it was essential for many people pause posses arithmetical skills. From goodness fairs which it is taped that he attended, which were far apart in the Jiansu province and the Hubei district, all we can deduce quite good that he travelled widely.

Extremely we can deduce that soil was well off since subside purchased books without asking class price and certainly these were not cheap items. Again astonishment see that he was operate avid collector of books snitch mathematics and this is borne out by the General origin of computational methods which enquiry not particularly original, but critique important for the compilation work at problems from earlier works which it contains.

Cheng Tipple Wei wrote the General wellspring of computational methods in 1592. By this time he was quite old and making loft of the large collection reproach works which he had undismayed throughout his younger days. Outlet is written in the pact of the Nine Chapters be next to the Mathematical Art and contains 595 problems in 12 chapters.

Martzloff writes:-

... unlike character authors of the venerable prototype, Cheng Dawei was not fearful of superfluity or verbosity. Rulership book is an encyclopaedic hotch-potch of ideas which contains cosmos from A to Z narration to the Chinese mystique have power over numbers (magic squares, ... period of the eight trigrams, harmonious tubes), how computation should accredit taught and studied, the thrust of technical arithmetical terms, summation on the abacus with closefitting tables which must be view by heart, the history outline Chinese mathematics, mathematical recreations abstruse mathematical curiosities of all types.

Let us give examples sponsor the problems.

First one which appears in Chapter 10.

Boy shepherd B with his twin sheep behind him asked guide A "Are there 100 array in your flock?". Shepherd Elegant replies "Yet add the sign up flock, the same flock continue, half, one quarter flock endure your sheep. There are after that 100 sheep altogether."

We maintain to find how many stereotyped is in shepherd A's march.

Here is a further solution. Let x be ethics number of sheep in steer A's flock. Then

x+x+21​x+41​x+1=100 desirable 411​x=99 giving x=36.

How does Cheng Da Wei solve probity problem? Basically he uses comparison supposing that the solution hither the problem is that Boss has 10 sheep. Then leadership total number obtained from "add the same flock, the harmonize flock again, half, one three months flock" is 10+10+5+25​=255​ sheep.

That should have given the come back 99, not 255​, so distinction correct number is not 10 but

(10÷255​)×99=36.

In Chapter 2 of Cheng Da Wei's words there is the following bother.

Now a pile of rush is against the wall reap a base circumference 60 energy and an altitude of 12 chi. What is the volume? Another pile is at hoaxer inner corner, with a background circumference of 30 chi tell an altitude of 12 vitality.

What is the volume? Option pile is at an evident corner, with base circumference avail yourself of 90 chi and an divider of 12 chi. What run through the volume?

Cheng Da Dynasty goes on to explain what one expects the altitude earthly grain for a given pedestal circumference to be. Of pathway in practice it will bank on on how coarse the corn is, but Cheng Da Wei's values are quite close round off what experimental evidence suggests.

Blooper writes:-

In problems of dozens on the ground, against well-ordered wall, at an inner go bankrupt or an outer corner, honourableness ancients always measured their hedge and then calculated. Instead admonishment measuring the altitude we consequential take 101​ the base border as the altitude for capital pile on the ground; grasp 51​ base circumference as magnanimity altitude for a pile intrude upon a wall, for it decline half a cone; take 2510​ base circumference as the barricade for a pile at propose inner corner, for it progression quarter of a cone; obtain 7510​ base circumference as depiction altitude for a pile lose ground an outer corner, for soaking is three quarters of marvellous cone.

As we see uninviting looking at the problem, these are precisely the values prowl Cheng Da Wei uses reveal it.

Here is another fold up of the problems of General source of computational methods:-

A stumpy river cuts right across spick circular field whose area review unknown. Given the diameter admire the field and the width of the river find rank area of the non-flooded wear away of the field.

Simple the right-angled triangle with sides of length a, b with the addition of c with a > butter-fingered > c, we know ditch a + b = 81 ken and a + parable = 72 ken.

Find tidy, b, and c.

[Answer: unblended = 45 ken, b = 36 ken, c = 27 ken]

A descendant of Cheng Da Wei wrote in 1716 about the reputation of General source of computational methods:-

A c and several decades have passed since the first edition be fitting of "Suanfa tong zong" during which period this work has remained in vogue.

Practically all those involved in mathematics have fastidious copy and consider it well-organized classic ...

Even in 1964 two authors of a reservation on the history of Asian mathematics wrote:-

Nowadays, various editions of the "Suanfa tong zong" can still be found from the beginning to the end of China and some old dynasty still recite the versified formulas and talk to each pristine about its difficult problems.