The Nine Chapters on the Mathematical Art: Companion and Commentary

by John N. Crossley (Translator), K'Ang-Shen Shen

The Nine Chapters on the Mathematical Art has been the most important mathematical source in China for the past 2000 years, comparable in significance to Euclid's Elements in the West. The Nine Chapters quickly acquired a distinguished reputation, and was the standard mathematics textbook in China and the surrounding regions until Western science was introduced in about 1600. This volume contains the first complete English translation of the Nine Chapters , together with the illuminating commentary of Liu Hui written in the 3rd century AD and other early century commentaries and further insights provided by the translators. The Nine Chapters contains 246 problems and their solutions, which fall into nine categories that are firmly based on practical needs. There are methods for solving problems in areas such as land measurement, construction, agriculture, commerce, and taxation, while the Chinese commentators provide the algorithms needed to solve the problems, and explanations of
how the algorithms work. The translators' commentary provides clear and accessible background material for the Western reader, explanations of technicalities, and notes on the treatment of similar or identical mathematical problems in other countries. This first, full-English translation gives us an idea of the distinctive style and important contributions that have been made by traditional Chinese mathematics.

Genres: Mathematics

612 pages, Hardcover

First published January 20, 1999

Reviews

[Brit Cheung · Rating 4 out of 5]

It took a few days to explore the books, a few chapters more exactly speaking.
For the Chinese version, it is profoundly intricate to decifer the ancient language into modern Chinese.I wouldn't have penetrated the meaning of each Maths problem if they hadn't been paraphrased into modern language. I could say these ancient Maths language was formidable and annoying to understand.

And for the English version, you need to decode those terminologies prior to the solutions of each Maths riddle.

A combination of exploration of the two is tough and time- consuming. It's alright to select only a few chapters to delve into.

The book would left you to admire the ancient knowledge on Maths that were no easy tasks to solve even today. You may be quite interested by how they figured out π to an so precise extent that we would feel amazed today.

Just one or two examples.
The idea of equations and functions manifested in those problems with different variables is not new to us today, but how did they do this in ancient days?

For instance, In modern Maths it's rather easy to figure out the problem as: x+2y=2z+6;
3x-z=2y-1; x+y=z;
It's the equation learned in preliminary （junior high）school for teenagers. It may not take minutes to figure out the answers asfollows: x=-6; y=-11/3；z=-29/3；But in ancient time when equations were not devised,the way of how to solve such problems is quite interesting.

Another instance for the famous Pythagorean theorem, if you didn't know it in the first place, can you figure it out or prove it? Memorizing the formula is of no great avail, because the deduction of its process is the key. Suppose we were knowing nothing about it, I don't assume we can figure it out easily.

And there are much more intricate Maths Problem like how to confirm the Volume of an Ellipsoid, which should be involved with the Definite Integral deduction knowledge , evidently the knowledge of modern Maths（Differential and Integral Calculus）. It is fascinating to see how the ancient people to understand and tackle this.

The book may rekindle interests for those Maths common sense we took for granted everyday but failed to grasp its essence. This book could allure us to tap a little deeper of their mechanisms behind them.

Avert the intricate ones and only confine to those that piqued real interests.
Just For Fun!!