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发帖数: 8441 | 1 http://rhart.org/algebra/
https://jhupbooks.press.jhu.edu/content/chinese-roots-linear-algebra
The Chinese Roots of Linear Algebra
Roger Hart
A monumental accomplishment in the history of non-Western mathematics, The
Chinese Roots of Linear Algebra explains the fundamentally visual way
Chinese mathematicians understood and solved mathematical problems. It
argues convincingly that what the West "discovered" in the sixteenth and
seventeenth centuries had already been known to the Chinese for 1,000 years.
Accomplished historian and Chinese-language scholar Roger Hart examines Nine
Chapters of Mathematical Arts—the classic ancient Chinese mathematics text
—and the arcane art of fangcheng, one of the most significant branches of
mathematics in Imperial China. Practiced between the first and seventeenth
centuries by anonymous and most likely illiterate adepts, fangcheng involves
manipulating counting rods on a counting board. It is essentially
equivalent to the solution of systems of N equations in N unknowns in modern
algebra, and its practice, Hart reveals, was visual and algorithmic.
Fangcheng practitioners viewed problems in two dimensions as an array of
numbers across counting boards. By "cross multiplying" these, they derived
solutions of systems of linear equations that are not found in ancient Greek
or early European mathematics. Doing so within a column equates to Gaussian
elimination, while the same operation among individual entries produces
determinantal-style solutions.
Mathematicians and historians of mathematics and science will find in The
Chinese Roots of Linear Algebra new ways to conceptualize the intellectual
development of linear algebra.
Roger Hart is an assistant professor in the Department of History at the
University of Texas, Austin. | w*********g
发帖数: 30882 | | p*********r
发帖数: 7944 | |
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