Liu Hui
fl. c. 263
Chinese Mathematician
The first non-Greek mathematician of distinction, Liu Hui developed an early approximation of π. He is also known for his commentary on an ancient Chinese mathematical work and for his use of calculating rods, a form of computing developed by mathematicians in China centuries earlier.
Liu Hui lived in the era of the Three Kingdoms (221-265), a period of anarchy immediately following the collapse of the Han Dynasty. Despite the confusion of the times, the age produced a great number of cultural and scientific advancements; in the fourteenth century a popular book entitled Romance of the Three Kingdoms would celebrate this period in Chinese history.
The three kingdoms were Wu, Shu, and Wei, in whose government Liu Hui served as an official. The only certain date of his life is 263, when he wrote a commentary on Chiu-chang Suan-shu or Jiuzhang Suanshu (Nine chapters of mathematical art). Two years later, in 265, Wei came under the control of the Western Ch'in Dynasty, which eventually absorbed Wu and Shu. The Western Ch'in would maintain power until 316, when China experienced one of the many invasions by nomadic tribes from the north that characterized its history in the premodern period. Only in 589, nearly four centuries after the collapse of the Han Dynasty, would China reunify.
As for the "Nine Chapters," this was a text of unknown authorship dating back to the first century B.C. The oldest known Chinese mathematical text, it contained 246 problems, which as the title suggested were presented in nine chapters. The first of these concerned arithmetic and the fundamentals of geometry, and included a discussion of the counting rods.
The latter, which probably originated in the fifth century B.C., were small bamboo sticks positioned in such a way as to provide something like a decimal place-value system. A space signified zero, a concept that had yet to be formalized even by the mathematicians of India, who are typically credited with this idea. The countingrod system arranged numbers from left to right—a notable fact in a country where people read from right to left.
Liu Hui is often credited with using red counting rods for positive numbers and black ones for negatives—a concept that, like zero,had yet to gain formal definition. (The articulation of these and other fundamental ideas is typically credited to mathematicians of India's Gupta Empire, c. 320-540.). In fact the use of red and black counting rods can be traced to Chapter 4 of the "Nine Chapters."
The second, third, and sixth chapters involved applications of mathematics for the purposes of governing—for instance, calculation of fair taxes in chapter 6—and chapter 5 explored measurements of various figures. The seventh chapter examined mathematical logic; the eighth simultaneous linear equations and negative numbers; and the ninth the applications of what mathematicians in the West would have called the Pythagorean Theorem. (The latter may have been discovered by the Babylonians as many as a thousand years before Pythagoras [c. 580-c. 500 B.C.], and it is likely that the Chinese discovery of the principle took place independently.)
Chapter 5 also included a figure of 3 for π, but in his commentary on the "Nine Chapters," Liu Hui presented a much more accurate figure. This he did by using polygons to approximate circles: by working from a 96- to a 192-sided polygon, he reached a figure of 3.141014. Today, of course, mathematicians have calculated the value of this irrational number to well over 1 million places, but 3.141592 is the abbreviated form. A century before Liu Hui, Ptolemy (c. 100-170) had calculated it at 3.1416, and two centuries later, the Chinese mathematician Tsu Ch'ung-chih (Zu Chongzhi; 429-500) offered the figure of 355/113, very close to the number accepted today.
In addition to his commentary on the "Nine Chapters," Liu Hui wrote Haidao suanjing, or "Sea Island Mathematical Manual." This began as an appendix to the earlier work, but eventually grew to include, among other things, nine surveying problems.
This is the complete article, containing 654 words
(approx. 2 pages at 300 words per page).
