## Nine Chapters on the Mathematical Art

*China*

In 212 BCE, the Emperor Qin Shi Huang commanded all books in the Qin Empire other than officially sanctioned ones be burned. This decree was not universally obeyed, but as a consequence of this order little is known about ancient Chinese mathematics before this date. After the book burning of 212 BCE, the Han dynasty (202 BCE–220 CE) produced works of mathematics which presumably expanded on works that are now lost.

After the book burning of 212 BCE, the Han dynasty (202 BCE–220 CE) produced works of mathematics which presumably expanded on works that are now lost. The most important of these is The Nine Chapters on the Mathematical Art, the full title of which appeared by CE 179, but existed in part under other titles beforehand. It consists of 246 word problems involving agriculture, business, employment of geometry to figure height spans and dimension ratios for Chinese pagoda towers, engineering, surveying, and includes material on right triangles.^{[79]} It created mathematical proof for the Pythagorean theorem,^{[81]} and a mathematical formula for Gaussian elimination.^{[80]} The treatise also provides values of π,^{[79]} which Chinese mathematicians originally approximated as 3 until Liu Xin (d. 23 CE) provided a figure of 3.1457 and subsequently Zhang Heng (78–139) approximated pi as 3.1724,^{[82]} as well as 3.162 by taking the square root of 10.^{[83]}

Negative numbers appear for the first time in history in the Nine Chapters on the Mathematical Art but may well contain much older material.^{[84]} The mathematician Liu Hui (c. 3rd century) established rules for the addition and subtraction of negative numbers.