Chinese Mathematics Overview

Chinese Mathematics

• Chinese mathematics emerged independently in China by the 11th century BCE.
• The Chinese independently developed a real number system that includes significantly large and negative numbers, more than one numeral system (binary and decimal), algebra, geometry, number theory and trigonometry.

### Nature of Chinese Mathematics

• Chinese mathematics was defined by Chinese times as the “art of calculation”.
•  This art was both a practical and spiritual one, and covered a wide range of subjects from religion and astronomy to water control and administration.

Materials Used:

• Oracle Bone Script: First ancient Chinese number system written on flat cattle bones and tortoise shells. The largest number found using this method was 30,000.
• Counting Rods: The second form of Chinese number used small bamboo rods arranged to represent the numbers 1 to 9. This method was based on the decimal system and employed a positional value system.
• Abacus: The first Chinese Abacus or suanpa uses beads sliding on a wire to represent numbers. For numbers up to 4, slide the required number of beads in the lower part up to the middle bar. For five or above, slide one bead above the middle bar down (representing 5), and 1, 2, 3 or 4 beads up to the middle bar for the numbers 6, 7, 8, or 9 respectively.

Nine Chapters on the Mathematical Art

• Also called “JiuzhangSuanshu”.
• A practical handbook of mathematics consisting of 246 problems intended to provide methods to solve everyday problems.
•  Played a fundamental role in the development of mathematics in China.
•  The concept of proof is important to note.
•  It became an important tool in the education of civil servants, covering hundreds of problems in practical uses such as trade, taxation, engineering and the payment of wages.

Contribution to the Life of People

• The construction of canals, dams, and other water-infrastructure created a safer environment for the society.
•  Jiuzhang Suanshu or “Nine Chapters on the Mathematical Art” is regarded as an important tool in the education of civil servants, covering problems in practical uses such as trade, taxation, engineering and the payment of wages.

Prominent People

• Liu Hui: (220-280 CE) Solved linear equations using matrices (similar to Gaussian elimination). Calculated the value of Pi correct to five decimal places. He also formulated the early forms of integral and differential calculus.
•  Yang Hui: (1238-1319 CE) Flourished c. 1261–75, Qiantang, Zhejiang province, China. Yang’s Jiuzhang suan fa zuan lei (c. 1275; “Reclassification of the Mathematical Procedures in the Nine Chapters”)—a compilation and reclassification, (c. 100 BC–AD 50; Nine Chapters on the Mathematical Procedures)—contains the oldest representation of what is known in the West as Blaise Pascal’s triangle.
• Qin Jiushao: (1202-1261 CE) Developed a method of solving simultaneous linear congruence. He started formulating the solution of quadratic, cubic and high power equations using method of repeated approximations. Wrote his only mathematical book, now known as Shushu jiuzhang during mourning period. His book is divided into nine “categories,” each containing nine problems related to calendrical computations, meteorology, surveying of fields, surveying of remote objects, taxation, fortification works, construction works, military affairs, and commercial affairs.
• Sun Tzu: (200 CE) SunTzu was a Chinese mathematician, flourishing between the 3rd and the 5th century A D. Interested in astronomy and trying to develop a calendar, he investigated Diophantine equations. He is only known for authoring Sun Tzu Suan Ching (pinyin: Sun Zi Suan Jing; literally,"Sun Tzu's Calculation Classic"), which contains the Chinese remainder theorem.
• The Lo Shu Square (650 BCE) Sometimes called the Magic Square, is also at the root of ancient feng shui astrology, the flying star school Xuan Kong, as well as the I-Ching. The Lo Shu square is a 3X3 square where each row, column and diagonal adds up to 15.
• Contribution to the development of math: The existence of the dualistic theory of YIN and YANG, Yin represents even numbers and Yang represents odd numbers through the 3x3 magic square.
• The development of the decimal place value system: Used both in counting rods and the abacus.