1. By: Joseph Venusto and Brianna Nilsen
Chinese Mathematics
By: Joseph Venusto and
Brianna Nilsen

2. Mathematicians
The Chinese mathematician Sun-tzi wrote a book containing one of the first Chinese problems in “indeterminate analysis”: “There are things of an unknown number which when divided by 3 leave 2, by 5 leave 3 and by 7 leave 2. What is the smallest number?”
This leads to the Chinese Remainder Theorem

3. Mathematicians Continued
After Sun-tzi’s period there were a number of mathematicians spending time on the computation of pi
One such person, Wang Fan, approximated pi as 142/45 = 3.155

4. 430 AD—501AD
Two centuries after Wang Fan’s discovery , Tsu Ch’ung-chih and his son, who wrote a joint book (now lost), discovered that <pi< and rationalized this as 355/113 which describes pi correctly to 6 decimal places
Europe did not discover this until 1585

5. Ch’in Kiu-shao
This mathematician picked up indeterminate equations where Sun-tzi ended
He was the first Chinese to give the symbol “0” for the number zero

6. Li Yeh
Li Yeh is a Chinese mathematician who created a notation for negative numbers
This notation is a diagonal stroke through the far right digit when the negative number is written in the Chinese scientific system

7. Yang Hui
Yang Hui presented the earliest known version of Pascal’s Triangle
(x+y)6= x6+6x5y+15x4y2+20x3y3+15x2y4+6xy5+y6
(x+y)7= x7+7x6y+21x5y2+35x4y3+35x3y4+21x2y5+7xy6+y7

8. Pascal’s Triangle

9. Chu Shi-kie
Chu Shi-kie spoke of the Chinese Pascal’s Triangle as if it was already old in his time
This suggests that China had known the binomial Theorem for a long time
He also used various matrix methods known today

10. Multiplication Trick
There is an old Chinese multiplication trick to multiply easily without any technology.
17x29=493
321x123=39483

11. The Nine Chapters on the Mathematical Art
This is a book composed from generations of scholars ranging from the 10th to 2nd century BC
This book describes an approach to mathematics centered on solving problems

12. The Nine Chapters on the Mathematical Art
Entries in the book are usually as follows:
A statement of a problem
The statement of the solution
An explanation of the procedure leading to the solution

13. The Nine Chapters on the Mathematical Art

14. The Nine Chapters on the Mathematical Art
This book is far advanced from what Europe had
Chapter 7’s method was not found until the 13th century
Chapter 8’s method uses Gaussian elimination (row-echelon and reduced row) before Carl Friedrich Gauss (1777—1855)
It also includes a proof of the Pythagorean Theorem

15. The Nine Chapters on the Mathematical Art
Table of Contents:
方田 Fangtian - Rectangular fields. Areas of fields of various shapes; manipulation of vulgar fractions.
粟米 Sumi - Millet and rice. Exchange of commodities at different rates; pricing.
衰分 Cuifen - Proportional distribution. Distribution of commodities and money at proportional rates.
少廣 Shaoguang - The lesser breadth. Division by mixed numbers; extraction of square and cube roots; dimensions, area and volume of circle and sphere.
商功 Shanggong - Consultations on works. Volumes of solids of various shapes.

16. The Nine Chapters on the Mathematical Art
Table of Contents
均輸 Junshu - Equitable taxation. More advanced problems on proportion.
盈不足 Yingbuzu - Excess and deficit. Linear problems solved using the principle known later in the West as the rule of false position.
方程 Fangcheng - The rectangular array. Systems of linear equations, solved by a principle similar to Gaussian elimination.
勾股 Gougu - Base and altitude. Problems involving the principle known in the West as the Pythagorean Theorem.

17. Abacus
The abacus is a ancient math tool that allows you to add and subtract using beads on a pole.

18. Sources

19. That’s All Folks!