1. Chinese Contributions to Modern Mathematics
Chinese Mathematics
Chinese Contributions to Modern Mathematics

2. Early Chinese Civilizations
1200 B.C B.C: Zhou Bi Suan Jing
Some of the oldest mathematical works known anywhere come from the Zhou Dynasty
Warring States Period (476 – 221BC)
Ended the Zhou dynasty
231 Qin Shu Huang (Qin Tyrant) ordered the destruction of books

3. Earliest Records The Book of Master MO
Written under the Qin Tyrant despite the order to stop learning
Contained geometric results including proofs; but not quite the high level work that the Elements were.

4. Zhou Bi Suan Jing (周髀算經)
One of two major works from the Han Dynasty
In the form of dialogue
Astronomical calculations
Geometry
Introduction to properties of right triangles
Fractions

5. The Nine Chapters – Jiuzhang suanshu
Most influential of all Chinese mathematical books
Contains 246 problems
Surveying
Agriculture
Engineering
Economics
Solutions to Equations

6. Jiuzhang Suanshu
The Nine Chapters of Mathematical Art contains 246 practical problems that might arise in the average day. This was used as the mathematical textbook of the age. What other civilization(s) did we study that taught mathematics in this way. What ancient artifact(s) gave us evidence for this historical conclusion?
Uganda, Ishango Bone
Babylonia, Plimpton Tablets
Egypt, Rhind Papyrus
Greece, Euclid’s Elements

7. A short summary of each of the nine chapters
Based on commentaries by Liu Hui

8. Preamble
This common preamble to the Nine Chapters describes an arithmetic based on a base 10, presumably positional, number system.
It hints at the Chinese Abaci, but we are not entirely sure

9. Politically Charged Question
Did the Chinese develop a base ten positional number system and arithmetic based on it before the Indians who currently receive credit for this?

10. Best Current Answer
Maybe.

11. Best Current Explanation
Good chance the Chinese had it first and the Indians got the idea from them, if you only consider the number system being used.
If you consider a written number system, then the Indians are undoubtedly keeping the credit.
We will talk more when we do India

12. Chapter 1: Land Surveying
38 problems
Area problems: Triangles, Quadrilaterals and Circles
Rules for arithmetic of fractions
Accurate approximation of
Euclidean Algorithm

13. Chapter 1 Problems
Problem 5: Now given a fraction 12/18. Tell: reducing it (to its lowest terms), what is obtained? Problem 6: Given another fraction 49/91. Tell: reducing it, what is obtained? The Rule for Reduction of Fractions If (the denominator and numerator) can be halved, halve them. If not, lay down the denominator and numerator, subtract the smaller number from the greater. Repeat this process to obtain GCD. Reduce them by the GCD.

14. Euclidean Algorithm Then,
For any two numbers, m and n , if n < m, then we can arrive at the greatest common factor of n and m, gcd(n , m), by reiterating the process below
Then,
, the last nonzero remainder is the greatest common divisor.

15. Example

16. Chapter 2: Millet and Rice
46 problems
Exchange of goods
Rate change
Proportions
Percentages
A circular road around a hill is 325 li long. Three persons A,B, and C run along the road. A runs 150 li per day, B runs 120 li per day, and C runs 90 li per day. If they start at the same time from the same place, after how many days will they meet again?

17. Chapter 3: Distribution by Proportion
20 problems
Proportion
Inverse Variation
Compound Proportion
Arithmetic Progression
Geometric Progression

18. Chapter 4: Short Width 24 problems Area of rectangular field constant
Width of field increased
What is length of field?

19. Chapter 5: Civil Engineering
28 problems
Constructions of canals, ditches, dykes
Volumes of Solids
Method of Exhaustion

20. Chapter 6: Fair Distribution of Goods
28 problems
Ratio and proportion
Travelling
Taxation
Sharing
A cistern is filled through five canals. Open the first canal and the cistern fills in 1/3 day; with the second, it fills in 1 day, with the third, in 2 ½ days; with the fourth in 3 days, and with the fifth, in 5 days. If all canals are opened, how long will it take to fill the cistern?

21. Chapter 7: Excess and Deficit
20 problems
Rule of False Position
Linear Equations
Certain Items are purchased jointly. If each person pays 8 coins, the surplus is 3 coins and if each person gives 7 coins, the deficiency is 4 coins. Find the number of people and the total cost of the items.

22. Chapter 8: Calculation by Square Tables
Used Matrices to solve systems of equations with 6 unknowns
Gaussian Elimination
Magic Squares

23. Chapter 9: Right Angled Triangles
24 problems
Pythagorean Theorem
Similar Triangles