Chinese MathematicsBy: Joseph Venusto and

Brianna Nilsen

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

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

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 3.1415926<pi<3.1415927 and rationalized this as 355/113 which describes pi correctly to 6 decimal places

• Europe did not discover this until 1585

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

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

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

Pascal’s Triangle

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

Multiplication Trick

• There is an old Chinese multiplication trick to multiply easily without any technology.

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

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

The Nine Chapters on the Mathematical Art

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

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.

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.

Abacus

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

• http://www.youtube.com/watch?v=CvsnftXXKdw

Sources• http://library.thinkquest

.org/27694/Chinese%20Mathematicians.htm• http://en.wikipedia.

org/wiki/The_Nine_Chapters_on_the_Mathematical_Art• http://en.wikipedia.org/wiki/Chinese_mathematics• http://etagor.blogspot.com/2009/05/chinese-pascals-

triangle.html• http://www.google.com/imgres?imgurl=http://

img.youtube.com/vi/d4svbYKRnZ8/0.jpg• http://www.google.com/imgres?imgurl=http://

gwydir.demon.co.uk/jo/numbers/machine/abacus.jpg• http://commons.wikimedia.org/wiki/

File:Chinese_Temple_Roof_2.jpg

That’s All Folks!