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Chinese Mathematics

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

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Chinese Mathematics

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  1. 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 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

  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.

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

  18. 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

  19. That’s All Folks!

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