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Copy of Chinese Civilization - Mathematics

Scientific Discoveries of Mathematics

Celeste Mae Chan

on 19 November 2013

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Transcript of Copy of Chinese Civilization - Mathematics

Mathematics x
Scientific Discovers =
Beginning of time
The End

Chinese mathematics made early contributions to the development and study of mathematics such as place value system, counting rods
Most of the inspiration of mathematics came from the study of astronomy in order to perfect the agricultural calender
Ancient Chinese mathematics very difference from Greek mathematics

Influential people through the development of mathematics
400 BC Gan De
130 BC Luoxia Hong
78 AD Zhang Heng
Suanpan (Also referred to as an Abacus)
Zhao Shuang (mathematician)
The Tree Kingdoms Period
Qin Jiushao (mathematician)
Song and Yuan Dynasty
Zu Chongzhi (Mathematician)
Northern and Southern Dynasties (429 - 500AD).
Significance of the Discoveries
Neolithic Era (3000 - 1500 B.C.)
Suanpans can be used for doing decimal computations, division, multiplication and for taking square roots and cube roots.
1000BC Chinese counting boards originate
500BC Greeks and Romans are using counting devices based on the same principles as the abacus
500AD The abacus is used in Europe.
Introduced elsewhere:
His notes summarized the importance of Gougu mathematics in the Eastern Han Dynasty.
He wrote notes for:
The Arithmetical Classic of the Gnomon.
The Circular Paths of Heaven.
He composed detailed solutions of the Problems in:
The Nine Mathematics Chapters of Huang Di (9 volumes).
The Collection of Calculating Method Instructions (2 volumes).
Jia Xian (Mathematician)
Song Dynasty
The principles and procedures of synthetic division in today's secondary-school mathematics are similar to Jia Xian's method.
Used 700 years later by a European mathematician, Horner.
In 1247, he composed Mathematical Treatise in Nine Sections (18 volumes).
Because of these achievements, the Song-Dynasty mathematical treatise gained a prominent status in the mathematical history of the Middle Ages.
It was made up of 81 problems in 9 categories.

His major contribution to math was deriving two approximations of pi.
His best approximation was between 3.1415926 and 3.1415927 (with the significance lying in the indication of the error range).
That was the world's most remarkable achievement at that time.
The two values of pi that he calculated had the detailed approximation of 22/7(≈3.14).
How to use abacus
Chinese Numbering System
The Chinese original writing system was simple, but efficient.
Xu Yue (born c. 185 - c. 227)

Student of Liu Hong

An influential government astronomer and mathematician

He was most credited for his accuracy for the new calendar

"Memoir on the Methods of Numbering"
uncertainty with his works
Provided methods of assigning the powers of 10
mentioned method of indefinite generation of even larger numbers
descriptions of various devices for representation; resembled the later creation of abacus
Magic Square
Over a thousand years later it was adopted in the west.
2nd Millennium BC
Introduced Elsewhere:
The Chinese were able to complete equations in a timely fashion.
Introduced Elsewhere:
2800 BC
Squares of numbers in each row, column and diagonal add up to the same total and were considered as having great spiritual and religious significance.
It is believed that it was first introduced to India, then the Arab countries, and then onto Europe.
the diagram on the right side of the page is usually called the "hypotenuse diagram" and illustrates the proof of the theorem in the 3-4-5 case. The diagram on the left shows how a square of side 3 fits into a square of side 5.
Gougu Theorem
(Later known as the Pythagorean Theorem)
This diagram illustrates a square of side 4 fitting into a square of side 5.
Interesting fact
Chinese mathematics evolved independently of Greek mathematics and is consequently of great interest to historians of mathematics
The Chinese were using the decimal system as early as the fourteenth century B.C., nearly 2,300 years before the first known use of the system in European mathematics. The Chinese were also the first to use a place for zero
Zhang Heng
Noticed an inaccuracy in the diameter of the ratio 4:3 (area of a square to area inscribed circle)

Began the calculation of pi

Compared the celestial circle to the diameter of the earth

Provided theoretical calculations of the square r of 10 initially which equaled 3.162.
The first step into mathematics
Nine Chapters on The Mathematical Art and Liu Hui
Lived in kingdom of Wei

Important commentary on the Jiuzhang suanshu also known as "Nine Chapters on the Mathematical Art"

Handbook filled with 246 problems and methods used to solve everyday problems of engineering, surveying, trade, and taxation

"I read the Nine Chapters as a boy, and studied it in full detail when I was older."
Leanne + Katsni - Kaoni
The Nine Chapters on the Mathematical Art
Chapter 1: Land Surveying.

Chapter 2: Millet and Rice.

Chapter 3: Distribution by Proportion.

Chapter 4: Short Width.

Chapter 6: Fair Distribution of Goods.

Chapter 7: Excess and Deficit.

Chapter 8: Calculation by Square Tables.

Chapter 9: Right angled triangles.
The foundation in the development of mathematics in China
Intro to History of Ancient Chinese Math
Prior to Qin Dynasty
Inscriptions on tortoise shells and animal bones in Shang Dynasty
13 symbols represented: 1-10 and multiples of 10 up to 10,000.
Suan Chou
aka 'Counting Rods'
First appearance: N/A
Built the foundation of Ancient Chinese Math
Can be written horizontal or vertical
Red = positive
Black = Negative
Xia Dynasty
"Records of the Great Historian" by Sima Qian
used compasses, rulers, and other geometrical tools
Warring States Period (770-476 BC)
"Book of Diverse Crafts" aka "Kao Gong Ji"
wrote about tools, measurements, and angles
Han Dynasty
Increase in mathematical systems
"Zhoubi Suanjing" 1st Century BC
wrote about astronomy and math
Western Han Dynasty (206BC-24 AD)
"Jiuzhang Suanshu"
(Nine Chapters on the Mathematical Art)
early Eastern Han Dynasty (25 AD -220 AD)
Sui Dynasty (581-618)
constructions and buildings believed to have an effect on calculations
4th-5th century
Pi (3.14) calculated to 7 decimal places by Zu Chongzhi
Linear and Quadratic equations
Negative numbers
Tang Dynasty (618-907)
Recognition in Schools
Imperial College (Guozijian)'s math department emerged in 656.
Textbooks: Suanjing Shishu
Ten textbooks important for classic ancient chinese mathematics
Not as recognized because China had their own system aka Chong Cha
Sine, tan, and secant existed
Quadratic interpolation (number root-finding)
Created in need of a calendar
Later influenced Song/Yuan Dynasty
Song and Yuan Dynasty
Ancient Chinese Math reached its peak
Suan Chou's influence increased significantly in 11th-14th century
Solutions to higher leveled equations
Some of which were not used in Europe until 18th century
Introduction of symbols
Development of mathematical tools and theories
Introduction of the "0"
Huangdi Juizhang Suanfa Xicao
Yigu Genyuan
Shushu Jizhang
Ceyuan Haijing
Yigu Yanduan
Xiang Jie Jiuzhang Suanfa
Riyong Suanfa
Yang Hui Suanfa
Suanxue Qimeng
Siyuan Yujian
Jia Xian
Liu Yi
Qin Jiushao
Li Ye
Li Ye
Yang Hui
Yang Hui
Yang Hui
Zhu Shijie
Zhu Shijie
Important works
Western Math
Ming and Qing dynasties
Downhill of Mathematics
End of 16th Century, Western Math began influencing China
19th century: algebra emerged in China
The abacus
Introduction of Trigonometry (Liu Hui)
In between Qing Dynasty and the Republic of China (1911-1949), beginning of students studying abroad
later becoming famous mathematicians
Mathematics in China today
1951: First National Conference of Chinese Mathematic Institutes

1966: Approximately 20,000 dissertations released

1/2 of 1960s: Unfortunately, suspension of mathematical research

1973: Chen Jingrui made a significant discovery in one of the oldest math problems (Goldbach's conjecture)
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