**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

References

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.

Invention:

Significance:

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.

Invention:

He wrote notes for:

The Arithmetical Classic of the Gnomon.

The Circular Paths of Heaven.

Significance:

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.

Invention:

Introduced

Elsewhere:

Used 700 years later by a European mathematician, Horner.

Significance:

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.

Invention:

It was made up of 81 problems in 9 categories.

Significance:

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).

Invention:

Significance:

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

Invention:

Over a thousand years later it was adopted in the west.

2nd Millennium BC

Introduced Elsewhere:

Invention:

Significance:

The Chinese were able to complete equations in a timely fashion.

Introduced Elsewhere:

Significance:

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

http://www-history.mcs.st-andrews.ac.uk/HistTopics/Nine_chapters.html

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

Geometry

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

Trigonometry

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)