Chinese mathematics facts for kids

Kids Encyclopedia Facts

Mathematics in China began to develop on its own around 1100 BCE. Chinese mathematicians created a number system that included very large and negative numbers. They also used different ways to write numbers, like binary (base 2) and decimal (base 10). They made big steps in algebra, geometry, number theory, and trigonometry.

Starting with the Han dynasty, Chinese mathematicians became very good at solving complex equations. They found ways to calculate the roots of numbers and solutions to equations. Important books from this time, like The Nine Chapters on the Mathematical Art and the Book on Numbers and Computation, showed how to solve many everyday math problems. These calculations were often done using a counting board. The methods in these books were similar to modern ways of solving many equations at once. Chinese algebra reached its peak in the 13th century during the Yuan dynasty with the development of tian yuan shu, a special way of using algebra.

Because of language and distance, Chinese mathematics developed mostly on its own, separate from ancient Mediterranean math. However, some ideas likely traveled across Asia. Many early mathematical discoveries in China, like the Pythagorean theorem, were found centuries before similar discoveries in other parts of the world. For example, the Pythagorean theorem was known in China around the time of the Duke of Zhou. Also, the pattern known as Pascal's triangle was known in China centuries before Blaise Pascal in Europe, as shown by the scholar Shen Kuo during the Song dynasty.

Early Chinese Mathematics

Visual proof for the (3, 4, 5) triangle as in the Zhoubi Suanjing (500–200 BCE)

Oracle bone script numeral system

counting rod place value decimal

During the Shang dynasty (around 1600–1050 BCE), one of the oldest mathematical works was the I Ching. This book used complex patterns called hexagrams. Later, the mathematician Leibniz noted that the I Ching contained ideas similar to binary numbers.

The Chinese developed a full decimal system during the Shang period. Early on, they understood basic arithmetic, algebra, equations, and negative numbers. They used counting rods for these calculations. While they focused a lot on math for astronomical purposes, they were also pioneers in using negative numbers and decimals.

Math was one of the Six Arts that students had to master during the Zhou dynasty (1122–256 BCE). Learning these arts perfectly was important for becoming a well-rounded person, much like the idea of a "Renaissance man" in Europe. These arts were rooted in Confucian philosophy.

The oldest known geometry text in China comes from the Mohist canon, written around 330 BCE by followers of Mozi. This book, called the Mo Jing, discussed many scientific topics, including math. It described geometric ideas like points, lines, and planes. It also defined terms like circumference, diameter, radius, and volume.

There are still some debates about the exact dates of ancient Chinese math books. For example, the Zhoubi Suanjing is thought to be from around 1200–1000 BCE, but some scholars believe it was written later. This book includes a detailed proof of the Gougu Theorem, which is a special case of the Pythagorean theorem. It also focused on astronomical calculations. A recent discovery of the Tsinghua Bamboo Slips, from around 305 BCE, showed an early decimal multiplication table.

The abacus, a tool for calculations, was first mentioned around the 2nd century BCE. It was used alongside "calculation with rods," where small bamboo sticks were placed on a checkerboard.

Qin Dynasty Mathematics

Not much is known about mathematics during the Qin dynasty (221–206 BCE) because many ancient writings were lost due to historical events. However, we can learn about their math skills from their large construction projects. The Qin dynasty created a standard system of weights and measures. Emperor Qin Shi Huang ordered the building of many grand structures, including his tomb with life-sized statues and parts of the Great Wall of China. These projects required advanced math for calculating volume, area, and proportions.

Recent discoveries of Qin bamboo slips have shown early examples of mathematical writings.

Han Dynasty Discoveries

The Nine Chapters on the Mathematical Art

During the Han dynasty (206 BCE – 220 CE), numbers were organized into a place-value decimal system. This system was used on a counting board with counting rods. These rods used nine symbols, and a blank space on the board represented zero. Negative numbers and fractions were also used in solving problems.

Important math books from this time, like the Book on Numbers and Computation and Jiuzhang suanshu, covered basic math operations such as addition, subtraction, multiplication, and division. They also showed how to find square and cube roots, which helped solve more complex equations. Both books made big steps in linear algebra, which is about solving systems of equations with many unknowns.

In these early texts, the value of pi was often considered to be three. However, mathematicians like Liu Xin (died 23 CE) and Zhang Heng (78–139 CE) found more accurate estimates for pi. Chinese mathematics during this period focused on solving practical problems, such as dividing land or calculating payments. They were less focused on theoretical proofs in the way modern geometry or algebra does.

Book on Numbers and Computation

The Book on Numbers and Computation is a text of about seven thousand characters, written on 190 bamboo strips. It was found in 1984 in a tomb in Hubei province that was sealed in 186 BCE. This book contains many basic math problems, some of which are similar to those in The Nine Chapters. It shows how to approximate square roots and solve systems of two equations with two unknowns using a method called "false position."

The Nine Chapters on the Mathematical Art

The Nine Chapters on the Mathematical Art is a very important Chinese math book. It dates back to at least 179 CE, though some parts might be older. The author(s) are unknown. The book presents 246 problems with answers and step-by-step solutions, but without formal proofs. Later, the mathematician Liu Hui added explanations and proofs to these problems.

This book was highly influential and became a key part of math education in later centuries. It covers problems in surveying, agriculture, engineering, taxation, and solving equations, including those related to right triangles. The Nine Chapters also made important contributions to solving quadratic equations and to fangcheng, which is now known as linear algebra. It showed how to solve systems of linear equations using methods similar to modern Gaussian elimination. These problems were often solved using negative numbers and fractions on a counting board.

Calculating Pi

In The Nine Chapters on the Mathematical Art, pi was often used as three for problems involving circles and spheres. Historians believe this came from observing the 3:1 relationship between a circle's circumference and its diameter.

Some Han mathematicians tried to find a more precise value for pi. Liu Xin estimated pi to be about 3.154. Later, Liu Hui improved this by calculating pi as 3.141024. He did this by using polygons with many sides inside a circle. Even later, Zu Chongzhi (429–500 CE) found an incredibly accurate range for pi: between 3.1415926 and 3.1415927. This level of accuracy was not achieved in Europe until the 16th century.

Division and Root Extraction

Basic math operations like addition, subtraction, multiplication, and division were known before the Han dynasty. The Nine Chapters on the Mathematical Art assumes readers know these. Han mathematicians calculated square and cube roots using a method similar to division, through a process of "successive approximation." This method was also used to solve more complex equations.

Fangcheng on a counting board

Linear Algebra

The Book of Computations was the first known text to solve systems of equations with two unknowns. It used the "false position method" for practical problems. The Nine Chapters on the Mathematical Art also used this method for similar problems.

Chapter Eight of The Nine Chapters focused on solving many equations with many unknowns. This was called the "fangcheng procedure." This chapter used methods similar to modern Gaussian elimination to solve these systems. Calculations were done on a counting board and included negative numbers and fractions. The counting board acted like a matrix, helping to organize the variables and equations.

Three Kingdoms, Jin, and Sixteen Kingdoms

Liu Hui's Survey of sea island

Sunzi algorithm for division 400 AD

al Khwarizmi division in the 9th century

Statue of Zu Chongzhi.

In the 3rd century, Liu Hui wrote important comments on The Nine Chapters. He also wrote Haidao Suanjing, which used the Pythagorean theorem and advanced surveying techniques. He was the first Chinese mathematician to calculate pi as 3.1416. He also used Cavalieri's principle to find the volume of a cylinder and developed early ideas of infinitesimal calculus.

fraction interpolation for pi

In the 5th century, Zu Chongzhi created the Da Ming Li calendar, which predicted many astronomical cycles. He improved Liu Hui's pi calculation, finding a value between 3.1415926 and 3.1415927. This was the most accurate value for pi for the next 900 years. He also found a very good fraction approximation for pi, $\tfrac{355}{113}$ , which was not discovered in Europe until the 16th century.

Zu Chongzhi, with his son Zu Geng, also used Cavalieri's principle to find an accurate way to calculate the volume of a sphere. His book, Zhui Shu, contained formulas for spheres and cubic equations, but it was unfortunately lost.

A math book called Sunzi Mathematical Classic, from between 200 and 400 CE, gave detailed steps for multiplication and division using counting rods. This book might have influenced how place-value systems and division methods developed in the West.

By the 5th century, the manual "Zhang Qiujian Suanjing" discussed linear and quadratic equations, showing that the Chinese already understood negative numbers.

Tang Dynasty Mathematics

By the Tang dynasty (618–907 CE), math was a standard subject in schools. The Ten Computational Canons was a collection of ten Chinese math books, put together by mathematician Li Chunfeng (602–670 CE). These became the official textbooks for imperial math exams.

Wang Xiaotong, a great mathematician at the start of the Tang dynasty, wrote Jigu Suanjing. This book was the first to show how to solve general cubic equations.

During the Tang dynasty, the Tibetans also began to learn arithmetic from China.

Indian mathematical ideas, like Aryabhata's sine table, were translated into Chinese in 718 CE. While the Chinese excelled in other math areas, early trigonometry was not as widely used as in India and the Islamic world.

The Buddhist monk and mathematician Yi Xing was known for calculating a tangent table. He also famously tried to calculate the number of possible positions on a game of Go.

Song and Yuan Dynasties

Yang Hui triangle (Pascal's triangle) using rod numerals, as depicted in a publication of Zhu Shijie in 1303 AD

During the Northern Song dynasty, mathematician Jia Xian developed a method for finding square and cube roots, similar to what is now called Horner's rule.

Four important mathematicians lived during the Song dynasty (960–1279) and Yuan dynasty (1271–1368): Yang Hui, Qin Jiushao, Li Zhi, and Zhu Shijie. They all used methods similar to the Horner-Ruffini method to solve various types of equations, centuries before these methods were known in Europe. Yang Hui was also the first to discover and prove "Pascal's Triangle" in China.

Li Zhi explored a type of algebraic geometry based on tiān yuán shù. His book, Ceyuan haijing, changed how problems about circles inside triangles were solved, using algebra instead of traditional geometry. Guo Shoujing also worked on spherical trigonometry for accurate astronomical calculations.

Qin Jiushao (around 1202–1261) was the first to use a zero symbol in Chinese mathematics. Before this, blank spaces were used. He also developed methods for solving high-order equations.

Pascal's triangle was first shown in China by Yang Hui in his book Xiangjie Jiuzhang Suanfa, though it was described earlier by Jia Xian around 1100 CE.

Algebra

Ceyuan haijing

Li Ye's inscribed circle in triangle:Diagram of a round town

Yang Hui's magic concentric circles – numbers on each circle and diameter (ignoring the middle 9) sum to 138

Ceyuan haijing (Sea-Mirror of the Circle Measurements), written by Li Zhi (1192–1272 CE), is a collection of formulas and problems about circles inside triangles. He used Tian yuan shu to turn complex geometry problems into algebra problems. He then used a method similar to Horner's method to solve equations with degrees as high as six.

Jade Mirror of the Four Unknowns

Facsimile of the Jade Mirror of Four Unknowns

Jade Mirror of the Four Unknowns, written by Zhu Shijie in 1303 CE, represents a high point in Chinese algebra. It used four symbols (heaven, earth, man, and matter) for four unknown quantities in algebraic equations. The book deals with solving many equations at once and equations with degrees as high as fourteen, using a method similar to Horner's method.

The book also includes many summation series equations, such as: $1^2 + 2^2 + 3^2 + \cdots + n^2 = {n(n + 1)(2n + 1)\over 3!}$

Mathematical Treatise in Nine Sections

The Mathematical Treatise in Nine Sections, written by Qin Jiushao (around 1202–1261), introduced a method for solving simultaneous congruences. This was a major achievement in Chinese indeterminate analysis.

Magic Squares and Circles

The earliest known magic squares with more than three rows and columns are credited to Yang Hui (around 1261–1275). He worked with magic squares up to ten rows and columns. He also explored magic circles.

Trigonometry

Early trigonometry in China began to grow during the Song dynasty (960–1279). Mathematicians started to see the need for spherical trigonometry in calendar science and astronomy. The scholar Shen Kuo (1031–1095) used trigonometric functions to solve problems involving chords and arcs. His work laid the foundation for spherical trigonometry, which was further developed in the 13th century by astronomer Guo Shoujing (1231–1316). Guo used spherical trigonometry for precise astronomical calculations and to improve the Chinese calendar.

Despite these achievements, another major work in Chinese trigonometry was not published until 1607. This was the translation of Euclid's Elements by Chinese official Xu Guangqi (1562–1633) and Italian Jesuit Matteo Ricci (1552–1610).

Ming Dynasty Mathematics

After the Yuan dynasty fell, China became less interested in some types of knowledge, including advanced math and physics. Imperial exams included very little mathematics, and recent discoveries were ignored. Many older math texts became hard to understand without teachers to explain them.

An abacus

Instead, math progress focused on tools for calculation. In the 15th century, the abacus became very popular in its suan pan form. It was easy to use, fast, and accurate, quickly replacing counting rods. The use of the abacus, called Zhusuan, led to new math books. Suanfa Tongzong (General Source of Computational Methods), published in 1592 by Cheng Dawei, was used for over 300 years. Zhu Zaiyu, Prince of Zheng, used an 81-position abacus to calculate square and cube roots with high accuracy, which helped him develop the equal-temperament system in music.

In the late 16th century, Matteo Ricci and Xu Guangqi translated Euclid's Elements into Chinese. Other missionaries also translated Western math books. However, Chinese scholars at the time found the Western focus on proofs confusing, as they were used to step-by-step problem-solving.

Qing Dynasty Mathematics

Under the Kangxi Emperor, who learned Western mathematics from Jesuit missionaries, Chinese mathematics received some official support. The emperor ordered a 53-volume work called Shuli Jingyun ("The Essence of Mathematical Study"), which was printed in 1723. This work introduced Western mathematical knowledge in a systematic way.

In 1773, the Qianlong Emperor ordered the compilation of the Complete Library of the Four Treasuries. Scholar Dai Zhen (1724–1777) selected and proofread The Nine Chapters on the Mathematical Art and other ancient math works. Lost math books from the Song and Yuan dynasties, like Si-yüan yü-jian and Ceyuan haijing, were also found and printed. This led to new research into China's mathematical past.

Western Influences

The First Opium War in 1840 led to China opening up to the outside world, bringing in many Western mathematical studies. In 1852, Chinese mathematician Li Shanlan and British missionary Alexander Wylie translated parts of Euclid's Elements and books on algebra. More works on astronomy and calculus followed.

Initially, Chinese scholars debated whether to embrace Western knowledge. However, by the end of the 19th century, it became clear that adopting Western ideas was important for China's progress. Chinese scholars, often trained in Western missionary schools, began to lose touch with their own traditional math. By 1911, Western mathematics became the main focus in China.

Modern Chinese Mathematics

After the establishment of the Chinese republic in 1912, Chinese mathematics saw a great revival. Modern Chinese mathematicians have made many important contributions to various fields of math.

Some famous modern Chinese mathematicians include:

Shiing-Shen Chern, a leader in geometry and one of the greatest mathematicians of the 20th century.
Ky Fan, who contributed to fixed point theory and influenced nonlinear functional analysis.
Shing-Tung Yau, a Fields Medal winner who has influenced both physics and mathematics.
Terence Tao, a Fields Medal winner and child prodigy who is the youngest participant and medalist in the history of the International Mathematical Olympiad.
Yitang Zhang, a number theorist who found the first finite bound on gaps between prime numbers.
Chen Jingrun, a number theorist who proved Chen's theorem, an important step towards Goldbach's conjecture.

People's Republic of China

When the People's Republic of China was founded in 1949, the government strongly supported science, even with limited funds. The Chinese Academy of Sciences was established in 1949, and the Institute of Mathematics in 1952. The Chinese Mathematical Society and its journals were restarted and expanded. In the 18 years after 1949, the number of published math papers greatly increased, with many reaching advanced international standards.

During the Cultural Revolution, scientific progress slowed. However, mathematicians like Chen Jingrun and Hua Luogeng continued their work. After this period, Chinese science and mathematics experienced a revival. A new math development plan was created in Beijing in 1977, and math societies, journals, and education were strengthened.

Important achievements by Chinese mathematicians include Xia Zhihong's proof of the Painleve conjecture in 1988, which deals with the movement of celestial bodies. More recently, in 2007, Shen Weixiao and others proved the Real Fatou conjecture, a significant development in conformal dynamics.

International Mathematical Olympiad Performance

China has consistently performed very well at the International Mathematical Olympiad, often achieving the highest team scores and winning many gold medals.

Mathematics Education in China

The first mention of a book used for learning math in China dates back to the 2nd century CE. Scholars like Ma Xu and Zheng Xuan studied the Nine Chapters on Mathematical Procedures. It is believed that math, like medicine, was often taught orally. The style of the Suàn shù shū suggests it was put together from different sources and then organized.