# Research Paper on 3000-Year History: How Mathematics Education in China Led to Development

 Paper Type:Â  Term paper Pages:Â  7 Wordcount:Â  1840 Words Date:Â  2023-05-07
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## Introduction

China's mathematical history is over 3000 years old. In China, mathematics was seen as a necessity and a utility. It was important to educate and build a country with great development, with Architecture, Commerce, Finances, and Surveying being the basis for this growth. The mathematics education practice in China has attracted much attention not only from educational communities but also the entire society (Wang et al., 2017). The development of this science occurred because of the needs of these people. The construction of the Great Wall, around 220 BC, was a triumph of engineering and mathematical calculation; the construction of sundials and the use of Abacus are also examples of mathematical advances in this region. The Chinese were one of the first civilizations to understand that calculations performed in a decimal system are simpler and more effective. For this, they used a positional system, a type of counting board with separate compartments for the units, tens, hundreds, etc. The operations performed by this method are very similar to the current one, with the difference that they are performed from left to right.

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In China, to have fun and spend time, several games and pastimes were created that used mathematics. Several of these Chinese Puzzles are famous to this day and among them, there is the famous legend of the magic squares. In this story, Emperor Yu, of the Xia dynasty, found on the banks of the Lo River a sacred turtle with the numbers 1 to 9 drawn on its shell, arranged in 3 rows and 3 columns, with the numbers for each row, column and diagonal having the same sum. Another famous puzzle is the Tangram, composed of fifteen geometric figures (Martzloff, 2009). This challenge is very useful, as it teaches important relationships between the areas of flat figures. Most of the ancient Chinese mathematics was inscribed on bamboo or paper, which perishes over time. This period includes 400 years of mathematical development history from the Qin and Han dynasties, Wei Jin, and the Northern and Southern Dynasties. Qin and Han's dynasties were the period of the formation of the ancient Chinese mathematics system. To systematically and theoretically enrich the mathematical knowledge, special books on mathematics appeared one after another.

The oldest suspected3 mathematical text is the Zhou Bi Suan Jing (The Mathematical Classic of the Zhou Gnomon4 and the Circular Paths of Heaven). It was probably compiled sometime in the period 500-200 BCE (Ancient Chinese Mathematics, 2016). Around the year 1400 BC there was evidence of the use of the abacus and the decimal system. In ancient China, specifically in the centuries before the imperial era, the study of mathematics was essential in the education of students: it was one of the six arts necessary to be a perfect knight (Martzloff, 2009). Some of China's oldest texts are preserved from that time, the Suan Shu Shu a compendium, written on bamboo rods, about problems of basic arithmetic, use of fractions and calculation of roots, the Jiuzhang Suanshu or treatise on the nine chapters of mathematical art, this text contains chapters dedicated to geometry, proportions, systems of linear equations. One of the most interesting things about this book is an approximation of the number pi and the "Gaogu theorem" in the Chinese version of the Pythagorean Theorem.

The history of mathematics dates back from the days of Zhang Heng: an ancient Chinese teacher who embraced different disciplines ranging from mathematics and astronomy to literature. Zhang made a good approximation to the volume of a sphere. In astronomy, he made a much more complete catalog of stars and constellations than that of the Greek master Hipparchus. Zhang Heng (78-139) studied various fields such as mathematics, engineering, and invention. He created the first seismograph in history. Later mathematicians criticized his fanaticism for ancient methods that unnecessarily led to mistakes.

The earliest monograph on mathematics in Chinese history is a book written in the numeracy book of the Han Dynasty, unearthed in Zhangjiashan, Jiangling, Hubei in 1984, and a book of Han resumes unearthed at the same time is written in the second year of Lu (186 BC) Year), so the book was written to 186 BC (should be before). In the Western Han Dynasty in the first century BC, the "Zhou Hua Shu Jing" was produced, although it is an astronomical work about Gaitan's theory of cosmology, contains a lot of mathematical content, and has two major achievements in mathematics: (1) Pythagorean A special case of the theorem and its general form; (2) Chen Zi's method of measuring the sun's height and distance, which was the pioneer of later gravity difference method (Pythagorean method). Besides, there are more complex root problems and fraction operations.

The extraordinary piece, Jiu Zhang Suan Shu (Nine Chapters of Mathematical Art), was written in 200 BC. For centuries this work has been used in schools, as its nine chapters are rich in content, from practical day-to-day resolutions to complex mathematical statements (Yuan, 2012). Some Chinese (for example, Liu Hui) believe that the basis of 9 Chapters was written about 1000 BC, and later some mathematicians contributed to it (Finashin, 2013). It was written in the early Eastern Han Dynasty in the first century BC. The book is written in the form of a problem set. It collects a total of 246 problems and their solutions, which belong to the nine chapters of Fengtian, Corn, Decay, Shaoguang, Commercial Power, Loss, Insufficient, Equation, and Pythagorean. The main content includes the four rules of fractions and the proportional algorithm, the calculation of various areas and volumes, and the calculation of Pythagorean measurements.

In terms of algebra, the concept of negative numbers and the law of addition and subtraction of positive and negative numbers introduced in the "Equations" chapter are the earliest records in the history of world mathematics; the solution of linear equations in the book is the same as the method taught in middle schools. As far as the characteristics of "Nine Chapters of Arithmetic" are concerned, it focuses on application, attaches theory to practice, and forms a mathematical system centered on calculations, which has a profound influence on ancient Chinese arithmetic. Some of its achievements, such as the decimal value system, today's technique, and profit-deficit technique, have also spread to India and Arabia, and through these countries to Europe, which has promoted the development of world mathematics.

During the Wei and Jin Dynasties, Chinese mathematics had a great development in theory. Among them, the work of Zhao Shuang (the date of birth and death is unknown) and Liu Hui (the date of birth and death is unknown) are considered to be the beginning of the ancient Chinese mathematical theory system. Zhao Shuang, a Wu person from the Three Kingdoms, was one of the earliest mathematicians to prove mathematical theorems and formulas in ancient China. His Pythagorean theorem was proved, and his method has embodied the idea of the cut and fill principle. Zhao Shuang also proposed a new method for solving quadratic equations using geometric methods.

In 263, Liu Hui of the Three Kingdoms commented on "Nine Chapters of Arithmetic". He not only explained and derived the methods, formulas, and theorems of the original book in a general way, but also systematically expounded the theoretical system of traditional Chinese mathematics and Mathematical principles, and there are many creations in its discourse (Schwartz, 2015). In Volume 1 "Fang Tian", a circle-cutting technique was created (that is, a method of infinitely approximating the area of a circle with a regular polygon area inscribed in the circle) to lay a theoretical foundation and provided with a scientific algorithm. To establish the polyhedral volume theory, Liu Hui successfully proved the Yang equestrian technique by using extreme methods. He also authored the "Islands of the Sea" and carried forward the ancient Pythagorean measurement technique.

The time between the years 221 and 581 is known as the three kingdoms and six dynasties. During this period, China suffered internal divisions and the attack of several nomadic peoples (Tibetans, Turks, and Mongols). However, this troubled time did not put an end to the mathematical activity. In this period, lived the mathematician Liu Hui (c. 260), who commented on the Nine Chapter and wrote Haidao Suanjing - The island's arithmetic manual - initially written as an appendix to the 9th chapter of the Nine Chapters the book contains 9 problems, dealing with the theorem Pythagoras, with solutions. The Sunzi Suanjing - Arithmetic Manual of Master Sol (c. 300 AD) - written by Sun Zi is also from this time. The book is divided into 3 chapters, the last of which has a collection of arithmetical problems.

In the fifth century AD, the work of Zu Chongzhi and Zuyi were the most representative of this period. Based on Liu Hui's note in "Nine Chapters of Arithmetic", they took traditional mathematics a step forward, becoming a focus on mathematical thinking and a model of mathematical reasoning. Contemporaneous astronomer He Chengtian created a method of adjusting the sun, and approximated real numbers with rational fractions, and developed ancient indefinite analysis and numerical approximation algorithms.

In the second half of the 5th century, the Arithmetic Manual written by Zhang Quijan appeared; this book contained 92 problems divided into 3 chapters. In 581, the Sui dynasty (581 to 618) reunited the country again. The Tang dynasty (618-906) followed. During that time, China experienced great artistic (poetry and painting) and scientific development and came into contact with other civilizations, such as the Japanese, the Korean, the Indian and the Arab. This period was characterized by a strong foreign influence. It is from this time that the text Jigu Suanjing - Continuation of Ancient Mathematics (around 625) appeared. It was written by Wang Xiatong, and contained 22 problems with irrigation, building granaries and solving right triangles. Also from this period an encyclopedia on classical mathematics from the past - Suan Ching Shih Shu - The Ten Manuals of Mathematics appeared.

The great civil engineering in the Sui Dynasty promoted the development of mathematics objectively. At the beginning of the Tang Dynasty, Wang Xiaotong wrote "The Ancient Classic of Suspension", which mainly discussed how to build a cubic polynomial equation geometrically through the practical problems of calculating earthwork, engineering division and acceptance in civil engineering, and warehouse and cellar calculation.

The Sui and Tang dynasties were the periods for the establishment of the feudal bureaucracy in China. With the establishment of the imperial examination system and the Guozijian system, mathematics education developed significantly. In the Tang and Song Dynasties, the size of the mathematics school was further enlarged, reaching 200 students at peak time (Zhang, 2016). In 656, the Guozijian set up a maths hall with a doctorate in maths and a teaching assistant. Tai Shiling Li Chunfeng and others compiled and commented the "Book of Ten Books", including "Book of Zhouyue", "Nine Chapters of Arithmetic", "Island Arithmetic", " Sun Zi Suan Jing, Zhang Qiu Jian Suan Jing, Xia Houyang Suan Jing, Qi Gu Suan Jing, Wu Cao Suan Jing, Wu Jing Arithmetic, and Suffix Shu, for students of the math school textbook. It played an important role in preserving ancient mathematical classics.

As some major astronomical discoveries of the Northern and Southern Dynasties began to be implemented into the calendar calculation at the turn of...

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