**Suanfa tongzong** (**General Source of Computational Methods**) is a mathematical text written by sixteenth century Chinese mathematician Cheng Dawei (1533–1606) and published in the year 1592. The book contains 595 problems divided into 17 chapters. The book is essentially general arithmetic for the abacus. The book was the main source available to scholars concerning mathematics as it developed in China's tradition.^{ [1] } Six years after the publication of Suanfa Tongzong, Cheng Dawei published another book titled *Suanfa Zuanyao* (*A Compendium of calculating Methods*). About 90% of the content of the new book came from the contents of four chapters of the first book with some rearrangement. It is said that when Suanfa Tongzong was first published, it sold so many copies that the cost of paper went up and the lucrative sales resulted in unscrupulous people beginning to print pirated copies of the book with many errors. It was this that forced the author to print an abridged version.^{ [2] }

*Suanfa Tongzong* has some noteworthy features. As Jean-Claude Martzloff, a historian of Chinese mathematics has observed, it is an encyclopedic hotch-potch of ideas which contains everything from A to Z relating to the Chinese mystique of numbers.^{ [3] } There are sections in the book which explains how computation should be taught and studied. The book is considered as an authoritative text on Chinese Zhusuan which is the knowledge and practices of arithmetic calculation through the abacus. There are descriptions of topics generally thought of as mathematical recreations and mathematical curiosities of different types. In particular, the book contains descriptions of several different types of magic circles. There is a collection of problems without solutions given as challenges to the readers. Also, some of the formulas and some of the problems are presented in verse for easy remembrance.^{ [3] }

**Magic circles and squares in Suanfa Tongzong**

The following is a list of sample problems appearing in the book:^{ [4] }^{ [3] }

- "Boy shepherd B with his one sheep behind him asked shepherd A "Are there 100 sheep in your flock?". Shepherd A replies "Yet add the same flock, the same flock again, half, one quarter flock and your sheep. There are then 100 sheep altogether."
- "Now a pile of rice is against the wall with a base circumference 60 chi and an altitude of 12 chi. What is the volume? Another pile is at an inner corner, with a base circumference of 30 chi and an altitude of 12 chi. What is the volume? Another pile is at an outer corner, with base circumference of 90 chi and an altitude of 12 chi. What is the volume?"
- "A small river cuts right across a circular field whose area is unknown. Given the diameter of the field and the breadth of the river find the area of the non-flooded part of the field."
- "In the right-angled triangle with sides of length
*a*,*b*, and*c*with*a*>*b*>*c*, we know that*a*+*b*= 81 and*a*+*c*= 72. Find*a*,*b*, and*c*."

After its first publication in 1592, it was republished several times later and it became widely popular. Practically everybody who is involved in mathematics had a copy of the book. It was popular even beyond the limited circle of people interested in mathematics. Even in the mid-20th century (1964), the well-known historians of Chinese mathematics Li Yan and Du Shiran remarked that: "Nowadays, various editions of the Suanfa Tongzong can still be found throughout China and some old people still recite the versified formulae and talk to each other about its difficult problems."^{ [3] }

Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers (arithmetic).

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* The Nine Chapters on the Mathematical Art* is a Chinese mathematics book, composed by several generations of scholars from the 10th–2nd century BCE, its latest stage being from the 2nd century CE. This book is one of the earliest surviving mathematical texts from China, the first being

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**Ancient Egyptian mathematics** is the mathematics that was developed and used in Ancient Egypt c. 3000 to c. 300 BCE, from the Old Kingdom of Egypt until roughly the beginning of Hellenistic Egypt. The ancient Egyptians utilized a numeral system for counting and solving written mathematical problems, often involving multiplication and fractions. Evidence for Egyptian mathematics is limited to a scarce amount of surviving sources written on papyrus. From these texts it is known that ancient Egyptians understood concepts of geometry, such as determining the surface area and volume of three-dimensional shapes useful for architectural engineering, and algebra, such as the false position method and quadratic equations.

**Mathematics in China** emerged independently by the 11th century BC. The Chinese independently developed a real number system that includes significantly large and negative numbers, more than one numeral system, algebra, geometry, number theory and trigonometry.

The * Book on Numbers and Computation*, or the

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*This page supplements counter machine.*

The * Treviso Arithmetic*, or

**Magic circles** were invented by the Song dynasty (960–1279) Chinese mathematician Yang Hui. It is the arrangement of natural numbers on circles where the sum of the numbers on each circle and the sum of numbers on diameter are identical. One of his magic circles was constructed from 33 natural numbers from 1 to 33 arranged on four concentric circles, with 9 at the center.

**Wang Xiaotong** (王孝通), also known as Wang Hs'iao-t'ung, was a Chinese mathematician, calendarist, politician, and writer of the early Tang dynasty. He is famous as the author of the *Jigu Suanjing* one of the *Ten Computational Canons*.

This is a timeline of pure and applied mathematics history.

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* Jigu suanjing* was the work of early Tang dynasty calendarist and mathematician Wang Xiaotong, written some time before the year 626, when he presented his work to the Emperor.

The * Ten Computational Canons* was a collection of ten Chinese mathematical works, compiled by early Tang dynasty mathematician Li Chunfeng (602–670), as the official mathematical texts for imperial examinations in mathematics.

* Sunzi Suanjing* was a mathematical treatise written during 3rd to 5th centuries AD which was listed as one of the Ten Computational Canons during the Tang dynasty. The specific identity of its author Sunzi is still unknown but he lived much later than his namesake Sun Tzu, author of

**Cheng Dawei** (1533–1606), also known as **Da Wei Cheng** or **Ch'eng Ta-wei**, is a Chinese mathematician known mainly as the author of *Suanfa Tongzong*. He has been described as "the most illustrious Chinese arithmetician."

**Zhusuan** is the knowledge and practices of arithmetic calculation through the suanpan or Chinese abacus. In the year 2013, it has been inscribed on the UNESCO Representative List of the Intangible Cultural Heritage of Humanity. While deciding on the inscription, the Intergovernmental Committee noted that "Zhusuan is considered by Chinese people as a cultural symbol of their identity as well as a practical tool; transmitted from generation to generation, it is a calculating technique adapted to multiple aspects of daily life, serving multiform socio-cultural functions and offering the world an alternative knowledge system." The movement to get Chinese Zhusuan inscribed in the list was spearheaded by Chinese Abacus and Mental Arithmetic Association.

**Fangcheng** is the title of the eighth chapter of the Chinese mathematical classic Jiuzhang suanshu composed by several generations of scholars who flourished during the period from the 10th to the 2nd century BC. This text is one of the earliest surviving mathematical texts from China. Several historians of Chinese mathematics have observed that the term *fangcheng* is not easy to translate exactly. However, as a first approximation it has been translated as "rectangular arrays" or "square arrays". The term is also used to refer to a particular procedure for solving a certain class of problems discussed in the Chapter 8 of The Nine Chapters book.

- ↑ Karine Carole Chemla. "East Asian Mathematics".
*Encyclopædia Britannica*. Retrieved 29 November 2016. - ↑ Catherine Jami, Peter Mark Engelfriet, Gregory Blue (Editors) (2001).
*Statecraft and Intellectual Renewal in Late Ming China: The Cross-Cultural Synthesis of Xu Guangqi (1562–1633)*. BRILL. p. 287.CS1 maint: multiple names: authors list (link) CS1 maint: extra text: authors list (link) - 1 2 3 4 Jean-Claude Martzloff.
*A History of Chinese Mathematics*. Springer-Verlag. pp. 160–161. - ↑ J J O'Connor and E F Robertson. "Cheng Dawei". University of St Andrews, Scotland. Retrieved 29 November 2016.

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