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.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.
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.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.
Magic circles and squares in Suanfa Tongzong
The following is a list of sample problems appearing in the book:
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."
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).
Liber Abaci is a historic 1202 Latin manuscript on arithmetic by Leonardo of Pisa, posthumously known as Fibonacci.
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 Suan shu shu and Zhoubi Suanjing. It lays out an approach to mathematics that centres on finding the most general methods of solving problems, which may be contrasted with the approach common to ancient Greek mathematicians, who tended to deduce propositions from an initial set of axioms.
The suanpan, also spelled suan pan or souanpan) is an abacus of Chinese origin first described in a 190 CE book of the Eastern Han Dynasty, namely Supplementary Notes on the Art of Figures written by Xu Yue. However, the exact design of this suanpan is not known. Usually, a suanpan is about 20 cm tall and it comes in various widths depending on the application. It usually has more than seven rods. There are two beads on each rod in the upper deck and five beads on each rod in the bottom deck. The beads are usually rounded and made of a hardwood. The beads are counted by moving them up or down towards the beam. The suanpan can be reset to the starting position instantly by a quick jerk around the horizontal axis to spin all the beads away from the horizontal beam at the center.
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 Writings on Reckoning, is one of the earliest known Chinese mathematical treatises. It was written during the early Western Han dynasty, sometime between 202 BC and 186 BC.
A counter machine is an abstract machine used in a formal logic and theoretical computer science to model computation. It is the most primitive of the four types of register machines. A counter machine comprises a set of one or more unbounded registers, each of which can hold a single non-negative integer, and a list of arithmetic and control instructions for the machine to follow. The counter machine is typically used in the process of designing parallel algorithms in relation to the mutual exclusion principle. When used in this manner, the counter machine is used to model the discrete time-steps of a computational system in relation to memory accesses. By modeling computations in relation to the memory accesses for each respective computational step, parallel algorithms may be designed in such a matter to avoid interlocking, the simultaneous writing operation by two threads to the same memory address.
This page supplements counter machine.
The Treviso Arithmetic, or Arte dell'Abbaco, is an anonymous textbook in commercial arithmetic written in vernacular Venetian and published in Treviso, Italy, in 1478.
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.
Ganita-yukti-bhasa is either the title or a part of the title of three different books:
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. Jigu Suanjing was included as one of the requisite texts for Imperial examination; the amount of time required for the study of Jigu Suanjing was three years, the same as for The Nine Chapters on the Mathematical Art and Haidao Suanjing.
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 The Art of War. From the textual evidence in the book, some scholars concluded that the work was completed during the Southern and Northern Dynasties. Besides describing arithmetic methods and investigating Diophantine equations, the treatise touches upon astronomy and attempts to develop a calendar.
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.