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**Zhu Shijie** (simplified Chinese :朱世杰; traditional Chinese :朱世傑; pinyin :*Zhū Shìjié*; Wade–Giles :* Chu Shih-chieh*, 1249–1314), courtesy name

The *Suan hsüeh Ch'i-mong* (算學啓蒙), written in 1299, is an elementary textbook on mathematics in three volumes, 20 chapters and 259 problems. This book also showed how to measure different two-dimensional shapes and three-dimensional solids. The *Introduction* had an important influence on the development of mathematics in Japan. The book was once lost in China until Qing dynasty mathematician Luo Shilin bought a Korean printed edition, and re-published in Yangzhou. Since then this book was reprinted several times.

Zhu's second book, * Jade Mirror of the Four Unknowns *, written in 1303, is his most important work. With this book, Zhu advanced Chinese algebra. The first four of the 288 problems for solution illustrate his method of the four unknowns. He shows how to convert a problem stated verbally into a system of polynomial equations (up to 14th order), by using up to four unknowns: 天 Heaven, 地 Earth, 人 Man, 物 Matter, and then how to reduce the system to a single polynomial equation in one unknown by successive elimination of unknowns. He then solved the high order equation by Southern Song dynasty mathematician Qin Jiushao's "Ling long kai fang" method published in Shùshū Jiǔzhāng (“Mathematical Treatise in Nine Sections”) in 1247 (more than 570 years before English mathematician William Horner's method using synthetic division). To do this, he makes use of what is currently known as the Pascal triangle, which he labels as the diagram of an ancient method first discovered by Jia Xian before 1050. The final equation and one of its solutions is given for each of the 288 problems.

Zhu also found square and cube roots by solving quadratic and cubic equations, and added to the understanding of series and progressions, classifying them according to the coefficients of the Pascal triangle. He also showed how to solve systems of linear equations by reducing the matrix of their coefficients to diagonal form. His methods pre-date Blaise Pascal, William Horner, and modern matrix methods by many centuries. The preface of the book describes how Zhu traveled around China for 20 years as a teacher of mathematics.

The methods of *Jade Mirror of the Four Unknowns* form the foundation for Wu's method of characteristic set.

* 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

**Zhu Xi**, also known by his courtesy name **Yuanhui**, and self-titled **Hui'an**, was a Chinese calligrapher, historian, philosopher, politician, and writer of the Song dynasty. He was a Confucian scholar who was the most influential Neo-Confucian in China. His contributions to Chinese philosophy including his editing of and commentaries to the Four Books, which later formed the curriculum of the civil service exam in Imperial China from 1313 to 1905; and his emphasis on the process of the "investigation of things" and meditation as a method for self cultivation.

**Seki Takakazu**, also known as **Seki Kōwa**, was a Japanese mathematician and author of the Edo period.

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.

**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.

**Yang Hui**, courtesy name **Qianguang** (謙光), was a Chinese mathematician and writer during the Song dynasty. Originally, from Qiantang, Yang worked on magic squares, magic circles and the binomial theorem, and is best known for his contribution of presenting Yang Hui's Triangle. This triangle was the same as Pascal's Triangle, discovered by Yang's predecessor Jia Xian. Yang was also a contemporary to the other famous mathematician Qin Jiushao.

**Zhu Zaiyu** was a Chinese mathematician, physicist, choreographer, and musician. He was a prince of the Chinese Ming dynasty. In 1584, Prince Zhu innovatively described the equal temperament via accurate mathematical calculation.

Algebra can essentially be considered as doing computations similar to those of arithmetic but with non-numerical mathematical objects. However, until the 19th century, algebra consisted essentially of the theory of equations. For example, the fundamental theorem of algebra belongs to the theory of equations and is not, nowadays, considered as belonging to algebra.

**Zhu** is the pinyin romanization of four Chinese surnames: 朱, 祝, 竺, and 諸. It is alternatively spelled **Chu**, **Gee** in the United States, and **Choo**. It is the 17th name in the *Hundred Family Surnames* poem.

**Jia Xian** was a Chinese mathematician from Kaifeng of the Song dynasty.

**Li Ye**, born **Li Zhi**, courtesy name **Li Jingzhai**, was a Chinese scientist and writer who published and improved the tian yuan shu method for solving polynomial equations of one variable. Along with the 4th-century Chinese astronomer Yu Xi, Li Ye proposed the idea of a spherical Earth instead of a flat one before the advances of European science in the 17th century.

* Tian yuan shu* is a Chinese system of algebra for polynomial equations. Some of the earliest existing writings were created in the 13th century during the Yuan dynasty. However, the tianyuanshu method was known much earlier, in the Song dynasty and possibly before.

**Counting rods** are small bars, typically 3–14 cm long, that were used by mathematicians for calculation in ancient East Asia. They are placed either horizontally or vertically to represent any integer or rational number.

* 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.

* 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

* Jade Mirror of the Four Unknowns*,

**Chia-Kun (John) Chu** is a Chinese-American applied mathematician who is the Fu Foundation Professor Emeritus of Applied Mathematics at Columbia University. He has been on Columbia faculty since 1965 and served as the department chairman of applied physics and nuclear engineering three times.

During the Mongol-ruled Yuan dynasty (1271–1368), many scientific and technological advancements were made in areas such as mathematics, medicine, printing technology, and gunpowder warfare.

**Lu Jiaxi** was a self-taught Chinese mathematician who made important contributions in combinatorial design theory. He was a high school physics teacher in a remote city and worked in his spare time on the problem of large sets of disjoint Steiner triple systems.

- Yoshio Mikami Development of Mathematics in China and Japan, Chapter 14 Chu Shih-chieh p89-98. 1913 Leipzig. Library of Congress catalog card number 61-13497.
- Du, Shiran, "Zhu Shijie".
*Encyclopedia of China*(Mathematics Edition), 1st ed. - LAM Lay-yong: Chu shih-chieh's Suan hsüeh ch'i-meng,
*Archive for the history of sciences*, Vol 21, Berlin, 1970. - Guo Shuchun (tr. modern Chinese), Chen Zaixin (English tr.), Guo Jinhai (annotation), Zhu Shijie:
*Jade mirror of the Four Unknowns*, Chinese and English bilingual, vol I & 2,Liaoning education Press, China, 2006. ISBN 7-5382-6923-1 - Hoe, J.:
*The jade mirror of the four unknowns*, Mingming Bookroom, New Zealand, 2007. ISBN 1-877209-14-7 - Hoe, J.:
*Les systèmes d'équations polynômes dans le Siyuan Yujian (1303)*, Paris, Collège de France (Mémoires de l'Institut des Hautes Etudes Chineoises, Vol VI),1977. - MARTZLOFF, J-C.:
*A history of Chinese Mathematics*, Springer-Verlag, Berlin, 1997. - GRATTAN-GUINNESS, I.:
*The Norton History of the Mathematical Sciences*, 1998. - KONANTZ, E.L.:The Precious Mirror of the Four Elements,
*China journal of Science and Arts*, Vol 2, No 4, 1924. - HO Peng-Yoke: Article on Chu Shih-chieh in the
*Dictionary of Scientific Biography*, New York, 1970.hi

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