**Qin Jiushao** (Chinese :秦九韶; pinyin :*Qín Jiǔsháo*; Wade–Giles :* Ch'in Chiu-shao*, ca. 1202–1261), courtesy name Daogu (道古), was a Chinese mathematician, meteorologist, inventor, politician, and writer. He is credited for discovering Horner's method as well as inventing Tianchi basins, a type of rain gauge instrument used to gather meteorological data.

Although Qin Jiushao was born in Ziyang, Sichuan, his family came from Shandong province. He is regarded as one of the greatest mathematicians in Chinese history. This is especially remarkable because Qin did not devote his life to mathematics. He was accomplished in many other fields and held a series of bureaucratic positions in several Chinese provinces.

Qin wrote *Shùshū Jiǔzhāng* (“Mathematical Treatise in Nine Sections”) in 1247 AD. This treatise covered a variety of topics including indeterminate equations and the numerical solution of certain polynomial equations up to 10th order, as well as discussions on military matters and surveying. In the treatise Qin included a general form of the Chinese remainder theorem that used *Da yan shu* (大衍术) or algorithms to solve it. In geometry, he discovered “Qin Jiushao's formula” for finding the area of a triangle from the given lengths of three sides. This formula is the same as Heron’s formula, proved by Heron of Alexandria about 60 BCE, though knowledge of the formula may go back to Archimedes.

As precipitation was important agriculture and food production, Qin developed precipitation gauges that was widely used in 1247 during the Southern Song dynasty to gather meteorological data. Qin Jiushao later records the application of rainfall measurements in the mathematical treatise. The book also discusses the use of large snow gauges made from bamboo situated in mountain passes and uplands which are speculated to be first referenced to snow measurement.^{ [2] }^{ [3] }

Qin recorded the earliest explanation of how Chinese calendar experts calculated astronomical data according to the timing of the winter solstice. Among his accomplishments are the introduction techniques for solving certain types of algebraic equations using a numerical algorithm (equivalent to the 19th century Horner's method) and for finding sums of arithmetic series. He also introduced the use of the zero symbol into written Chinese mathematics.

After he completed his work on mathematics, he ventured into politics. As a government official he was boastful, corrupt, and was accused of bribery and of poisoning his enemies. As a result, he was relieved of his duties multiple times. Yet in spite of these problems he managed to become very wealthy (Katz, 1993).

*Shushu Jiuzhang (Mathematical Treatise in Nine Sections)*(1248)

**Zhu Shijie**, courtesy name **Hanqing** (漢卿), pseudonym **Songting** (松庭), was a Chinese mathematician and writer. He was a Chinese mathematician during the Yuan Dynasty. Zhu was born close to today's Beijing. Two of his mathematical works have survived. *Introduction to Computational Studies*, and *Jade Mirror of the Four Unknowns*.

A **rain gauge** is an instrument used by meteorologists and hydrologists to gather and measure the amount of liquid precipitation over an area in a predefined period of time. It is used for determining the depth of precipitation that occurs over a unit area and thus measuring rainfall amount.

**Zu Chongzhi**, courtesy name **Wenyuan**, was a Chinese astronomer, mathematician, politician, inventor, and writer during the Liu Song and Southern Qi dynasties. He was most notable for calculating pi as between 3.1415926 and 3.1415927, a record which would not be surpassed for 800 years.

* 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

**Bhāskara** also known as **Bhāskarācārya**, and as **Bhāskara II** to avoid confusion with Bhāskara I, was an Indian mathematician and astronomer. He was born in Bijapur in Karnataka.

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

**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.

A **snow gauge** is a type of instrument used by meteorologists and hydrologists to gather and measure the amount of solid precipitation over a set period of time.

Mathematics during the Golden Age of Islam, especially during the 9th and 10th centuries, was built on Greek mathematics and Indian mathematics. Important progress was made, such as full development of the decimal place-value system to include decimal fractions, the first systematised study of algebra, and advances in geometry and trigonometry.

**Pei Xiu** (224–271), courtesy name **Jiyan**, was a Chinese politician, geographer, writer, and cartographer of the state of Cao Wei during the late Three Kingdoms period and Jin dynasty of China. He was very much trusted by Sima Zhao, and participated in the suppression of Zhuge Dan's rebellion. Following Sima Yan taking the throne of the newly established Jin dynasty, he and Jia Chong had Cao Huan deprived of his position to accord to the will of heaven. In the year 267, Pei Xiu was appointed as the Minister of Works in the Jin government.

The * Mathematical Treatise in Nine Sections* is a mathematical text written by Chinese Southern Song dynasty mathematician Qin Jiushao in the year 1247. The mathematical text has a wide range of topics and is taken from all aspects of the society of that time, including agriculture, astronomy, water conservancy, urban layout, construction engineering, surveying, taxation, armament, military and so on.

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.

**Rod calculus** or rod calculation was the mechanical method of algorithmic computation with counting rods in China from the Warring States to Ming dynasty before the counting rods were replaced by the more convenient and faster abacus. Rod calculus played a key role in the development of Chinese mathematics to its height in Song Dynasty and Yuan Dynasty, culminating in the invention of polynomial equations of up to four unknowns in the work of Zhu Shijie.

This is a timeline of pure and applied mathematics history. It is divided here into three stages, corresponding to stages in the development of mathematical notation: a "rhetorical" stage in which calculations are described purely by words, a "syncopated" stage in which quantities and common algebraic operations are beginning to be represented by symbolic abbreviations, and finally a "symbolic" stage, in which comprehensive notational systems for formulas are the norm.

**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.

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.

* Jade Mirror of the Four Unknowns*,

** Tianchi basins** were meteorological measuring instruments used to gather and measure the amount of liquid precipitation over a period of time during the Song Dynasty. The instrument was devised by the Song Chinese mathematician and inventor Qin Jiushao in 1247.

**Xiangfeng wu** were wind surveying instruments used to gather and measure the direction of the wind in ancient China.

- ↑ Selin, Helaine (2008).
*Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures*(2nd ed.). Springer (published April 16, 2008). p. 736. ISBN 978-1402045592. - ↑ Strangeways, Ian (2011).
*Precipitation: Theory, Measurement and Distribution*. Cambridge University Press (published April 14, 2011). p. 140. ISBN 978-0521172929. - ↑ Selin, Helaine (2008).
*Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures*(2nd ed.). Springer (published April 16, 2008). p. 736. ISBN 978-1402045592.

- Guo, Shuchun.
*Encyclopedia of China*(Mathematics Volume), 1st ed. - Qin Jiushao, . (Chinese History Timeline), 2007.
- Ulrich Libbrecht:
*Chinese Mathematics in the Thirteenth Century*(The Shu-Shu-Chiu-Chang of Chin Chiu shao) Dover Publication ISBN 0-486-44619-0 - Victor J. Katz "A history of mathematics: an introduction." New York (1993).

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