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Jia Xian

Jia Xian (Simplified Chinese: 贾宪, Traditional Chinese: 賈憲, Pinyin Alphabet: Jiǎ Xiàn, Wade-Giles /Beijing Chinese: Chia Hsien; 1010-1070) was a Chinese mathematician and astronomer. Besides the fact that he succeeded in defining Pascal’s triangle in the eleventh century, he made many mathematical inventions and astronomical discoveries.

APA 7: Çarıkçıoğlu, A. E. (2023, May 20). Jia Xian. PerEXP Teamworks. [Article Link]

His life and contributions

Jia Xian (Appeared on the historical scene in 1050, China) was a mathematician and astronomer who carried out active studies at the beginning of the greatest period of traditional Chinese mathematics.

Little is known about Jia’s life, except that he held a relatively low–ranking military post during the reign of emperor Renzong of the Song Dynasty (1022/23-1063/64). In 1023, the “Chongtian calendar” (Has similarities with the Turkish calendar with twelve animals.) he was a student of the mathematician and astronomer Chu Yan, who contributed to its renovation and served in the Imperial Astronomical Bureau in the middle of the eleventh century. Jia’s name is mainly commemorated by his method of subtracting the roots (Solutions/degrees) of polynomials of higher degree from three and the “Jia Xian triangle”, which includes binomial coefficients for equations up to the sixth degree. This triangle is similar to Blaise Pascal’s triangle, which was later discovered independently in the West. [1]

His works

Jia wrote two reviews, only part of the first of which has survived: “Huangdi Jiuzhang Suanfa Xicao (Detailed Drafts of the Yellow Emperor’s Nine Chapters on Mathematical Methods)” and “Suanfa Xiaoguji (Collection/Collection of Mathematical Methods according to the Ancients)”. In 1261, “Yongle Dadian (The Great Encyclopedia of the Reign of Yongle, published in 1408)”, in which about two-thirds of the mathematical problems contained in the first book were included in Yang Hui’s “Xiangjie Jiuzhang Suanfa (Detailed Analysis of Nine Chapters on Mathematical Procedures)” is thought to have been compiled in the work and preserved as an edition since 1842. [2]

His mathematical inventions

One of Jia Xian’s most important contributions is his role in the development of trigonometry. In particular, his studies on trigonometric functions have made great progress. “Detailed Analysis of Nine Chapters on Mathematical Procedures” is an important book by Jia Xian on trigonometry. In this book, he includes concepts similar to trigonometric functions that we call “Sine” and “Cosine” today. These studies have led to trigonometry becoming a part of mathematical analysis. [3]

Chinese astronomy

Jia Xian was also interested in Chinese astronomy. He attracts attention with his contributions to celestial science, especially with his studies on the motion and orbit of the Sun. Jia Xian used trigonometry methods to describe the motion of the Sun and made a breakthrough in this field. [4]

The importance of Jia Xian for science

Jia Xian’s mathematical discoveries and studies gave a great impetus to mathematical thinking at that time. Trigonometry had been mostly limited to geometry and measurement until then. The innovations introduced by Jia Xian to trigonometry have contributed to mathematics becoming a more abstract and analytical discipline. [5]

More research needs to be done on Jia Xian’s mathematical legacy and work. A more comprehensive look at the period in which he lived, and his work, is important for understanding the history of mathematics and ensuring that other mathematicians can base their work on it. In addition, the place and influence of Jia Xian in the history of Chinese mathematics should also be studied in more depth. [6]


  1. DICTIONARY ENTRY Breard, A. (2017, January 23). Jia XianEncyclopedia Britannica. [Britannica]
  2. WEBSITE O’Connor, J. J., & Robertson, E. F. (2003). Jia Xian. Maths History. [Maths History]
  3. BOOK Smith, D. E. (1958). History of Mathematics. Courier Corporation.
  4. WIKIPEDIA ENTRY Jia Xian. (2023, May 16). In Wikipedia. [Wikipedia English]
  5. BOOK Plofker, K. (2009). Mathematics in India. Princeton University Press.
  6. BOOK Eves, H. (1990). An Introduction to the History of Mathematics. Cengage Learning.

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