Yang Hui (, ca. 1238–1298),

courtesy name A courtesy name ( zh, s=字, p=zì, l=character), also known as a style name, is an additional name bestowed upon individuals at adulthood, complementing their given name. This tradition is prevalent in the East Asian cultural sphere, particula ...

Qianguang (), was a Chinese mathematician and writer during the

Song dynasty The Song dynasty ( ) was an Dynasties of China, imperial dynasty of China that ruled from 960 to 1279. The dynasty was founded by Emperor Taizu of Song, who usurped the throne of the Later Zhou dynasty and went on to conquer the rest of the Fiv ...

. Originally, from Qiantang (modern

Hangzhou Hangzhou, , Standard Mandarin pronunciation: ; formerly romanized as Hangchow is a sub-provincial city in East China and the capital of Zhejiang province. With a population of 13 million, the municipality comprises ten districts, two counti ...

Zhejiang ) , translit_lang1_type2 = , translit_lang1_info2 = ( Hangzhounese) ( Ningbonese) (Wenzhounese) , image_skyline = 玉甑峰全貌 - panoramio.jpg , image_caption = View of the Yandang Mountains , image_map = Zhejiang i ...

), Yang worked on

magic square In mathematics, especially History of mathematics, historical and recreational mathematics, a square array of numbers, usually positive integers, is called a magic square if the sums of the numbers in each row, each column, and both main diago ...

magic circles A magic circle is a circle of space marked out by practitioners of some branches of Ceremonial magic, ritual magic, which they generally believe will contain energy and form a sacred space, or will provide them a form of magical protection, or b ...

and the

binomial theorem In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial. According to the theorem, the power expands into a polynomial with terms of the form , where the exponents and a ...

, and is best known for his contribution of presenting Yang Hui's triangle. This triangle was the same as

Pascal's triangle In mathematics, Pascal's triangle is an infinite triangular array of the binomial coefficients which play a crucial role in probability theory, combinatorics, and algebra. In much of the Western world, it is named after the French mathematician Bla ...

, discovered by Yang's predecessor

Jia Xian Jia Xian (; ca. 1010–1070) was a Chinese mathematician from Kaifeng of the Song dynasty. He described Pascal's triangle during the 11th century. Biography According to the history of the Song dynasty, Jia was a palace eunuch of the Left Duty ...

. Yang was also a contemporary of

Qin Jiushao Qin Jiushao (, 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 gau ...

, another well-known Chinese mathematician.

Written work

The earliest extant Chinese illustration of '

' is from Yang's book ''Xiángjiě Jiǔzhāng Suànfǎ '' () of 1261 AD, in which Yang acknowledged that his method of finding square roots and cubic roots using "Yang Hui's triangle" was invented by mathematician

Needham, Volume 3, 134-137. who expounded it around 1100 AD, about 500 years before Pascal. His book (now lost), known as ''Rújī Shìsuǒ'' () or ''Piling-up Powers and Unlocking Coefficients'', was known through his contemporary mathematician Liu Ruxie ().Needham, Volume 3, 137. Jia described the method used as 'li cheng shi suo' (the tabulation system for unlocking binomial coefficients). It appeared again in a publication of

Zhu Shijie Zhu Shijie (, 1249–1314), courtesy name Hanqing (), pseudonym Songting (), was a Chinese mathematician and writer during the Yuan Dynasty. Zhu was born close to today's Beijing. Two of his mathematical works have survived: ''Introduction to C ...

's book ''Jade Mirror of the Four Unknowns'' () of 1303 AD.Needham, Volume 3, 134-135. Around 1275 AD, Yang finally had two published mathematical books, which were known as the ''Xùgǔ Zhāijī Suànfǎ'' () and the ''Suànfǎ Tōngbiàn Běnmò'' (, summarily called ''Yáng Huī Suànfǎ'' ).Needham, Volume 3, 104. In the former book, Yang wrote of arrangement of natural numbers around concentric and non-concentric circles, known as

and vertical-horizontal

diagram A diagram is a symbolic Depiction, representation of information using Visualization (graphics), visualization techniques. Diagrams have been used since prehistoric times on Cave painting, walls of caves, but became more prevalent during the Age o ...

s of complex

combinatorial Combinatorics is an area of mathematics primarily concerned with counting, both as a means and as an end to obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many ...

arrangements known as

magic squares In mathematics, especially historical and recreational mathematics, a square array of numbers, usually positive integers, is called a magic square if the sums of the numbers in each row, each column, and both main diagonals are the same. The " ...

, providing rules for their construction.Needham, Volume 3, 59-60. In his writing, he harshly criticized the earlier works of

Li Chunfeng Li Chunfeng (; 602–670) was a Chinese astronomer, historian, mathematician, and politician who was born in today's Baoji, Baoji, Shaanxi, during the Sui dynasty, Sui and Tang dynasty, Tang dynasties. He was first appointed to the Imperial Astr ...

and Liu Yi (), the latter of whom were both content with using methods without working out their theoretical origins or principle. Displaying a somewhat modern attitude and approach to

mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

, Yang once said: :''The men of old changed the name of their methods from problem to problem, so that as no specific explanation was given, there is no way of telling their theoretical origin or basis.'' In his written work, Yang provided theoretical proof for the proposition that the complements of the

parallelogram In Euclidean geometry, a parallelogram is a simple polygon, simple (non-list of self-intersecting polygons, self-intersecting) quadrilateral with two pairs of Parallel (geometry), parallel sides. The opposite or facing sides of a parallelogram a ...

s which are about the diameter of any given parallelogram are equal to one another. This was the same idea expressed in the Greek mathematician

Euclid Euclid (; ; BC) was an ancient Greek mathematician active as a geometer and logician. Considered the "father of geometry", he is chiefly known for the '' Elements'' treatise, which established the foundations of geometry that largely domina ...

's (fl. 300 BC) forty-third proposition of his first book, only Yang used the case of a rectangle and

gnomon A gnomon (; ) is the part of a sundial that casts a shadow. The term is used for a variety of purposes in mathematics and other fields, typically to measure directions, position, or time. History A painted stick dating from 2300 BC that was ...

. There were also a number of other geometrical problems and theoretical mathematical propositions posed by Yang that were strikingly similar to the Euclidean system.Needham, Volume 3, 105. However, the first books of Euclid to be translated into Chinese was by the cooperative effort of the Italian Jesuit

Matteo Ricci Matteo Ricci (; ; 6 October 1552 – 11 May 1610) was an Italian Jesuit priest and one of the founding figures of the Jesuit China missions. He created the , a 1602 map of the world written in Chinese characters. In 2022, the Apostolic See decl ...

and the

Ming The Ming dynasty, officially the Great Ming, was an imperial dynasty of China that ruled from 1368 to 1644, following the collapse of the Mongol-led Yuan dynasty. The Ming was the last imperial dynasty of China ruled by the Han people, t ...

official

Xu Guangqi Xu Guangqi or Hsü Kuang-ch'i (April 24, 1562– November 8, 1633), also known by his baptismal name Paul or Paul Siu, was a Chinese agronomist, astronomer, mathematician, scholar-bureaucrat, politician, and writer during the late Ming dynasty ...

in the early 17th century.Needham, Volume 3, 106. Yang's writing represents the first in which

quadratic equation In mathematics, a quadratic equation () is an equation that can be rearranged in standard form as ax^2 + bx + c = 0\,, where the variable (mathematics), variable represents an unknown number, and , , and represent known numbers, where . (If and ...

s with negative coefficients of 'x' appear, although he attributes this to the earlier Liu Yi.Needham, Volume 3, 46. Yang was also well known for his ability to manipulate decimal fractions. When he wished to multiply the figures in a rectangular field with a breadth of 24 paces 3 ⁴⁄₁₀ ft. and length of 36 paces 2 ⁸⁄₁₀, Yang expressed them in decimal parts of the pace, as 24.68 X 36.56 = 902.3008.Needham, Volume 3, 45.

The Yang-Hui Award

The Yang-Hui Award is presented to mathematicians or scientists who have gained international recognition for their exceptional contributions throughout their careers. It was awarded to Salvatore Capozziello for his work with Noether symmetries; Mahouton Norbert Hounkonnou for his work in deformed quantum algebras; and to Delfim F. M. Torres for his mathematical modelling of

COVID-19 Coronavirus disease 2019 (COVID-19) is a contagious disease caused by the coronavirus SARS-CoV-2. In January 2020, the disease spread worldwide, resulting in the COVID-19 pandemic. The symptoms of COVID‑19 can vary but often include fever ...

in 2023 at the International Conference on Mathematical Analysis, Applications and Computational Simulation (ICMAACS 2023), Shanghai, China, November 22-26, 2023.

Notes

References

*Needham, Joseph (1986). ''Science and Civilization in China: Volume 3, Mathematics and the Sciences of the Heavens and the Earth''. Taipei: Caves Books, Ltd. *Li, Jimin
"Yang Hui"
''

Encyclopedia of China The ''Encyclopedia of China'' () is the first large-entry modern encyclopedia in the Chinese language. The compilation began in 1978. Published by the Encyclopedia of China Publishing House, the encyclopedia was issued one volume at a time, be ...

'' (Mathematics Edition), 1st ed.

External links

Yang Hui at MacTutor
{{DEFAULTSORT:Yang, Hui 1230s births 1298 deaths 13th-century Chinese mathematicians Magic squares Mathematicians from Zhejiang Mathematicians from Imperial China Song dynasty science writers Writers from Hangzhou

Written work

The Yang-Hui Award

See also

Notes

References

External links