Yang Hui

Last updated • 3 min readFrom Wikipedia, The Free Encyclopedia
Yang Hui triangle (Pascal's triangle) using rod numerals, as depicted in a publication of Zhu Shijie in 1303 AD. Yanghui triangle.gif
Yang Hui triangle (Pascal's triangle) using rod numerals, as depicted in a publication of Zhu Shijie in 1303 AD.
1433 Korean edition of Yang Hui suan fa Yang Hui suan fa.jpg
1433 Korean edition of Yang Hui suan fa
Yang Hui's construction of 3rd order magic square Yanghui magic square.GIF
Yang Hui's construction of 3rd order magic square

Yang Hui (simplified Chinese :杨辉; traditional Chinese :楊輝; pinyin :Yáng Huī, ca. 1238–1298), courtesy name Qianguang (謙光), was a Chinese mathematician and writer during the Song dynasty. Originally, from Qiantang (modern Hangzhou, Zhejiang), 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 of Qin Jiushao, another well-known Chinese mathematician.

Contents

Written work

The earliest extant Chinese illustration of 'Pascal's triangle' is from Yang's book Xiángjiě Jiǔzhāng Suànfǎ (詳解九章算法) [1] 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 Jia Xian [2] who expounded it around 1100 AD, about 500 years before Pascal. His book (now lost), known as Rújī Shìsuǒ (如積釋鎖) or Piling-up Powers and Unlocking Coefficients, was known through his contemporary mathematician Liu Ruxie (劉汝諧). [3] Jia described the method used as 'li cheng shi suo' (the tabulation system for unlocking binomial coefficients). [3] It appeared again in a publication of Zhu Shijie's book Jade Mirror of the Four Unknowns (四元玉鑒) of 1303 AD. [4]

Around 1275 AD, Yang finally had two published mathematical books, which were known as the Xùgǔ Zhāijī Suànfǎ (續古摘奇算法) and the Suànfǎ Tōngbiàn Běnmò (算法通變本末, summarily called Yáng Huī Suànfǎ楊輝算法). [5] In the former book, Yang wrote of arrangement of natural numbers around concentric and non concentric circles, known as magic circles and vertical-horizontal diagrams of complex combinatorial arrangements known as magic squares, providing rules for their construction. [6] In his writing, he harshly criticized the earlier works of Li Chunfeng and Liu Yi (劉益), the latter of whom were both content with using methods without working out their theoretical origins or principle. [5] Displaying a somewhat modern attitude and approach to mathematics, 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. [5]

In his written work, Yang provided theoretical proof for the proposition that the complements of the parallelograms which are about the diameter of any given parallelogram are equal to one another. [5] This was the same idea expressed in the Greek mathematician Euclid's (fl. 300 BC) forty-third proposition of his first book, only Yang used the case of a rectangle and gnomon. [5] There were also a number of other geometrical problems and theoretical mathematical propositions posed by Yang that were strikingly similar to the Euclidean system. [7] However, the first books of Euclid to be translated into Chinese was by the cooperative effort of the Italian Jesuit Matteo Ricci and the Ming official Xu Guangqi in the early 17th century. [8]

Yang's writing represents the first in which quadratic equations with negative coefficients of 'x' appear, although he attributes this to the earlier Liu Yi. [9] 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 3 410 ft. and length of 36 paces 2 810, Yang expressed them in decimal parts of the pace, as 24.68 X 36.56 = 902.3008. [10]

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. [11] 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 in 2023 at the International Conference on Mathematical Analysis, Applications and Computational Simulation (ICMAACS 2023), Shanghai, China, November 22-26, 2023. [12] [13]

See also

Notes

  1. Fragments of this book was retained in the Yongle Encyclopedia vol 16344, in British Museum Library
  2. Needham, Volume 3, 134-137.
  3. 1 2 Needham, Volume 3, 137.
  4. Needham, Volume 3, 134-135.
  5. 1 2 3 4 5 Needham, Volume 3, 104.
  6. Needham, Volume 3, 59-60.
  7. Needham, Volume 3, 105.
  8. Needham, Volume 3, 106.
  9. Needham, Volume 3, 46.
  10. Needham, Volume 3, 45.
  11. "International Conference on Mathematical Analysis, Applications and Computational Simulation - Awards". ICMAACS.
  12. "International Conference on Mathematical Analysis, Applications and Computational Simulation - Awardees". ICMAACS. 2023-10-13.
  13. Gayet, Donald Kévin (2023-10-15). "Mathématique : le Béninois Norbert Hounkonnou distingué en Chine par le prix Yang-Hui" [Mathematics: Beninese Norbert Hounkonnou, distinguished in China by the Yang-Hui Prize]. Banouto (in French). Retrieved 2024-08-20.

Related Research Articles

<span class="mw-page-title-main">History of geometry</span> Historical development of geometry

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).

<span class="mw-page-title-main">History of mathematics</span>

The history of mathematics deals with the origin of discoveries in mathematics and the mathematical methods and notation of the past. Before the modern age and the worldwide spread of knowledge, written examples of new mathematical developments have come to light only in a few locales. From 3000 BC the Mesopotamian states of Sumer, Akkad and Assyria, followed closely by Ancient Egypt and the Levantine state of Ebla began using arithmetic, algebra and geometry for purposes of taxation, commerce, trade and also in the field of astronomy to record time and formulate calendars.

<span class="mw-page-title-main">Zhu Shijie</span> Chinese mathematician during the Yuan dynasty

Zhu Shijie, courtesy name Hanqing (漢卿), pseudonym Songting (松庭), 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 Computational Studies and Jade Mirror of the Four Unknowns.

<span class="mw-page-title-main">Zu Chongzhi</span> Chinese mathematician-astronomer (429–500)

Zu Chongzhi, courtesy name Wenyuan, was a Chinese astronomer, inventor, mathematician, politician, 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 in precision which would not be surpassed for nearly 900 years.

<span class="mw-page-title-main">Liu Hui</span> Chinese mathematician and writer

Liu Hui was a Chinese mathematician who published a commentary in 263 CE on Jiu Zhang Suan Shu. He was a descendant of the Marquis of Zixiang of the Eastern Han dynasty and lived in the state of Cao Wei during the Three Kingdoms period of China.

<i>The Nine Chapters on the Mathematical Art</i> Ancient Chinese mathematics text

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 1st century CE. This book is one of the earliest surviving mathematical texts from China, the others being the 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.

<span class="mw-page-title-main">Seki Takakazu</span> Japanese mathematician (c. 1642–1708)

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

<span class="mw-page-title-main">Chinese mathematics</span>

Mathematics emerged independently in China by the 11th century BCE. 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 method of exhaustion is a method of finding the area of a shape by inscribing inside it a sequence of polygons whose areas converge to the area of the containing shape. If the sequence is correctly constructed, the difference in area between the nth polygon and the containing shape will become arbitrarily small as n becomes large. As this difference becomes arbitrarily small, the possible values for the area of the shape are systematically "exhausted" by the lower bound areas successively established by the sequence members.

<i>Zhoubi Suanjing</i> Pre-2nd century AD Chinese treatise

The Zhoubi Suanjing, also known by many other names, is an ancient Chinese astronomical and mathematical work. The Zhoubi is most famous for its presentation of Chinese cosmology and a form of the Pythagorean theorem. It claims to present 246 problems worked out by the Duke of Zhou as well as members of his court, placing its composition during the 11th century BC. However, the present form of the book does not seem to be earlier than the Eastern Han (25–220 AD), with some additions and commentaries continuing to be added for several more centuries.

<span class="mw-page-title-main">History of trigonometry</span>

Early study of triangles can be traced to the 2nd millennium BC, in Egyptian mathematics and Babylonian mathematics. Trigonometry was also prevalent in Kushite mathematics. Systematic study of trigonometric functions began in Hellenistic mathematics, reaching India as part of Hellenistic astronomy. In Indian astronomy, the study of trigonometric functions flourished in the Gupta period, especially due to Aryabhata, who discovered the sine function, cosine function, and versine function.

<span class="mw-page-title-main">History of science and technology in China</span>

Ancient Chinese scientists and engineers made significant scientific innovations, findings and technological advances across various scientific disciplines including the natural sciences, engineering, medicine, military technology, mathematics, geology and astronomy.

<span class="mw-page-title-main">Jamshid al-Kashi</span> Persian astronomer and mathematician

Ghiyāth al-Dīn Jamshīd Masʿūd al-Kāshī was an astronomer and mathematician during the reign of Tamerlane.

<span class="mw-page-title-main">Magic circle (mathematics)</span> Chinese mathematical arrangement

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 diameters are identical. One of his magic circles was constructed from the natural numbers from 1 to 33 arranged on four concentric circles, with 9 at the center.

<span class="mw-page-title-main">Jia Xian</span> Chinese mathematician

Jia Xian was a Chinese mathematician from Kaifeng of the Song dynasty. He described Pascal's triangle during the 11th century.

The mathematical field of combinatorics was studied to varying degrees in numerous ancient societies. Its study in Europe dates to the work of Leonardo Fibonacci in the 13th century AD, which introduced Arabian and Indian ideas to the continent. It has continued to be studied in the modern era.

Li Ye, born Li Zhi, courtesy name Li Jingzhai, was a Chinese mathematician, politician, 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.

<span class="mw-page-title-main">Cheng Dawei</span> Chinese mathematician

Cheng Dawei, also known as Da Wei Cheng or Ch'eng Ta-wei, was a Chinese mathematician and writer who was known mainly as the author of Suanfa Tongzong (算法統宗). He has been described as "the most illustrious Chinese arithmetician."

Suanfa tongzong 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. 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.

References