Chinese and Indian Mathematics

Other Chinese Mathematicians
• Yang Hui worked on magic squares and binomial theorem, and is best known for his contribution of presenting “Pascal's Triangle”, discovered independently by Yang Hui and his predecessor Jia Xian • Qin Jiushao (c. 1202–1261) was the first to introduce the zero symbol into Chinese mathematics. Qin also solved a 10th order equations!
Calculating Devices
Reproduction of a Roman Bronze “Pocket” Abacus Babylonian Marble Counting Board c. 300 BC Chinese Wooden Abacus
The Abacus 算盤
• There are two beads on each rod in the upper deck and five beads each in the bottom for both decimal and hexadecimal computation • For five or above, slide one bead above the middle bar down (representing 5), and 1, 2, 3 or 4 beads up to the middle bar for the numbers 6, 7, 8, or 9 respectively
Chinese Mathematics
• Ancient Chinese mathematics differs from Greek mathematics. Unlike Greek mathematics there is no axiomatic development of mathematics. The Chinese concept of mathematical proof is radically different from that of the Greeks, yet one must not in any sense think less of it because of this • Chinese mathematics was, like their language, very concise. It was very much problem based, motivated by problems of the calendar, trade, land measurement, architecture, government records and taxes • 4th century BC counting boards were used for calculating, which effectively meant that a decimal place valued number system was in use
Hindu Numbers and Zero
• Hindu numbers are the precursor to the numbers we have today which are called the Hindu – Arabic numbers • An inscription on a stone tablet from 876 from the town of Gwalior, 400 km south of Delhi, where they planted a garden 187 by 270 “hastas” which would produce 50 garlands per day to be given to the local temple. Both of the numbers 270 and 50 are written almost as they appear today although the 0 is smaller and slightly raised • This is the first recorded case of 0 as a number
Shipbuilding and Navigation
• King Hiram of Tyre (Phoenicia) in 975 BC traded with India through the port of Ophir (Supara) near modern Mumbai • Yukti Kalpa Taru, explains how to build ships, ship types, sizes and materials, including suitability of different types of wood • Bhoja had advised the builders of the sea-faring ships not to join the planks with iron, since the magnetic iron in sea water could expose the ship to danger
46802 is represented
Ancient Chinese Number Systems
Counting rod place value decimal
Oracle bone script decimal
Japanese Mathematics
= 16 = 60
• The Japanese numerals in writing are entirely based on the Chinese numerals and the grouping of large numbers follow the Chinese tradition of grouping by 10,000 • Like in Chinese numerals, there exists in Japanese a separate set of kanji for numerals called daiji (大字) used in legal and financial documents to prevent unscrupulous individuals from adding a stroke or two, turning a one into a two or a three • The formal numbers are identical to Chinese formal numbers except for minor stroke variations
Four Great Inventions 四大发明
The compass, gunpowder, papermaking, and printing 1. Printing was recorded in the Tang Dynasty 2. Ceramic movable type printing by Bi Sheng (990 - 1051), wooden movable type of Wang Zhen in 1298 and the bronze metal movable type of Hua Sui in 1490 3. The development time of the compass is unsure. The first undisputed magnetized needles in Chinese literature appear in AD 1086 4. By AD 300, Ge Hong, an alchemist of the Jin Dynasty, recorded the chemical reactions caused when saltpeter, pine resin and charcoal were heated together, in Book of the Master of the Preservations of Solidarity. This was the early gunpowder
From Yang Hui’s book: 详 解九章算法
Magic Square of order 3
INDIA
Indian Mathematics
• Mathematics today owes a huge debt to the outstanding contributions made by Indian mathematicians • One of the “huge debt” is the beautiful number system invented by the Indians (and Arabs) which we use today • They used algebra to solve geometric problems
Chinese Mathematics
• Chinese mathematics has developed greatly since at least 100 BC. Although the Chinese refer back to their ancient texts, many of which were written on strips of bamboo, they are constantly coming up with ways of working out problems • Hong Luoxia (130 BC – 30 BC) designed a new calendar for the Emperor, which featured 12 months, based on a cycle of 12 years. This inspired many people to design calendars and is similar to the tion of the Gou Gu (Pythagorean) Theorem
From The Nine Chapters on the Mathematical Art This book consists chapters of: 1. Three involve surveying and engineering formulas 2. Three are devoted to problems of taxation and bureaucratic administration 3. Three to specific computational techniques
Chinese and Indian Mathematics
History of Math and Its Effect on World Cultures
CHINA
From Along the River During the Qingming Festival; daily life of people from the Song dynasty at the capital, Bianjing, today's Kaifeng
The Nine Chapters on the Mathematical Art
• Written by Liu Hui, a great mathematician in the Wei Jin Dynasty, ushered in an era of mathematical theorization in ancient China • Using regular polygons with 3 × 2n sides inscribed in a circle, he found approximation of π = 3.14159 which he achieved from a regular polygon of 3072 sides! • Uses Pythagoras's theorem to calculate heights of objects and distances to objects