Download Zhoubi suanjing (Arithmetical Classic of the Gnomon and the

MATH 300 History of Mathematics
Figures in Chinese Mathematics
Shang Dynasty, 18th to 12th c. BCE
First evidence of numeration: decimal and positional
Basic arithmetic performed with mechanical aids: counting rods on a grid
Zhou Dynasty, 12th to 3rd c. BCE
K’ung Fu-tzu (Master K’ung) = Confucius (6th c.), Taoist philosopher, emphasized family piety,
humanism and traditional values
Classical period of the arts and humanities during the 7th and 6th c.
Qin Dynasty, 221-206 BCE
Shih Huang Ti united China under a central government
He burned books throughout the empire and ordered that “History begins with Qin!”
Gave China its name (Qin-a) and built the Great Wall
Han Dynasty, 207BCE-220CE
Instituted the silk trade with the West (Persians)
Began system of civil service which required education in mathematics
Zhoubi suanjing (Arithmetical Classic of the Gnomon and the Concentric Paths of Heaven)
Written during Zhou Dynasty but final edition around by 100CE
Work on cosmology, involving use of rational arithmetic and Pythagorean relationship (Fig. 5.2)
Jiuzhang suanshu (Nine Chapters on the Mathematical Arts)
Written between 100BCE and 50CE
Compilation of 246 problems with solutions:
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arithmetic with fractions, exchange rates, pricing, taxation and accounting
area and volume computations, Pythagorean relation
area of circle (four methods, incl. one with π = 3), volume of sphere
square and cube roots
linear equations solved via “the rectangular array” (Gaussian elimination procedures)
Three Kingdoms period, Jin Dynasties, 3rd - 6th c.
China divided; political choas reigns
Buddhism enters China from India
Liu Hui: Haidao suanjing (Sea Island Mathematical Manual)
Nine surveying problems, solved with plane geometry (similar triangles = “double differences”)
Determines area of circle by approximating it with an inscribed regular polygon (the 12-gon
has area 3 units, the 96-gon is equivalent to π ≈ 3.14)
Zu Chongzhi: Zhui shu (Method of Interpolation)
Work is now lost
Devised an improved calendar (Ta ming)
Said to have calculated volume of sphere and numerical solution to cubic equations
Approximated the circle with a regular 12,288-gon (210 × 12) to approximate π as 3.1415926, or
355
(milu = “detailed”) and 22
between 113
7 (yuelu = “rough”)
Sui Dynasty, 6th c.
Grand Canal begun to link Yellow and Yangtze Rivers
Tang Dynasty, 7th - 8th c.
Li Po and Tu Fu, great Chinese poets, flourished
Printing was invented
Yi Xing: Ta yen li (Great Extension of Days)
Astronomer, who devised a calendrical system based on computing the distance traveled by the
sun along the ecliptic via measuring lengths of shadows
Prepared a “tangent table” for various angles of such shadows
Song Dynasty, 9th - 13th c.
Marked by reforms of Confucianism
Qin Jiushao: Shushu jiuzhang (Mathematical Treatise in Nine Parts)
Develops algorithms (equivalent to Horner’s Method) for solving polynomial equations
Formulates the Chinese Remainder Theorem (ta yen rule) for solving systems of linear equations in whole numbers
Uses the Euclidean algorithm (!) for computing GCDs
Explains how Jia Xian (ca. 1050) builds the Pascal Triangle (!) to help compute roots of polynomial equations
Yuan Dynasty, 13th - 14th c.
Ushered in by the Mongol Invasion led by Kublai Khan (grandson of Genghis)
Completed the Grand Canal
Increased trade with the West
Ming Dynasty, 14th - 17th c.
Established Beijing as capital
Sent explorers to India and Southeast Asia
Invited the first Western scientists (Matteo Ricci, SJ, 1583)