China
Mathematician
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Sun Zi was a scholar who wrote the Sunzi Suanjing text which covered measurement, the abacus, two systems for designating high powers of ten, fractions, areas, and volumes. In his text, Zi posed the earliest known occurrence of the Chinese remainder theorem. Problem 1Suppose that, after going through a town gate, you see 9 dykes, with 9 trees on each dyke, 9 branches on each tree, 9 nests on each branch, and 9 birds in each nest, where each bird has 9 fledglings and each fledgling has 9 feathers with 9 different colors in each feather. How many are there of each?
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Mathematician |
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In 1261 Yang Hui wrote a Detailed analysis of the Nine Chapters on the Mathematical Art , the classical Chinese handbook of mathematics. The handbook contains 246 problems with practical applications to engineering, surveying, trade, and taxation. Yang analyzed each problem logically, numerically, and practically. In addition, he explored other areas of mathematics: Pascal's triangle (up to the sixth row) and the natural numbers (sum of the squares from m 2 to 
). Hui also proved that 
and contributed to magic squares (
, 
, 
, 
, 
, 
, 
, and 
). Problem 1Now 1 cubic cun of jade weighs 7 liang, and 1 cubic cun of rock weighs 6 liang. Now there is a cube of side 3 cun consisting of a mixture of jade and rock which weighs 11 jin. What are the weights of jade and rock in the cube [note 1 jin = 16 liang]?
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Little is known about Zhang Qiujian, a learned teacher, except that he wrote a Mathematical Manual in which he outlined the calculation of square and cube roots, solving of equations and systems of equations, sum of arithmetic series, proportions and fractions, and geometry. Among Qiujian's solutions to the problems analyzed in his textbook, he solves systems of linear equations using a method developed by Gauss (Gaussian elimination). Problem 1A circular road around a hill is 325 li long. Three persons A , B , and C run along the road. A runs 150 li per day, B runs 120 li per day, and C runs 90 li per day. If they start at the same time from the same place, after how many days will they meet again.
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Mathematician
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Problem 1A right-angled triangle has area 30 bu. The sum of the base and height of the triangle is 17 bu. What is the sum of the base and the hypotenuse?
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and 
between the sides of a right angled triangle x , y , z where z is the hypotenuse. Determine 
.
where x, y, z are as defined below). Let x, y be the lengths of the two legs and z the length of the hypotenuse of the triangle. Given that
. Determine y .
Mathematician |
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In his youth Cheng Da Wei was academically gifted, but although he was well versed in scholarly matters, he continued to carry out his profession as a sincere Local Agent, without becoming a scholar. He never lagged behind either on the classics or on ancient writings with old style characters, but was particularly gifted in arithmetic. In the prime of his life he visited the fairs of Wu and Chu. When he came across books that talked about “square fields” or “grain with the husk removed” … he never looked at the price before purchasing them. He questioned respectable old men who were experienced in the practice of arithmetic and gradually and indefatigably formed his own collection of difficult problems. Problem 1Boy shepherd B with his one sheep behind him asked shepherd A “Are there 100 sheep in your flock?”. Shepherd A replies “Yet add the same flock, the same flock again, half, one quarter flock and your sheep. There are then 100 sheep altogether.” How many sheep is in shepherd A's flock?
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Interesting Tangram Links |
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Try solving the International Color Challenge!
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