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CHINESE PROBLEMS

CHINESE PROBLEMS. Index. Introduction: The Nine Chapters on the Mathematical Art The Pythagorean theorem vs Gougu theorem. Two Chinese problems: - At what height is the bamboo broken?. ¯ ˇ. - How deep is the pool?. 九章算术 ( Jiǔzhāng Suànshù).

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CHINESE PROBLEMS

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  1. CHINESE PROBLEMS

  2. Index • Introduction: The Nine Chapters on the Mathematical Art • The Pythagorean theorem vs Gougu theorem. • Two Chinese problems: - At what height is the bamboo broken? ¯ ˇ - How deep is the pool?

  3. 九章算术 (Jiǔzhāng Suànshù) The Nine Chapters on the Mathematical Art • There are 246 mathematical problems in total and they are divided in 9 chapters: • 方田 Fangtian(Boundingfields): Surfaces and countingrods. • 粟米 Sumi (Millet and rice): Exchange of commodities at different rates. • 衰分 Cuifen(Proportionaldistribution): Distribution of commodities and money at proportional rates • 少廣 Shaoguang(Reducingdimensions): divisionbymixednumbers, extraction of square and cube roots; diameter of sphere, perimeter and diameter of circle. • 商功Shanggong(Figuringforconstruction):Volumes of various shapes. • 均輸Junshu(Equitabletaxation): More advanced problems on proportion. • 盈不足 Yingbuzu(Equitabletaxation): Linear problems (two unknowns). • 方程 Fangcheng (Thetwo-sidedreference): systems of linear equations. • 勾股 Gougu (Base and altitude): ProblemsinvolvingtheGouguorPythagoreantheorem. ¯ ˇ ¯ ˇ

  4. Two different demonstrations for the same theorem GOUGU THEOREM PYTHAGOREAN THEOREM ¯ ˇ

  5. At what height is the bamboo broken? • A 10-foot tall bamboo cane has broken in such a way that the top of it is resting on the ground 3 feet from its base. At what height is the break?

  6. How deep is the pool? • Calculate the depth of a circular pool with a surface area of 10π square feet, where a cane growing in the centre, which stands one foot out of the water, reaches the surface when it is tilted against the walls of the pool.

  7. Wehope you have enjoyed it Pablo Miki García Pérez de Algaba & María de la Paz Llavero Ogalla. I.E.S Medina Azahara, 4º E.S.O.

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