The Chinese demonstrated their knowledge and understanding of mathematics by compiling sets of specific problems.
1) The Broken Bamboo Problem
The Broken Bamboo Problem, taken from the Arithmetic in Nine Sections, involves the use of right-angled triangles, and is given below:
“There is a bamboo 10 feet high, the upper end of which being broken reaches the ground 3 feet from the stem. Find the height of the break.”
The Problem of the Broken Bamboo, from a work of Yang Hui (1261)
Using Pythagoras’ Theorem, the problem can be solved to give 4.55 feet as the height of the break.
2) The Hundred Fowl Problem
This problem, dated to the fifth century, requires a combination of simultaneous equations, substitution and trial and error to solve:
“A cock is worth 5 qian, a hen 3 qian and 3 chicks 1 qian; with 100 qian we buy 100 of them; how many cocks, hens and chicks are there?”
By creating two equations with three unknowns, and then using trial and error to find the whole number solutions, the integral solutions to this problem are:
– 12 Cocks, 4 Hens, 84 Chicks
– 8 Cocks, 11 Hens, 81 Chicks
– 4 Cocks, 18 Hens, 78 Chicks.
3) The Rice Problem
Solving this problem requires the use of the Rule of Three, which is a proportion involving three known quantities and one unknown quantity, from which the unknown can be found:
“Two and one half picules of rice are purchased for three sevenths of a tael of silver. How many can be purchased for nine taels?”
The Rule of Three gives
(5/2)/(3/7) = x/9
and by rearranging this, x can be found to be 105/2 picules.
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