Rule Of Three

The Rule of Three is commonly considered as being of Indian origin. However, the proper founder is a Chinese man by the name of Chiu Chang. This rule is simply a proportion involving three knowns from which an unknown quantity is found.

The following is a Chinese example involving this rule:

"Two and one half picules of rice are purchased for three thirds of a tael of silver. How many can be purchased for nine taels?" (Swetz F and Kao T, 1977, p18)

If we alter this question by using the modern use of symbolism and the Rule of Three, the solution can be derived as follows:-

(5/2)/(3/7) = x/9

35/6 = x/9

x = (35x9)/6

x = 105/2 picules

Another problem involving series and this rule is concerned with a farmer's dilemma. This problem is stated below:-

"A cow, a horse and a goat were in a wheat field and consumed some stalks of wheat. Damage of five tou of grain were asked by the wheat field's owner. If the goat ate one half the number of stalks as the horse and the horse ate one half of what was eaten by the cow, how much should be paid by the owners of the goat, horse and cow respectively?" (Swetz F and Kao T, 1977, p19)

In today's society a mathematically minded student with a minimum amount of algebraic knowledge would interpret this problem with the following symbolic expressions:-

1/4x + 1/2x + x = 5

Although today this seems as simply knowledge to us it is interesting to see how the Chinese developed this knowledge.

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