- INDIA 139
Chapter 6 ("Fair Transportation") is concerned with the very important prob-
lem of fair allocation of the burdens of citizenship. The Chinese idea of fairness, like
that in many other places, including modern America, involves direct proportion.
For example, Problem 1 considers a case of collecting taxes in a given location from
four counties lying at different distances from the collection center and having dif-
ferent numbers of households. To solve this problem a constant of proportionality
is assigned to each county equal to the number of its households divided by its
distance from the collection center. The amount of tax (in millet) each county is
to provide is its constant divided by the sum of all the constants of proportionality
and multiplied by the total amount of tax to be collected. The number of carts (of
a total prescribed number) to be provided by each county is determined the same
way. The data in the problem are as follows.
County Number of Households Distance to Collection Center
A 10,000 8 days
 9,500 10 days
C 12,350 13 days
D 12,200 20 days
A total of 250,000 hu of millet were to be collected as tax, using 10,000 carts.
The proportional parts for the four counties were therefore 1250, 950, 950, and 610,
which the author reduced to 125, 95, 95, and 61. These numbers total 376. It
therefore followed that county A should provide · 250,000 hu, that is, approx-
imately 83,111.7 hu of millet and ^| · 10,000, or 3324 carts. The author rounded
off the tax to three significant digits, giving it as 83,100 hu.
Along with these administrative problems, the 28 problems of Chapter 6 also
contain some problems that have acquired an established place in algebra texts
throughout the world and will be continue to be worked by students as long as
there are teachers to require it. For example, Problem 26 considers a pond used for
irrigation and fed by pipes from five different sources. Given that these five canals,
each "working" alone, can fill the pond in |, 1, 2^, 3, and 5 days, the problem asks
how long all five "working" together will require to fill it. The author realized that
the secret is to add the rates at which the pipes "work" (the reciprocals of the times
they require individually to fill the pond), then take the reciprocal of this sum, and
this instruction is given. The answer is 1/(3 + 1 + 2/5 + 1/3 + 1/5) = 15/74.
3. India
We have noted a resemblance between the mathematics developed in ancient Egypt
and that developed in ancient China. We should not be surprised at this resem-
blance, since these techniques arose in response to universal needs in commerce,
industry, government, and society. They form a universal foundation for mathe-
matics that remained at the core of any practical education until very recent times.
Only the widespread use of computers and computer graphics has, over the past
two decades, made these skills obsolete, just as word processors have made it unim-
portant to develop elegant handwriting.
To avoid repetition, we simply note that much of the Hindu method of com-
putation is similar to what is now done or what is discussed in other sections of
this chapter. A few unusual aspects can be noted, however. Brahmagupta gives
the standard rules for handling common fractions. However, his arithmetic con-
tains some original ways of looking at many things that we take for granted. For