history of mathematics - National STEM Centre

Activity 5.
5 Arab mathematics
as much as a daughter; when a man died a widow was normally entitled to oneeighth
while a mother was entitled to one-sixth. However, if a legacy was left to a
stranger, the division became more complicated. The law stated that a stranger could
not receive more than one-third of the estate without the permission of the natural
heirs. If some of the natural heirs endorsed such a legacy but others did not, those
who did must pay, pro-rata, out of their own shares, the amount by which the
stranger's legacy exceeded one-third of the estate. In any case, the legacy to the
stranger had to be paid before the rest of the estate was shared out among the natural
heirs. You can clearly construct problems of varying degrees of complexity which
illustrate different aspects of the law. The following example is typical.
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A woman dies leaving a husband, a son and three daughters. She also
leaves a bequest consisting of ^ + \ of her estate to a stranger. Calculate
the shares of her estate that go to each of her beneficiaries.
Here is the solution. The stranger receives -g- + j = -j| of the estate, leaving ^ to be
shared out among the family. The husband receives one-quarter of what remains;
that is, \ of -^ = -$%. The son and the three daughters receive their shares in the
ratio 2:1:1:1; that is, the son's share is two-fifths of the estate after the stranger
and husband have taken their bequests. So, if the estate is divided into
5 x 224 = 1120 equal parts, the shares received by each beneficiary will be:
Stranger: •£ of 1120 = 300 parts Husband: -fa of 1120 = 205 parts
Son: | of (1120-505) = 246 parts Each daughter: } of (1120-505) = 123 parts.
Inheritance problems
Share out the estate for each beneficiary of the following inheritance problems.
Think how difficult they would be if you used the Babylonian number system.
1 A man dies leaving four sons and his widow. He bequeaths to a stranger as much
as the share of one of the sons less the amount of the share of the widow.
2 A man dies and leaves two sons and a daughter. He also bequeaths to a stranger
as much as would be the share of a third son, if he had one.
3 A man dies and leaves a mother, three sons and a daughter. He bequeaths to a
stranger as much as the share of one of his sons less the amount of the share of a
second daughter, in case one arrived after his death.
4 A man dies and leaves three sons. He bequeaths to a stranger as much as the
share of one of his sons, less the share of a daughter, supposing he had one, plus
one-third of the remainder of the one-third.
Trigonometry
Arab mathematicians inherited their knowledge of trigonometry from a variety of
sources. In 150 BC in Alexandria, Hipparchus is believed to have produced the first
trigonometric tables in order to study astronomy. These were tables of chords of a
circle of unit radius. Figure 5.2 shows one of these chords.
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