history of mathematics - National STEM Centre

5 Arab mathematics
If possible work in a group for Activity 5.8, You may be asked to make a short
report based on your work in this activity.
Historical background
The period of Arab intellectual ascendancy can be thought of as beginning with the
expansion of Islam in the first half of the 7th century. After a period of over a
century of war and expansion a new capital of the Arab civilisation was established
at Baghdad, which gradually became a centre of mathematical activity.
A 'House of Wisdom' was established, and mathematical and other scholars from
the whole Arab civilisation, as well as India and Greece, were welcomed. The Arabs
quickly absorbed the learning of their neighbours.
A multiplicity of influences therefore went into the creation of Arab mathematics.
First, there was Babylonian mathematics and astronomy dating back over 2500
years. This mathematics was passed down either through the medium of a religious
sect known as Sabeans, descendants of Babylonian star-worshippers who showed a
particular aptitude for astronomy and numerology, or through a number of practical
algorithms for solving linear and non-linear equations in one or more unknowns,
similar to the old Babylonian methods described in Chapter 2.
Second were the Greek written sources, regarded by many historians of mathematics
as of paramount importance in the development of Arab mathematics. Central to the
Greek tradition, as it was taken over by the Arab world, were Euclid's geometrical
text, Elements, and Ptolemy's astronomical text, Almagest.
Third, and less certain, were the Indian written sources. The line of influence is not
so clear as that of the Greek mathematicians. But, it is clear that the Indians did
much work on trigonometry and astronomy, which entered Arab mathematics
through the Arabs' interest in astronomy. For example, an astronomical work from
India, one of the Siddhantas, was translated into Arabic in about AD 775.
Other knowledge came from a variety of sources. There existed a vast treasure trove
of commercial practices, measurement techniques, number reckoning, recreational
problems and other examples of 'oral mathematics' which resulted from large
groups of merchants, diplomats, missionaries and travellers meeting one another
along the caravan routes and the sea routes from China to Cadiz in Spain. The
computational procedures or algorithms, arising from this source, often seemed
more like recipes than well-thought-out mathematical methods. But a number of
Arab mathematicians, inspired by these recipes, proceeded to devise their own
techniques for solving problems. In doing so, they sometimes translated their
recipes into a more suitable, theoretical form.
Numerals
One of the most far-reaching inventions of Indian mathematics was a positional, or
place value, decimal numeral system. With symbols or digits to represent numbers
from zero to nine, 0, 1, 2, ..., 9, it became possible to represent any integer both
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