The Decimal and Islamic Mathematics
The Decimal System
Muslim mathematicians were the first people to write numbers the way we do, and, although we are the heirs of the Greeks in geometry, part of our legacy from the Muslim world is our arithmetic. This is true even if it was Hindu mathematicians in India, probably a few centuries before the rise of Islamic civilization, who began using a numeration system with these two characteristics:
The numbers from one to nine are represented by nine digits, all easily made by one or two strokes.
The right-most digit of a numeral counts the number of units, and a unit in any place is ten of that to its right. Thus the digit in the second place counts the number of tens, that in the third place the number of hundreds (which is ten tens), and so on. A special mark, the zero, is used to indicate that a given place is empty.
These two properties describe our present system of
writing whole numbers, and we may summarize the above by saying the Hindus were
the first people to use a cipherized, decimal, positional system, "Cipherized"
means that the first nine numbers are represented by nine ciphers, or digits,
instead of accumulating strokes as the Egyptians and Babylonians did, and
"decimal" means that it is base 10. However, the Hindus did not extend this
system to represent parts of the unit by decimal fractions, and since it was the
Muslims who first did so, they were the first people to represent numbers as we
do. Quite properly, therefore, we call the system "Hindu-Arabic".
The problem of parallel lines, posed by Euclid's parallels postulate, received much attention from Islamic mathematicians throughout the history of medieval Arabic science. Nasir ad-Din at-Tusi's was probably the most mature treatment of the problem in Arabic, making sure use of Euclid's definition of parallel lines as non-secant lines and drawing on the results of his predecessors. TheModernReligion.com
It seems, then, that Christian scholars in the Middle East, writing only a few years after the great series of Arab conquests had begun, knew of Hindu numerals through their study of Hindu astronomy. The interest of Christian scholars in astronomy and calculation was, in the main, due to their need to be able to calculate the date of Easter, a problem that stimulated much of the Christian interest in the exact sciences during the early Middle Ages. It is not a trivial problem, because it requires the calculation of the date of the first new moon following the spring equinox. Even the great nineteenth-century mathematician and astronomer C.F. Gauss was not able to solve the problem completely, so it is no wonder that Severus Sebokht was delighted to find in Hindu sources a method of arithmetic that would make calculation easier.
We can perhaps explain the reference to the "nine signs" rather then the ten as follows: the zero (represented by a small circle) was not regarded as one of the digits of the system but simply a mark put in a place when it is empty, i.e. when no digit goes there. The idea that zero represents a number, just as any other digit does, is a modern notion, foreign to medieval though.
With this evidence that the Hindu system of numeration had spread so far by the year A.D. 662, it may be surprising to learn that the earliest Arabic work we know of explaining the Hindu system is one written early in the ninth century whose title may be translated as The Book of Addition and Subtraction According to the Hindu Calculation. The author was Muhammad ibn Musa al-Khwarizmi who, since the was born around the year A.D. 780, probably wrote his book after A.D. 800.
We mentioned in Chapter 1 that al-Khwarizmi, who was
one of the earliest important Islamic scientists, came from Central Asia and was
not an Arab. This was not unusual, for, by and large, in Islamic civilization it
was not a man's place (or people) of origin, his native language, or (within
limits) his religion that mattered, but his learning and his achievements in his
This article is excerpted from the book "Episodes in the Mathematics of Medieval Islam" by J. L. Berggren.
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