It took until the ninth century A. However, archaeological evidence unearthed in central India and Iran indicates the use of all nine numerals as far back as the seventh century A. Between the years and , Persian mathematician Al-Khwarizmi and Arab mathematician Al-Kindi each wrote separate books on the principles of using Arabic numerals. These books led to the diffusion of the numbers into the Middle East and parts of the West.
In the 10th century, Middle Eastern scholars used the numerals to develop fractions and percentages. Later that same century, a mathematician called Sind ibn Ali introduced the decimal point. With this came a new way of writing numbers called "sand-table.
The first mention of Arabic numbers in the West is found in the "Codex Vigilanus," a historical account of Hispania published in Scholars flocked to be part of the intellectual endeavour, and manuscripts were brought from across the Middle East and beyond to be translated and the knowledge they held put to use. Astronomy and mathematics were two of the subjects most urgently pursued, and the achievements of the scholars who studied them were truly astonishing. They built the first observatory in the Muslim world, where they produced data that transformed human understanding of the universe.
They translated, corrected and improved ancient Greek scientific theories, combining them with those from India and with their own ideas, propelling knowledge forward. His name suggests that his origins lay in the province of Khwarazm, far to the north-east on the shores of the Aral Sea.
Al-Khwarizmi was a visionary mathematician. Indeed, we would now describe him as an outlier. Yet, when this shift finally came, his book was to play a key role: it was translated into Latin in the 12th century, and became an important part of the European intellectual tradition.
In it, al-Khwarizmi defined this discipline for the first time by describing different kinds of quadratic equations. Interestingly, he did this in words rather than with the system of notation used in algebra today, which developed during the Renaissance. By the tenth century, they had reached Spain, most of which was under Muslim rule at that time. During the 11th and 12th centuries, Christian forces in the north of the Iberian peninsula began conquering the great cities of al-Andalus.
Toledo fell in , and over the following decades European scholars came to the city in search of Arabic books, including texts by al-Khwarizmi, which they translated into Latin. These scholars may have already been acquainted with the forms of the numerals themselves, which were present on a certain type of abacus counting board thought to have been introduced by a tenth-century monk named Gerbert later Pope Sylvester II whose talent and passion for mathematics took him to Spain in search of knowledge.
Thus the Hindu-Arabic numerals and system of place-value were gradually introduced to Europe. It was a slow process, in part because of resistance from Christians who regarded the numerals as evil and dangerous — simply because they came from the Muslim world. The most important figure in the transmission of the Hindu-Arabic system to Europe was not Spanish but Italian, and learned the numerals not in Spain but in Africa: Leonardo of Pisa, known today as Fibonacci though that name was applied to him only from the 19th century.
As a teenager, Fibonacci travelled around the eastern Mediterranean with his father, thereby enjoying opportunities to compare several systems of calculation in use at that time.
He quickly recognised the enormous potential of the Hindu-Arabic system to transform learning in the west. In he wrote a book titled Liber abbaci Book of Calculation. In this book, the first original work in Latin on the subject, he explained the workings of each of the numerals and the method of writing numbers in order according to their value. It detailed how to work out transactions in different currencies, and how to use different systems of weights and measures — methods that became increasingly important as Europe grew in prosperity and the mercantile world expanded and developed.
Merchants needed to be able to carry out complex calculations and record their accounts effectively — something that was made possible by the Hindu-Arabic system of numerals as expounded by Fibonacci.
The dust board allowed this in the same sort of way that one can use a blackboard, chalk and a blackboard eraser. Any student who has attended lectures where the lecturer continually changes and replaces parts of the mathematics as the demonstration progresses will understand the disadvantage of the dust board!
In it al-Uqlidisi argues that the system is of practical value:- Most arithmeticians are obliged to use it in their work: since it is easy and immediate, requires little memorisation, provides quick answers, demands little thought Therefore, we say that it is a science and practice that requires a tool, such as a writer, an artisan, a knight needs to conduct their affairs; since if the artisan has difficulty in finding what he needs for his trade, he will never succeed; to grasp it there is no difficulty, impossibility or preparation.
In the fourth part of this book al-Uqlidisi showed how to modify the methods of calculating with Indian symbols, which had required a dust board, to methods which could be carried out with pen and paper.
Certainly the fact that the Indian system required a dust board had been one of the main obstacles to its acceptance. For example As-Suli, after praising the Indian system for its great simplicity, wrote in the first half of the tenth century:- Official scribes nevertheless avoid using [ the Indian system ] because it requires equipment [ like a dust board ] and they consider that a system that requires nothing but the members of the body is more secure and more fitting to the dignity of a leader.
Al-Uqlidisi 's work is therefore important in attempting to remove one of the obstacles to acceptance of the Indian nine symbols.
It is also historically important as it is the earliest known text offering a direct treatment of decimal fractions. Despite many scholars finding calculating with Indian symbols helpful in their work, the business community continued to use their finger arithmetic throughout the tenth century. Abu'l-Wafa , who was himself an expert in the use of Indian numerals, nevertheless wrote a text on how to use finger-reckoning arithmetic since this was the system used by the business community and teaching material aimed at these people had to be written using the appropriate system.
Let us give a little information about the Arab letter numerals which are contained in Abu'l-Wafa 's work. The numbers were represented by letters but not in the dictionary order. The numbers from 1 to 9 were represented by letters, then the numbers 10 , 20 , 30 , There were 28 Arabic letters and so one was left over which was used to represent Arabic astronomers used a base 60 version of Arabic letter system.
Although Arabic is written from right to left, we shall give an example writing in the left to right style that we use in writing English. A contemporary of al-Baghdadi , writing near the beginning of the eleventh century, was ibn Sina better known in the West as Avicenna.
We know many details of his life for he wrote an autobiography. Certainly ibn Sina was a remarkable child, with a memory and an ability to learn which amazed the scholars who met in his father's home. A group of scholars from Egypt came to his father's house in about when ibn Sina was ten years old and they taught him Indian arithmetic.
He also tells of being taught Indian calculation and algebra by a seller of vegetables. All this shows that by the beginning of the eleventh century calculation with the Indian symbols was fairly widespread and, quite significantly, was know to a vegetable trader.
What of the numerals themselves. We have seen in the article Indian numerals that the form of the numerals themselves varied in different regions and changed over time. Exactly the same happened in the Arabic world. Here is an example of an early form of Indian numerals being used in the eastern part of the Arabic empire.
It comes from a work of al-Sijzi , not an original work by him but rather the work of another mathematician which al-Sijzi copied at Shiraz and dated his copy
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