For example, in the first century CE, one particular set of Brahmi numerals took on the following form: [4]. From the fourth century on, you can actually trace several different paths that the Brahmi numerals took to get to different points and incarnations. One of those paths led to our current numeral system, and went through what are called the Gupta numerals.
The Gupta numerals were prominent during a time ruled by the Gupta dynasty and were spread throughout that empire as they conquered lands during the fourth through sixth centuries.
They have the following form: [5]. How the numbers got to their Gupta form is open to considerable debate. Many possible hypotheses have been offered, most of which boil down to two basic types. This is not uncommon. The second type of hypothesis states that they were derived from some earlier number system.
However, there are other hypotheses that are offered, one of which is by the researcher Ifrah. His theory is that there were originally nine numerals, each represented by a corresponding number of vertical lines.
One possibility is this: [7]. Because these symbols would have taken a lot of time to write, they eventually evolved into cursive symbols that could be written more quickly. If we compare these to the Gupta numerals above, we can try to see how that evolutionary process might have taken place, but our imagination would be just about all we would have to depend upon since we do not know exactly how the process unfolded.
The Gupta numerals eventually evolved into another form of numerals called the Nagari numerals, and these continued to evolve until the eleventh century, at which time they looked like this: [8]. Note that by this time, the symbol for 0 has appeared! The Mayans in the Americas had a symbol for zero long before this, however, as we shall see later in the chapter.
These numerals were adopted by the Arabs, most likely in the eighth century during Islamic incursions into the northern part of India. The first mention of Arabic numbers in the West is found in the "Codex Vigilanus," a historical account of Hispania published in Pope Sylvester II began to spread knowledge of Arabic numerals throughout Europe beginning in the s.
As a student, Sylvester studied a form of mathematics and requested that Italian and Algerian scholars translate some of the earlier mathematical texts into common European languages. This was accomplished more fully in with a book by Leonardo of Pisa called "Liber Abaci. The acceptance of Arabic numerals in Europe was precipitated by the invention of the printing press in the 15th century. Other major events in Britain helped to bring greater awareness of math.
For example, an inscription on the bell tower of Heathfield Church in Sussex in , and a inscription on the tomb of the Earl of Huntly in Scotland, show the use of Arabic numbers by the powerful and elite.
By the midth century, Arabic numerals were in common use throughout most of Europe. This may have encouraged him to find out about the astronomy works of the Indians and in these, of course, he would find the arithmetic of the nine symbols. By AD the Arab empire was beginning to take shape and we have another reference to the transmission of Indian numerals. We quote from a work of al-Qifti Chronology of the scholars written around the end the 12 th century but quoting much earlier sources This is all contained in a work Al-Mansur ordered this book to be translated into Arabic, and a work to be written, based on the translation, to give the Arabs a solid base for calculating the movements of the planets Now in [ 1 ] where a longer quote is given Ifrah tries to determine which Indian work is referred to.
He concludes that the work was most likely to have been Brahmagupta 's Brahmasphutasiddhanta The Opening of the Universe which was written in Irrespective of whether Ifrah is right, since all Indian texts after Aryabhata I 's Aryabhatiya used the Indian number system of the nine signs, certainly from this time the Arabs had a translation into Arabic of a text written in the Indian number system.
It is often claimed that the first Arabic text written to explain the Indian number system was written by al-Khwarizmi. However there are difficulties here which many authors tend to ignore.
Unfortunately the Latin translation is known to be much changed from al-Khwarizmi 's original text of which even the title is unknown. The Latin text certainly describes the Indian place-value system of numerals based on 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , and 0.
The first use of zero as a place holder in positional base notation is considered by some to be due to al-Khwarizmi in this work. The difficulty which arises is that al-Baghdadi refers to the Arabic original which, contrary to what was originally thought, seems not to be a work on Indian numerals but rather a work on finger counting methods.
This becomes clear from the references by al-Baghdadi to the lost work. However the numerous references to al-Khwarizmi 's book on the Indian nine symbols must mean that he did write such a work. Some degree of mystery still remains. At first the Indian methods were used by the Arabs with a dust board. In fact in the western part of the Arabic world the Indian numerals came to be known as Guba or Gubar or Ghubar numerals from the Arabic word meaning "dust".
A dust board was used because the arithmetical methods required the moving of numbers around in the calculation and rubbing some out some of them as the calculation proceeded.
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.
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