Free Research: History Of Arabic Numbering System Research Paper Sample
Type of paper: Research Paper
Topic: System, Mathematics, Europe, Hinduism, Symbolism, Literature, Books, India
Going back in history, humans developed languages and systems of counting. What we now know as the decimal system of counting (based on ten digits) is probably no accident, bearing in mind that man has ten digits on his hands – eight fingers and two thumbs. Various counting systems have used ten as the basis, and to record numbers, ancient man would create notches in a piece of wood or soft stone.
Some of the known numbering systems from the past include the Egyptian system – dating from circa 3000 BC. Then there was the 60-based Babylonian numbering system dating from around 1750 BC, which is responsible for our present numbers like 60 seconds in a minute, the 180 degrees of angles within a triangle and the circle’s 360 degrees. An early and simple to use and understand system employed by Babylonian and Phoenician merchants was the abacus. The earliest form of the device was a series of furrows scraped in the ground in which pebbles represented the digits of the number (Gascoigne, 2001). Our focus in this research paper is the numbering system known as the Arabic or Hindu-Arabic system. The paper investigates its history in further detail as well as information regarding its original source – when and where it was believed to have been invented.
Babylonian and similar numbering systems produce written numbers which are awkward and unwieldy, and are less than ideal for arithmetical purposes. Furthermore, the zero symbol is not entirely effective. To make the zero effective and useful for mathematical calculations, each number up to the system’s base number requires its own specific symbol. This issue seems to have been resolved first in India, from around the 3rd century BC, when they used either a dot or a small circle to denote a position in a number which is “empty” or has zero value. By around 800 AD the system had been refined and was also adopted in Baghdad. It was perhaps that event which caused the numbers used in the system to be known as Arabic numerals, when – about two centuries afterwards – the system found its way to Europe in certain Arabic documents. Then, after several more centuries had passed, those ten Arabic numerals (0 to 9) began to be used in Europe instead of the Roman numbering system, which had earlier prevailed (Gascoigne, 2001).
According to Shanyuji (2010), the numbering system used in India prior to the adoption of this system was based on a similar system which not only had a different symbol for each of the numbers 1 to 9, but also had number symbols to represent numbers from 10 through to 90. Then, claims Shanyuji, those symbols for numbers greater than 9 were dropped at around 600 BC. He quotes a surviving work by a Syrian priest dating 662 BC, which refers to the Hindu calculation method “done by means of nine signs”, notably without mention of a zero symbol. Shanyuji reports the earliest documented reference to a zero symbol suggests it was used from some time in the seventh century. He also makes reference to a 683 AD Cambodian document which included the zero and states with some certainty that by the 8th century the numbering system including the zero was in full use in India (Shanyuji, 2010).
Bradley (n.d.) States that the nine-digit system we use today comes originally from a Brahmi (Indian) system of numerals, dating from around 300 BC. However, although it wasn’t until the ninth century AD that the zero appeared in academic documents, archaeological evidence from India and Iran suggests that all nine numeric symbols were in use some two hundred years earlier. Then, between 825 and 830 AD, two mathematicians – Al-Khwarizmi from Persia and Arab mathematician Al-Kindi – wrote books on the principles of use of this Arabic numbering system. From those books, the use of this numbering system spread into the Middle East and even as far as some parts of the West. Middle Eastern scholars used this system in the 10th century, developing the system further to include percentages and fractions. Some years later, another mathematician (Sind ibn Ali) refined this numbering system further to add the decimal point. That heralded a new era of writing down the numbers, known as “sand-table.” Those sand-table numbers eventually acquired the appearance and shapes of numbers as written today. Bradley states that the first mention of Arabic numbers in Western records is in a 976 AD published historical account. Then, a few years later, Pope Sylvester II began disseminating information about the Arabic numbering system throughout Europe. He studied mathematics and asked Italian and Algerian scholars to translate older mathematical texts into European languages. In 1202 AD this was accomplished in more depth in a book called “Liber Abaci” written by Leonardo of Pisa. In the 15th century, widespread European acceptance of Arabic numerals was aided by the newly-invented printing press. In Britain, greater exposure to the Arabic numbering system and increased awareness of its existence was facilitated in the 16th century by the elite and powerful, who used it for purposes such as church inscriptions and tombs of the nobility. By the middle of that century, the Arabic numbering system was commonly used throughout much of Europe (Bradley, n.d.).
Regarding the Persian mathematician referred to by Bradley in the previous article, a 2010 article published by Maslaha (an Islamic newsletter), describes him (Al-Khowarizmi) as “The most important mathematician working in Baghdad.” The article further states that it is largely due to the books he wrote that this Arabic-Hindu system of numbering was perceived as entirely Arabic in origin. Indeed, for a time, the series of numbers 0-9 were together known as “algorism,” which is a noun derived from his name. It is also closely linked to the English word “algorithm,” which describes a set of mathematical instructions. As regards introducing this Arabic-Hindu numbering system into Europe, the Maslaha article attributes the credit to three individuals. These were: Alexandre de Villedieu from France; John of Halifax (an English schoolteacher); and the best known of the three, an Italian named Leonardo of Pisa, better known in modern times as Fibonacci. He was a merchant’s son and travelled extensively, particularly in Egypt, Greece and Syria. Because he had a Muslim teacher, he became well-acquainted with the Arabic-Hindu system of numbers, including the books by Al-Khowarizmi and others. Today, Leonardo of Pisa (or Fibonacci) is well known for his treatise on algebraic techniques, called the Liber Abaci, or “Book of Abacus.” Its importance is that for European mathematicians it showed them how using the simple digits of the Arabic-Hindu system (0-9) could help them solve problems which at the time were very advanced. That book also contains details of the so-called “Fibonacci sequence” which is a formula in which each number in a sequence is the sum of the previous two. A simple formula, but according to the article it has helped mathematicians and scientists to understand many things “from the patterning of leaves and organic growth to the science of predicting outcomes” and has been a major influence on mathematics over the last five hundred years (“Arabic-Hindu Numerals and the Development of Modern Mathematics” (2010).
The History of the Arabic or Arabic-Hindu system of numerals reveals that its origins were in all probability in India, and that the complete set of numbers (including the zero) originated in India around the 7th century AD. Largely as a result of the works of a Persian and an Arab mathematician, the system eventually filtered through to Europe and other Western countries, revolutionizing the ease of performing complex mathematical calculations and allowing problems in other scientific fields to be solved.
“Arabic-Hindu Numerals and the Development of Modern Mathematics.” (Feb. 2010). Maslaha. Retrieved from: http://www.maslaha.org/articles/featured-article/arabic-hindu-numerals-and-development-modern-mathematics
Bradley, Jeremy C. (n.d.). “How Arabic Numbers Were Invented.” Synonym. Retrieved from: http://classroom.synonym.com/arabic-numbers-were-invented-6959.html
Gascoigne, Bamber. (From 2001, ongoing). “Counting Systems and Numerals.” History World. Retrieved from: http://www.historyworld.net/wrldhis/plaintexthistories.asp?historyid=ab34
Shanyuji, Ji. (Jun. 2010). “Hindu-Arabic Numeral System.” University of Houston. Retrieved from: http://www.math.uh.edu/~shanyuji/History/h-19.pdf