When did the Arabic numeral system develop?
Hindu–Arabic numeral system
It was invented between the 1st and 4th centuries by Indian mathematicians. The system was adopted in Arabic mathematics by the 9th century. Influential were the books of Muḥammad ibn Mūsā al-Khwārizmī ("On the Calculation with Hindu Numerals", ) and Al-Kindi ("On the Use of the Hindu Numerals", ). The system later spread to medieval Europe by the High Middle Ages.
History of mathematics
Other achievements of Muslim mathematicians during this period include the addition of the decimal point notation to the Arabic numerals, the discovery of all the modern trigonometric functions besides the sine, al-Kindi's introduction of cryptanalysis and frequency analysis, the development of analytic geometry by Ibn al-Haytham, the beginning of algebraic geometry by Omar Khayyam and the development of an algebraic notation by al-Qalasādī.
Arabic numerals
From the 980s, Gerbert of Aurillac (later, Pope Sylvester II) used his position to spread knowledge of the numerals in Europe. Gerbert studied in Barcelona in his youth. He was known to have requested mathematical treatises concerning the astrolabe from Lupitus of Barcelona after he had returned to France.
History of science
In mathematics, the mathematician Muhammad ibn Musa al-Khwarizmi (c. 780–850) gave his name to the concept of the algorithm, while the term algebra is derived from "al-jabr", the beginning of the title of one of his publications. What is now known as Arabic numerals originally came from India, but Muslim mathematicians made several key refinements to the number system, such as the introduction of decimal point notation.
Abjad numerals
Before the introduction of the Hindu–Arabic numeral system, the abjad numbers were used for all mathematical purposes. In modern Arabic, they are primarily used for numbering outlines, items in lists, and points of information. In English, points of information are sometimes referred to as "A", "B", and "C" (or perhaps use Roman numerals: I, II, III, IV), and in Arabic, they are "", then "", then "", not the first three letters of the modern " order.
Arabic alphabet
A goldsmith (like Gutenberg) designed and implemented an Arabic-script movable-type printing-press in the Middle East. The Greek Orthodox monk Abd Allah Zakhir set up an Arabic printing press using movable type at the monastery of Saint John at the town of Dhour El Shuwayr in Mount Lebanon, the first homemade press in Lebanon using Arabic script. He personally cut the type molds and did the founding of the typeface. The first book came off his press in 1734; this press continued in use until 1899.
History of algebra
'Abd al-Hamīd ibn Turk authored a manuscript entitled "Logical Necessities in Mixed Equations", which is very similar to al-Khwarzimi's "Al-Jabr" and was published at around the same time as, or even possibly earlier than, "Al-Jabr". The manuscript gives exactly the same geometric demonstration as is found in "Al-Jabr", and in one case the same example as found in "Al-Jabr", and even goes beyond "Al-Jabr" by giving a geometric proof that if the discriminant is negative then the quadratic equation has no solution. The similarity between these two works has led some historians to conclude that Arabic algebra may have been well developed by the time of al-Khwarizmi and 'Abd al-Hamid.
Number
Numbers should be distinguished from numerals, the symbols used to represent numbers. The Egyptians invented the first ciphered numeral system, and the Greeks followed by mapping their counting numbers onto Ionian and Doric alphabets. Roman numerals, a system that used combinations of letters from the Roman alphabet, remained dominant in Europe until the spread of the superior Arabic numeral system around the late 14th century, and the Arabic numeral system remains the most common system for representing numbers in the world today. The key to the effectiveness of the system was the symbol for zero, which was developed by ancient Indian mathematicians around 500 AD.
History of the metric system
During the early medieval era, Roman numerals were used in Europe to represent numbers, but the Arabs represented numbers using the Hindu numeral system, a positional notation that used ten symbols. In about 1202, Fibonacci published his book "Liber Abaci" (Book of Calculation) which introduced the concept of positional notation into Europe. These symbols evolved into the numerals "0", "1", "2" etc. At that time there was dispute regarding the difference between rational numbers and irrational numbers and there was no consistency in the way in which decimal fractions were represented.
Arabic keyboard
The first Arabic layout for typewriters was invented by Selim Shibli Haddad, a Syrian artist and inventor, in 1899.
History of mathematics
The earliest evidence of written mathematics dates back to the ancient Sumerians, who built the earliest civilization in Mesopotamia. They developed a complex system of metrology from 3000 BC. From around 2500 BC onwards, the Sumerians wrote multiplication tables on clay tablets and dealt with geometrical exercises and division problems. The earliest traces of the Babylonian numerals also date back to this period.
Babylonian mathematics were written using a sexagesimal (base-60) numeral system. From this derives the modern day usage of 60 seconds in a minute, 60 minutes in an hour, and 360 (60 x 6) degrees in a circle, as well as the use of seconds and minutes of arc to denote fractions of a degree. It is likely the sexagesimal system was chosen because 60 can be evenly divided by 2, 3, 4, 5, 6, 10, 12, 15, 20 and 30. Also, unlike the Egyptians, Greeks, and Romans, the Babylonians had a true place-value system, where digits written in the left column represented larger values, much as in the decimal system. The power of the Babylonian notational system lay in that it could be used to represent fractions as easily as whole numbers; thus multiplying two numbers that contained fractions was no different than multiplying integers, similar to our modern notation. The notational system of the Babylonians was the best of any civilization until the Renaissance, and its power allowed it to achieve remarkable computation accuracy and power; for example, the Babylonian tablet YBC 7289 gives an approximation of accurate to five decimal places. The Babylonians lacked, however, an equivalent of the decimal point, and so the place value of a symbol often had to be inferred from the context. By the Seleucid period, the Babylonians had developed a zero symbol as a placeholder for empty positions; however it was only used for intermediate positions. This zero sign does not appear in terminal positions, thus the Babylonians came close but did not develop a true place value system.
Mathematical notation
The development of zero as a number is one of the most important developments in early mathematics. It was used as a placeholder by the Babylonians and Greek Egyptians, and then as an integer by the Mayans, Indians and Arabs. (See The history of zero for more information.)
Arabic numerals
The numeral system came to be known to the court of Baghdad, where mathematicians such as the Persian Al-Khwarizmi, whose book "On the Calculation with Hindu Numerals" was written about 825 in Arabic, and the Arab mathematician Al-Kindi, who wrote four volumes, "On the Use of the Indian Numerals" ("Ketab fi Isti'mal al-'Adad al-Hindi") about 830, propagated it in the Arab world. Their work was principally responsible for the diffusion of the Indian system of numeration in the Middle East and the West.
Hindu–Arabic numeral system
In Christian Europe, the first mention and representation of Hindu-Arabic numerals (from one to nine, without zero), is in the ", an illuminated compilation of various historical documents from the Visigothic period in Spain, written in the year 976 by three monks of the Riojan monastery of San Martín de Albelda.
Between 967 and 969, Gerbert of Aurillac discovered and studied Arab science in the Catalan abbeys. Later he obtained from these places the book " ("On multiplication and division"). After becoming Pope Sylvester II in the year 999, he introduced a new model of abacus, the so-called Abacus of Gerbert, by adopting tokens representing Hindu-Arab numerals, from one to nine.
Arabic alphabet
The Arabic alphabet can be traced back to the Nabataean alphabet used to write Nabataean. The first known text in the Arabic alphabet is a late 4th-century inscription from ' (50 km east of ') in Jordan, but the first dated one is a trilingual inscription at Zebed in Syria from 512. However, the epigraphic record is extremely sparse, with only five certainly pre-Islamic Arabic inscriptions surviving, though some others may be pre-Islamic. Later, dots were added above and below the letters to differentiate them. (The Aramaic language had fewer phonemes than the Arabic, and some originally distinct Aramaic letters had become indistinguishable in shape, so that in the early writings 15 distinct letter-shapes had to do duty for 28 sounds; cf. the similarly ambiguous Pahlavi alphabet.) The first surviving document that definitely uses these dots is also the first surviving Arabic papyrus (PERF 558), dated April 643, although they did not become obligatory until much later. Important texts were and still are frequently memorized, especially in Qurʾan memorization, a practice which probably arose partially from a desire to avoid the great ambiguity of the script.
Arabic numerals
The decimal Hindu–Arabic numeral system with zero was developed in India by around AD 700. The development was gradual, spanning several centuries, but the decisive step was probably provided by Brahmagupta's formulation of zero as a number in AD 628. The system was revolutionary by including zero in positional notation, thereby limiting the number of individual digits to ten. It is considered an important milestone in the development of mathematics. One may distinguish between this positional "system", which is identical throughout the family, and the precise glyphs used to write the numerals, which varied regionally.
Arabic numerals (disambiguation)
Hindu-Arabic numerals or Indo-Arabic numerals are the ten digits of 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, which are the most popular digits in the world as of early 21st century.
History of mathematics
The Islamic Empire established across Persia, the Middle East, Central Asia, North Africa, Iberia, and in parts of India in the 8th century made significant contributions towards mathematics. Although most Islamic texts on mathematics were written in Arabic, most of them were not written by Arabs, since much like the status of Greek in the Hellenistic world, Arabic was used as the written language of non-Arab scholars throughout the Islamic world at the time. Persians contributed to the world of Mathematics alongside Arabs.
Arab-Berber
The Maghreb was gradually arabized with the spread of Islam in the 7th century AD, when the liturgical language Arabic was first brought to the Maghreb. However, the bulk of the population of northwestern Africa remained Berber or Roman Africans at least until the 14th century. Arabization was at least partly strengthened in the rural areas in the 11th century with the emigration of the Banu Hilal tribes from Egypt. However, many parts of the Maghreb were only arabized relatively recently in the 19th and 20th centuries, such as the area of the Aurès (Awras) mountains. Lastly, the mass education and promotion of Arabic language and culture through schools and mass media, during the 20th century, by the maghrebis governments, is regarded as the strongest contributor to the Arabization process in the Maghreb.
Decimal
Many numeral systems of ancient civilisations use ten and its powers for representing numbers, probably because there are ten fingers on two hands and people started counting by using their fingers. Examples are Brahmi numerals, Greek numerals, Hebrew numerals, Roman numerals, and Chinese numerals. Very large numbers were difficult to represent in these old numeral systems, and, only the best mathematicians were able to multiply or divide large numbers. These difficulties were completely solved with the introduction of the Hindu–Arabic numeral system for representing integers. This system has been extended to represent some non-integer numbers, called "decimal fractions" or "decimal numbers" for forming the "decimal numeral system".
History of mathematical notation
Despite their name, Arabic numerals actually started in India. The reason for this misnomer is Europeans saw the numerals used in an Arabic book, "Concerning the Hindu Art of Reckoning", by Mohommed ibn-Musa al-Khwarizmi. Al-Khwārizmī wrote several important books on the Hindu–Arabic numerals and on methods for solving equations. His book "On the Calculation with Hindu Numerals", written about 825, along with the work of Al-Kindi, were instrumental in spreading Indian mathematics and Indian numerals to the West. Al-Khwarizmi did not claim the numerals as Arabic, but over several Latin translations, the fact that the numerals were Indian in origin was lost. The word "algorithm" is derived from the Latinization of Al-Khwārizmī's name, Algoritmi, and the word "algebra" from the title of one of his works, "Al-Kitāb al-mukhtaṣar fī hīsāb al-ğabr wa’l-muqābala" ("The Compendious Book on Calculation by Completion and Balancing").
Musical notation
Cipher notation systems assigning Arabic numerals to the major scale degrees have been used at least since the Iberian organ tablatures of the 16th-century and include such exotic adaptations as "Siffernotskrift". The one most widely in use today is the Chinese "Jianpu", discussed in the main article. Numerals can of course also be assigned to different scale systems, as in the Javanese "kepatihan" notation described above.
Arabic numerals
The numeral system employed, known as algorism, is positional decimal notation. Various symbol sets are used to represent numbers in the Hindu–Arabic numeral system, potentially including both symbols that evolved from the Brahmi numerals, and symbols that developed independently. The symbols used to represent the system have split into various typographical variants since the Middle Ages:The evolution of the numerals in early Europe is shown here in a table created by the French scholar Jean-Étienne Montucla in his "Histoire de la Mathematique", which was published in 1757:
Fibonacci
Fibonacci travelled around the Mediterranean coast, meeting with many merchants and learning about their systems of doing arithmetic. He soon realised the many advantages of the Hindu-Arabic system, which unlike the Roman numerals used at the time, allowed easy calculation using a place-value system. In 1202, he completed the "Liber Abaci" ("Book of Abacus" or "The Book of Calculation") which popularized Hindu–Arabic numerals in Europe.
Arabic grammar
The formal system of cardinal numerals, as used in Classical Arabic, is extremely complex. The system of rules is presented below. In reality, however, this system is never used: Large numbers are always written as numerals rather than spelled out, and are pronounced using a simplified system, even in formal contexts.
Classical Arabic
Classical Arabic is the form of the Arabic language used in Umayyad and Abbasid literary texts from the 7th century AD to the 9th century AD.
Roman numerals
By the 11th century, Arabic numerals had been introduced into Europe from al-Andalus, by way of Arab traders and arithmetic treatises. Roman numerals, however, proved very persistent, remaining in common use in the West well into the 14th and 15th centuries, even in accounting and other business records (where the actual calculations would have been made using an abacus). Replacement by their more convenient "Arabic" equivalents was quite gradual, and Roman numerals are still used today in certain contexts. A few examples of their current use are:
Numerology
The examples above are calculated using decimal (base 10) arithmetic. Other number systems exist, such as binary, octal, hexadecimal and vigesimal; summing digits in these bases yields different results. The first example, shown above, appears thus when rendered in octal (base 8):The Arabic system of numerology is known as Abjad notation or Abjad numerals. In this system each letter of Arabic alphabet has a numerical value. This system is the foundation of "ilm-ul-cipher", the Science of Cipher, and "ilm-ul-huroof", the Science of Alphabet:
Numerical digit
The first true written positional numeral system is considered to be the Hindu–Arabic numeral system. This system was established by the 7th century in India, but was not yet in its modern form because the use of the digit zero had not yet been widely accepted. Instead of a zero sometimes the digits were marked with dots to indicate their significance, or a space was used as a placeholder. The first widely acknowledged use of zero was in 876. The original numerals were very similar to the modern ones, even down to the glyphs used to represent digits.
By the 13th century, Western Arabic numerals were accepted in European mathematical circles (Fibonacci used them in his "Liber Abaci"). They began to enter common use in the 15th century. By the end of the 20th century virtually all non-computerized calculations in the world were done with Arabic numerals, which have replaced native numeral systems in most cultures.
Arithmetic
The earliest written records indicate the Egyptians and Babylonians used all the elementary arithmetic operations as early as 2000 BC. These artifacts do not always reveal the specific process used for solving problems, but the characteristics of the particular numeral system strongly influence the complexity of the methods. The hieroglyphic system for Egyptian numerals, like the later Roman numerals, descended from tally marks used for counting. In both cases, this origin resulted in values that used a decimal base but did not include positional notation. Complex calculations with Roman numerals required the assistance of a counting board or the Roman abacus to obtain the results.
History of the Arabic alphabet
Cursive Nabataean writing changed into Arabic writing, likeliest between the dates of the an-Namāra inscription and the Jabal Ramm inscription. Most writing would have been on perishable materials, such as papyrus. As it was cursive, it was liable to change. The epigraphic record is extremely sparse, with only five certainly pre-Islamic Arabic inscriptions surviving, though some others may be pre-Islamic.
History of the Arabic alphabet
Less than a century later, Arab grammarians reorganized the alphabet, for reasons of teaching, putting letters next to other letters which were nearly the same shape. This produced a new order which was not the same as the numeric order, which became less important over time because it was being competed with by the Indian numerals and sometimes by the Greek numerals.
Arabic numerals
The first universally accepted inscription containing the use of the 0 glyph in India is first recorded in the 9th century, in an inscription at Gwalior in Central India dated to 870. Numerous Indian documents on copper plates exist, with the same symbol for zero in them, dated back as far as the 6th century AD, but their dates are uncertain. Inscriptions in Indonesia and Cambodia dating to AD 683 have also been found.
Eastern Arabic numerals
The Eastern Arabic numerals (also called Arabic–Hindu numerals, Arabic Eastern numerals and Indo–Persian numerals) are the symbols ( ० ۱ ۲ ۳ ۴ ۵ ۶ ۷ ۸ ۹) used to represent the Hindu–Arabic numeral system, in conjunction with the Arabic alphabet in the countries of the Mashriq (the east of the Arab world), the Arabian Peninsula, and its variant in other countries that use the Perso-Arabic script in the Iranian plateau and Asia.
Arabic numerals
The term "Arabic numerals" is ambiguous, it may also be intended to mean the numerals used by Arabs, in which case it generally refers to the Eastern Arabic numerals. Although the phrase "Arabic numeral" is frequently capitalized, it is sometimes written in lower case: for instance in its entry in the "Oxford English Dictionary", which helps to distinguish it from "Arabic numerals" as the Eastern Arabic numerals.
Divan
Under Abd al-Malik ibn Marwan (r. 685–705), the practices of the various departments were standardized and Arabized: instead of the local languages (Greek in Syria, Coptic and Greek in Egypt, Persian in former Sasanian lands) and the traditional practices of book-keeping, seals and time-keeping, only Arabic and the Islamic calendar were to be used henceforth. The process of Arabization was gradual: Iraq was the first in 697, followed by Syria in 700, Egypt in 705, and finally Khurasan in 742.
Babylonian numerals
This system first appeared around 2000 BC; its structure reflects the decimal lexical numerals of Semitic languages rather than Sumerian lexical numbers. However, the use of a special Sumerian sign for 60 (beside two Semitic signs for the same number) attests to a relation with the Sumerian system.
The Babylonian system is credited as being the first known positional numeral system, in which the value of a particular digit depends both on the digit itself and its position within the number. This was an extremely important development, because non-place-value systems require unique symbols to represent each power of a base (ten, one hundred, one thousand, and so forth), which can make calculations more difficult.
Ethnomathematics
The following is a sampling of some of the definitions of ethnomathematics proposed between 1985 and 2006:Some of the systems for representing numbers in previous and present cultures are well known. Roman numerals use a few letters of the alphabet to represent numbers up to the thousands, but are not intended for arbitrarily large numbers and can only represent positive integers. Arabic numerals are a family of systems, originating in India and passing to medieval Islamic civilization, then to Europe, and now standard in global culture—and having undergone many curious changes with time and geography—can represent arbitrarily large numbers and have been adapted to negative numbers, fractions, and real numbers.
Decimal separator
The following examples show the decimal separator and the thousands separator in various countries that use the Arabic numeral system.Used with Western Arabic numerals (0123456789):
Ancient Egyptian mathematics
Egyptian numerals date back to the Predynastic period. Ivory labels from Abydos record the use of this number system. It is also common to see the numerals in offering scenes to indicate the number of items offered. The king's daughter Neferetiabet is shown with an offering of 1000 oxen, bread, beer, etc.
Arithmetic
The gradual development of the Hindu–Arabic numeral system independently devised the place-value concept and positional notation, which combined the simpler methods for computations with a decimal base and the use of a digit representing 0. This allowed the system to consistently represent both large and small integers. This approach eventually replaced all other systems. In the early the Indian mathematician Aryabhata incorporated an existing version of this system in his work, and experimented with different notations. In the 7th century, Brahmagupta established the use of 0 as a separate number and determined the results for multiplication, division, addition and subtraction of zero and all other numbers, except for the result of division by 0. His contemporary, the Syriac bishop Severus Sebokht (650 AD) said, "Indians possess a method of calculation that no word can praise enough. Their rational system of mathematics, or of their method of calculation. I mean the system using nine symbols." The Arabs also learned this new method and called it "hesab".
Although the Codex Vigilanus described an early form of Arabic numerals (omitting 0) by 976 AD, Leonardo of Pisa (Fibonacci) was primarily responsible for spreading their use throughout Europe after the publication of his book "Liber Abaci" in 1202. He wrote, "The method of the Indians (Latin "Modus Indoram") surpasses any known method to compute. It's a marvelous method. They do their computations using nine figures and symbol zero".
History of ancient numeral systems
Sexagesimal numerals were a mixed radix system that retained the alternating base 10 and base 6 in a sequence of cuneiform vertical wedges and chevrons. Sexagesimal numerals became widely used in commerce, but were also used in astronomical and other calculations. This system was exported from Babylonia and used throughout Mesopotamia, and by every Mediterranean nation that used standard Babylonian units of measure and counting, including the Greeks, Romans and Syrians. In Arabic numerals, we still use sexagesimal to count time (minutes per hour), and angles (degrees).
Mathematics
The Hindu–Arabic numeral system and the rules for the use of its operations, in use throughout the world today, evolved over the course of the first millennium AD in India and were transmitted to the Western world via Islamic mathematics. Other notable developments of Indian mathematics include the modern definition of sine and cosine, and an early form of infinite series.
During the Golden Age of Islam, especially during the 9th and 10th centuries, mathematics saw many important innovations building on Greek mathematics. The most notable achievement of Islamic mathematics was the development of algebra. Other notable achievements of the Islamic period are advances in spherical trigonometry and the addition of the decimal point to the Arabic numeral system. Many notable mathematicians from this period were Persian, such as Al-Khwarismi, Omar Khayyam and Sharaf al-Dīn al-Ṭūsī.
History of the Hindu–Arabic numeral system
The development of the numerals in early Europe is shown below:
Arab tone system
The current tone system is derived from the work of al-Farabi (d. 950 CE) (heptatonic scales constructed from seconds), who used a 25-tone unequal scale (see tetrachord), and Mikha'il Mishaqah (1800–1889) who first presented the 24-tone equal-tempered division.
History of the Hindu–Arabic numeral system
During the Gupta period (early 4th century to the late 6th century), the Gupta numerals developed from the Brahmi numerals and were spread over large areas by the Gupta empire as they conquered territory. Beginning around 7th century, the Gupta numerals developed into the Nagari numerals.
Egyptian hieroglyphs
The use of hieroglyphic writing arose from proto-literate symbol systems in the Early Bronze Age, around the 32nd century BC (Naqada III), with the first decipherable sentence written in the Egyptian language dating to the Second Dynasty (28th century BC). Egyptian hieroglyphs developed into a mature writing system used for monumental inscription in the classical language of the Middle Kingdom period; during this period, the system made use of about 900 distinct signs. The use of this writing system continued through the New Kingdom and Late Period, and on into the Persian and Ptolemaic periods. Late survivals of hieroglyphic use are found well into the Roman period, extending into the 4th century AD.
History of the Hindu–Arabic numeral system
While the numerals in texts and inscriptions used a named place-value notation, a more efficient notation might have been employed in calculations, possibly from the 1st century CE. Computations were carried out on clay tablets covered with a thin layer of sand, giving rise to the term "dhuli-karana" ("sand-work") for higher computation. Karl Menninger believes that, in such computations, they must have dispensed with the enciphered numerals and written down just sequences of digits to represent the numbers. A zero would have been represented as a "missing place," such as a dot. The single manuscript with worked examples available to us, the Bakhshali manuscript (of unclear date), uses a place value system with a dot to denote the zero. The dot was called the "shunya-sthāna", "empty-place." The same symbol was also used in algebraic expressions for the unknown (as in the canonical "x" in modern algebra).
Cyrillic numerals
Cyrillic numerals are a numeral system derived from the Cyrillic script, developed in the First Bulgarian Empire in the late 10th century. It was used in the First Bulgarian Empire and by South and East Slavic peoples. The system was used in Russia as late as the early 18th century, when Peter the Great replaced it with Arabic numerals as part of his civil script reform initiative. Cyrillic numbers played a role in Peter the Great's currency reform plans, too, with silver wire kopecks issued after 1696 and mechanically minted coins issued between 1700 and 1722 inscribed with the date using Cyrillic numerals. By 1725, Russian Imperial coins had transitioned to Arabic numerals. The Cyrillic numerals may still be found in books written in the Church Slavonic language.
The Ciphers of the Monks
The numeral system was invented in the 1300s by French Cistercian monks. It was later replaced by the Hindu–Arabic numeral system. In any case, this numeral system later inspired several shorthands and secret ciphers.
Arabic numerals
Leonardo Fibonacci (Leonardo of Pisa), a mathematician born in the Republic of Pisa who had studied in Béjaïa (Bougie), Algeria, promoted the Indian numeral system in Europe with his 1202 book "Liber Abaci":
Arabic numerals
A distinctive West Arabic variant of the symbols begins to emerge around the 10th century in the Maghreb and Al-Andalus (sometimes called "ghubar" numerals, though the term is not always accepted), which are the direct ancestor of the modern "Arabic numerals" used throughout the world.
Woepecke has proposed that the Western Arabic numerals were already in use in Spain before the arrival of the Moors, purportedly received via Alexandria, but this theory is not accepted by scholars.
Abbasid Caliphate
Algebra was significantly developed by Persian scientist Muhammad ibn Mūsā al-Khwārizmī during this time in his landmark text, "Kitab al-Jabr wa-l-Muqabala", from which the term "algebra" is derived. He is thus considered to be the father of algebra by some, although the Greek mathematician Diophantus has also been given this title. The terms algorism and algorithm are derived from the name of al-Khwarizmi, who was also responsible for introducing the Arabic numerals and Hindu-Arabic numeral system beyond the Indian subcontinent.
Arab scientist Ibn al-Haytham (Alhazen) developed an early scientific method in his "Book of Optics" (1021). The most important development of the scientific method was the use of experiments to distinguish between competing scientific theories set within a generally empirical orientation, which began among Muslim scientists. Ibn al-Haytham's empirical proof of the intromission theory of light (that is, that light rays entered the eyes rather than being emitted by them) was particularly important. Alhazen was significant in the history of scientific method, particularly in his approach to experimentation, and has been referred to as the "world's first true scientist".
Ancient Egyptian mathematics
Ancient Egyptian mathematics is the mathematics that was developed and used in Ancient Egypt 3000 to c. 300 BC, from the Old Kingdom of Egypt until roughly the beginning of Hellenistic Egypt. The ancient Egyptians utilized a numeral system for counting and solving written mathematical problems, often involving multiplication and fractions. Evidence for Egyptian mathematics is limited to a scarce amount of surviving sources written on papyri. From these texts it is known that ancient Egyptians understood concepts of geometry, such as determining the surface area and volume of three-dimensional shapes useful for architectural engineering, and algebra, such as the false position method and quadratic equations.
Kufa
Kufa is also where the kufic script was developed, the earliest script of the Arabic language. As the scholar al-Qalqashandi maintained, "The Arabic script ["khatt"] is the one which is now known as Kufic. From it evolved all the present hands." The angular script which later came to be known as Kufic had its origin about a century earlier than the founding of the town of Kufa, according to Moritz in the "Encyclopaedia of Islam". The kufic script was derived from one of the four pre-Islamic Arabic scripts, the one called "al-Hiri" (used in Hirah). (The other three were "al-Anbari" (from Anbar), "al-Makki" (from Mecca) and "al-Madani" (from Medina)). The famous author of the "Kitab al-Fihrist", an index of Arabic books, Ibn al-Nadim (died ca. 999), was the first to use the word 'kufic' to characterize this script, which reached a state of decorative perfection in the 8th century, when surahs were used to decorate ceramics, for representations of nature were strictly forbidden under the Islamic regime.
History of the Arabic alphabet
The alphabet then had 28 letters, and so could be used to write the numbers 1 to 10, then 20 to 100, then 200 to 900, then 1000 (see Abjad numerals). In this numerical order, the new letters were put at the end of the alphabet. This produced this order: alif (1), b (2), j (3), d (4), h (5), w (6), z (7), H (8), T (9), y (10), k (20), l (30), m (40), n (50), s (60), ayn (70), f (80), S (90), q (100), r (200), sh (300), t (400), th (500), dh (600), kh (700), D (800), Z (900), gh (1000).
Arabic numerals
The Arabic numerals 0–9 are encoded in ASCII at positions 0x30 to 0x39. Masking to the lower 4 binary bits (or taking the last hexadecimal digit) gives the value of the digit, a great help in converting text to numbers on early computers. These positions were inherited in Unicode and in virtually all other encodings based in any way on ASCII. EBCDIC used different values, but also had the lower 4 bits equal to the digit value.
History of mathematical notation
Although the origin of our present system of numerical notation is ancient, there is no doubt that it was in use among the Hindus over two thousand years ago. The algebraic notation of the Indian mathematician, Brahmagupta, was syncopated. Addition was indicated by placing the numbers side by side, subtraction by placing a dot over the subtrahend (the number to be subtracted), and division by placing the divisor below the dividend, similar to our notation but without the bar. Multiplication, evolution, and unknown quantities were represented by abbreviations of appropriate terms. The Hindu–Arabic numeral system and the rules for the use of its operations, in use throughout the world today, likely evolved over the course of the first millennium AD in India and was transmitted to the west via Islamic mathematics.
Numerical digit
Between 2700 and 2000 BC, in Sumer, the round stylus was gradually replaced by a reed stylus that was used to press wedge-shaped cuneiform signs in clay. These cuneiform number signs resembled the round number signs they replaced and retained the additive sign-value notation of the round number signs. These systems gradually converged on a common sexagesimal number system; this was a place-value system consisting of only two impressed marks, the vertical wedge and the chevron, which could also represent fractions. This sexagesimal number system was fully developed at the beginning of the Old Babylonia period (about 1950 BC) and became standard in Babylonia.
Arabic Numeral Series
The Arabic Numeral Series, sometimes referred to as the Arabics, is a series of 19 short 16mm films completed by the American experimental filmmaker Stan Brakhage in 1981 and 1982. The "Arabic Numeral Series" gets its name from the fact that none of the films included in it have titles, instead opening with an arabic numeral. Brakhage produced another cycle, the "Roman Numeral Series", whose films all have Roman numerals instead of titles, around the same time. All of the "Arabics" are silent and are intended to be projected at 18 frames per second.
History of the Arabic alphabet
The first surviving document that definitely uses these dots is also the first surviving Arabic papyrus (PERF 558), dated April, 643. The dots did not become obligatory until much later. Important texts like the Qur'an were frequently memorized; this practice, which survives even today, probably arose partly to avoid the great ambiguity of the script, and partly due to the scarcity of books in times when printing was unheard-of in the area and every copy of every book had to be written by hand.
Hebrew numerals
The current numeral system is also known as the "Hebrew alphabetic numerals" to contrast with earlier systems of writing numerals used in classical antiquity. These systems were inherited from usage in the Aramaic and Phoenician scripts, attested from c. 800 BC in the so-called Samaria ostraca and sometimes known as "Hebrew-Aramaic numerals", ultimately derived from the Egyptian Hieratic numerals.
Arabic maqam
Since microtonal intervals are impractical to accurately notate, a simplified musical notation system was adopted in Arabic music at the turn of the 20th century. Starting with a chromatic scale, the Arabic scale is divided into 24 equal quarter tones, where a quarter tone equals half a semitone in a 12 tone equal-tempered scale. In this notation system all notes in a "maqam" scale are rounded to the nearest quarter tone.
Hindu–Arabic numeral system
These Indian developments were taken up in Islamic mathematics in the 8th century, as recorded in al-Qifti's "Chronology of the scholars" (early 13th century).
Arabic
Beginning in the 1st century CE, fragments of Northern Old Arabic are attested in the Nabataean script across northern Arabia. By the 4th century CE, the Nabataean Aramaic writing system had come to express varieties of Arabic other than that of the Nabataeans.
Real number
The Middle Ages brought the acceptance of zero, negative, integral, and fractional numbers, first by Indian and Chinese mathematicians, and then by Arabic mathematicians, who were also the first to treat irrational numbers as algebraic objects, which was made possible by the development of algebra. Arabic mathematicians merged the concepts of "number" and "magnitude" into a more general idea of real numbers. The Egyptian mathematician Abū Kāmil Shujā ibn Aslam was the first to accept irrational numbers as solutions to quadratic equations or as coefficients in an equation, often in the form of square roots, cube roots and fourth roots.
0
The Hindu–Arabic numeral system (base 10) reached Europe in the 11th century, via the Iberian Peninsula through Spanish Muslims, the Moors, together with knowledge of astronomy and instruments like the astrolabe, first imported by Gerbert of Aurillac. For this reason, the numerals came to be known in Europe as "Arabic numerals". The Italian mathematician Fibonacci or Leonardo of Pisa was instrumental in bringing the system into European mathematics in 1202, stating:
Codex Vigilanus
The "Codex" contains, among other pieces of useful information, the first mention and representation of Arabic numerals (save zero) in the West. They were introduced by the Arabs into Spain around 900.
Arabic numerals
Cyrillic numerals were a numbering system derived from the Cyrillic alphabet, used by South and East Slavic peoples. The system was used in Russia as late as the early 18th century when Peter the Great replaced it with Arabic numerals.
Eastern Arabic numerals
In Arabic-speaking Asia as well as Egypt and Sudan both kinds of numerals are used alongside each other with Western Arabic numerals gaining more and more currency, now even in very traditional countries such as Saudi Arabia. The United Arab Emirates uses both Eastern and Western Arabic numerals.
Arabic alphabet
Later still, vowel marks and the ' were introduced, beginning some time in the latter half of the 7th century, preceding the first invention of Syriac and Hebrew vocalization. Initially, this was done by a system of red dots, said to have been commissioned in the Umayyad era by Abu al-Aswad al-Du'ali a dot above = ', a dot below = ', a dot on the line = ', and doubled dots indicated nunation. However, this was cumbersome and easily confusable with the letter-distinguishing dots, so about 100 years later, the modern system was adopted. The system was finalized around 786 by ".
Euclidean division
Before the discovery of Hindu–Arabic numeral system, which was introduced in Europe during the 13th century by Fibonacci, division was extremely difficult, and only the best mathematicians were able to do it. In fact, the long division algorithm requires this notation.
Arabic numerals
The reason the digits are more commonly known as "Arabic numerals" in Europe and the Americas is that they were introduced to Europe in the 10th century by Arabic-speakers of North Africa, who were then using the digits from Libya to Morocco. Arabs, on the other hand, call the base-10 system (not just these digits) "Hindu numerals", referring to their origin in India. This is not to be confused with what the Arabs call the "Hindi numerals", namely the Eastern Arabic numerals ( - - - - - - - - - ) used in the Middle East, or any of the numerals currently used in Indian languages (e.g. Devanagari: ).
Egyptian Arabic
The Egyptians slowly adopted the Arabic as a written language following the Muslim conquest of Egypt in the seventh century. Until then, they had spoken either Koine Greek or Egyptian in its Coptic form. A period of Coptic-Arabic bilingualism in Lower Egypt lasted for more than three centuries. The period would last much longer in the south. Arabic may have been already familiar to Egyptians through pre-Islamic trade with Bedouins in the Sinai Peninsula and the easternmost part of the Nile Delta. Egyptian Arabic seems to have begun taking shape in Fustat, the first Islamic capital of Egypt, now part of Cairo.
Chinese numerals
During the Ming and Qing dynasties (after Arabic numerals were introduced into China), some Chinese mathematicians used Chinese numeral characters as positional system digits. After the Qing period, both the Chinese numeral characters and the Suzhou numerals were replaced by Arabic numerals in mathematical writings.
Arab world
Egypt was conquered in 639, and gradually Arabized during the medieval period. A distinctively Egyptian Arabic language emerged by the 16th century.
Arabic numerals
Arabic numerals are the ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9; or numerals written using them in the Hindu–Arabic numeral system (where the position of a digit indicates the power of 10 to multiply it by). It is the most common system for the symbolic representation of numbers in the world today.
Arabs
Paternal descent plays a strong part in the role of citizenship of an individual and maternal descent also plays an issue. Paternal descent is considered the main source of affiliation in the Arab world when it comes to membership into a kin group or clan.
Today, the main unifying characteristic among Arabs is Arabic, a Central Semitic language from the Afroasiatic language family. Modern Standard Arabic serves as the standardized and literary variety of Arabic used in writing. The Arabs are first mentioned in the mid-ninth century BCE as a tribal people dwelling in the central Arabian Peninsula subjugated by Upper Mesopotamia-based state of Assyria. The Arabs appear to have remained largely under the vassalage of the Neo-Assyrian Empire (911–605 BCE), and then the succeeding Neo-Babylonian Empire (605–539 BCE), Persian Achaemenid Empire (539–332 BCE), Greek Macedonian/Seleucid Empire and Parthian Empire.
Numerals in Unicode
Numerals (often called "numbers" in Unicode) are characters or sequences of characters that denote a number. The Hindu-Arabic numeral system (base-10) is used widely in various writing systems throughout the world and all share the same semantics for denoting numbers. However, the graphemes representing the numerals differ widely from one writing system to another. To support these grapheme differences, Unicode includes encodings of these numerals within many of the script blocks. The decimal digits are repeated in 22 separate blocks. In addition to many forms of the Hindu-Arabic numerals, Unicode also includes several less common numerals such as: Aegean numerals, Roman numerals, counting rod numerals, Cuneiform numerals and ancient Greek numerals. There is also a large number of typographical variations of the Arabic numerals provided for specialized mathematical use and for compatibility with earlier character sets, and also composite characters containing Arabic numerals such as ½.
Eastern Arabic numerals
In North Africa (excluding Egypt and Sudan), only Western Arabic numerals are now commonly used. In medieval times, these areas used a slightly different set (from which, via Italy, Western Arabic numerals derive).
Eastern Arabic numerals
The numeral system originates from an ancient Indian numeral system, which was re-introduced in the book "On the Calculation with Hindu Numerals" written by the medieval-era Iranian mathematician and engineer Khwarazmi, whose name was Latinized as "Algoritmi".
Arabic
In most of present-day North Africa, the Western Arabic numerals (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) are used. However, in Egypt and Arabic-speaking countries to the east of it, the Eastern Arabic numerals ( – – – – – – – – – ) are in use. When representing a number in Arabic, the lowest-valued position is placed on the right, so the order of positions is the same as in left-to-right scripts. Sequences of digits such as telephone numbers are read from left to right, but numbers are spoken in the traditional Arabic fashion, with units and tens reversed from the modern English usage. For example, 24 is said "four and twenty" just like in the German language ("vierundzwanzig") and Classical Hebrew, and 1975 is said "a thousand and nine-hundred and five and seventy" or, more eloquently, "a thousand and nine-hundred five seventy"
Arabic numerals
Arabic numerals were introduced to China during the Yuan Dynasty (1271–1368) by the Muslim Hui people. In the early 17th century, European-style Arabic numerals were introduced by Spanish and Portuguese Jesuits.
Arabic numerals
The first mentions of the numerals in the West are found in the "Codex Vigilanus" of 976.
List of countries where Arabic is an official language
The early Muslim conquests (, al-Futūḥāt al-Islāmiyya) and the following Expansion of Islam (, Intishar al-Islām) led to the expansion of the Arabic language in Northern Africa, the Iberian Peninsula, the Caucasus, Western Asia, Central Asia and South Asia. Along with the religion of Islam, the Arabic language, Arabic number system and Arab customs spread throughout the entire Arab caliphate. The caliphs of the Arab dynasty established the first schools inside the empire which taught Arabic language and Islamic studies for all pupils in all areas within the caliphate. The result was (in those areas which belonged to the Arab empire) the creation of the society that was mostly Arabic-speaking because of the assimilation of native inhabitants.
History of ancient numeral systems
Between 2700 BC and 2000 BC, the round stylus was gradually replaced by a reed stylus that had been used to press wedge shaped cuneiform signs in clay. To represent numbers that previously had been pressed with a round stylus, these cuneiform number signs were pressed in a circular pattern and they retained the additive sign-value notation that originated with tokens on a string. Cuneiform numerals and archaic numerals were ambiguous because they represented various numeric systems that differed depending on what was being counted. About 2100 BC in Sumer, these proto-sexagesimal sign-value systems gradually converged on a common sexagesimal number system that was a place-value system consisting of only two impressed marks, the vertical wedge and the chevron, which could also represent fractions. This sexagesimal number system was fully developed at the beginning of the Old Babylonian period (about 1950 BC) and became standard in Babylonia.
Abu al-Aswad al-Du'ali
Although effective, the large dots were difficult to use on small-size fonts and on any but a limited selection of scripts. They were also time-consuming to make on any size font or script. Thus, the Umayyad governor al-Hajjaj ibn Yusuf al-Thaqafi asked two of al-Duʾali’s students to create and codify a new system that was simpler and more efficient. A new "tashkil" system was developed by Al-Khalil ibn Ahmad al-Farahidi (d. 786). It has been universally used for Arabic script since the early 11th century.
ASMO 449
This character set was devised by the now extinct Arab Standardization and Metrology Organization in 1982 to be the 7-bit standard to be used in Arabic-speaking countries. The design of this character set is derived from the 7-bit ISO 646 (version of 1973) but with modifications suited for the Arabic language. In code points ranging from 0x41 to 0x72 (hexadecimal), Latin letters were replaced with Arabic letters. Punctuation marks which were identical the in Latin and Arabic scripts remained the same, but where they differed (comma, semicolon, question mark), the Latin ones were replaced by Arabic ones. Only nominal letters are encoded, no preshaped forms of the letters, so shaping processing is required for display. This character set is not bidirectional and was intended to be used in right to left writing. Therefore, symmetrical punctuation marks ("(", ")", "", "[", "]", "{" and "}") appears as reversed (")", "(", ">", "International Register of Coded Character Sets as IR 089 in 1985 and approved as an ISO standard as ISO 9036 in 1987.
Arabic script in Unicode
The basic Arabic range encodes the standard letters and diacritics, but does not encode contextual forms (U+0621–U+0652 being directly based on ISO 8859-6); and also includes the most common diacritics and Arabic-Indic digits.
The Arabic Supplement range encodes letter variants mostly used for writing African (non-Arabic) languages.
The Arabic Extended-A range encodes additional Qur'anic annotations and letter variants used for various non-Arabic languages.
The Arabic Presentation Forms-A range encodes contextual forms and ligatures of letter variants needed for Persian, Urdu, Sindhi and Central Asian languages.
The Arabic Presentation Forms-B range encodes spacing forms of Arabic diacritics, and more contextual letter forms.
The presentation forms are present only for compatibility with older standards, and are not currently needed for coding text.
The Arabic Mathematical Alphabetical Symbols block encodes characters used in Arabic mathematical expressions.
The Indic Siyaq Numbers block containing a specialized subset of Arabic script that was used for accounting in India under the Mughals by the 17th century through the middle of the 20th century.
Fibonacci
The 1228 edition, first section introduces the Hindu-Arabic numeral system and compares the system with other systems, such as Roman numerals, and methods to convert the other numeral systems into Hindu-Arabic numerals. Replacing the Roman numeral system, its ancient Egyptian multiplication method, and using an abacus for calculations, with a Hindu-Arabic numeral system was an advance in making business calculations easier and faster, which led to the growth of banking and accounting in Europe.
History of the Hindu–Arabic numeral system
Al-Uqlidisi developed a notation to represent decimal fractions.
The numerals came to fame due to their use in the pivotal work of the Persian mathematician Al-Khwarizmi, whose book "On the Calculation with Hindu Numerals" was written about 825, and the Arab mathematician Al-Kindi, who wrote four volumes (see [2]) "On the Use of the Indian Numerals" (Ketab fi Isti'mal al-'Adad al-Hindi) about 830. They, amongst other works, contributed to the diffusion of the Indian system of numeration in the Middle-East and the West.
Positional notation
The Babylonian numeral system, base-60, was the first positional system developed, and its influence is present today in the way time and angles are counted in tallies related to 60, like 60 minutes in an hour, 360 degrees in a circle. The Hindu–Arabic numeral system, base-10, is the most commonly used system in the world today for most calculations. The binary numeral system, base-2, is straightforwardly implemented in digital electronic circuitry and used by almost all computer systems and electronics for calculations and representations.
Abjad numerals
In the Abjad system, the first letter of the Arabic alphabet, ʾalif, is used to represent 1; the second letter, bāʾ, is used to represent 2, etc. Individual letters also represent 10s and 100s: yāʾ for 10, kāf for 20, qāf for 100, etc.
Brahmi numerals
The Brahmi numerals are a numeral system attested from the 3rd century BCE (somewhat later in the case of most of the tens). They are the direct graphic ancestors of the modern Indian and Hindu–Arabic numerals. However, they were conceptually distinct from these later systems, as they were not used as a positional system with a zero. Rather, there were separate numerals for each of the tens (10, 20, 30, etc.). There were also symbols for 100 and 1000 which were combined in ligatures with the units to signify 200, 300, 2000, 3000, etc.
History of the Arabic alphabet
The Nabataean alphabet was designed to write 22 phonemes, but Arabic has 28 phonemes; thus, when used to write the Arabic language, 6 of its letters must each represent two phonemes:
"d" also represented "ð",
"ħ" also represented "kh" %,
"ṭ" also represented "ẓ",
"ayin" also represented "gh" %, 
"ṣ" also represented "ḍ",%,
"t" also represented "þ".
: In the cases marked %, the choice was influenced by etymology, as Common Semitic "kh" and "gh" became Hebrew "ħ" and "ayin" respectively.
Arithmetic
The concept of 0 as a number comparable to the other basic digits is essential to this notation, as is the concept of 0's use as a placeholder, and as is the definition of multiplication and addition with 0. The use of 0 as a placeholder and, therefore, the use of a positional notation is first attested to in the Jain text from India entitled the "Lokavibhâga", dated 458 AD and it was only in the early 13th century that these concepts, transmitted via the scholarship of the Arabic world, were introduced into Europe by Fibonacci using the Hindu–Arabic numeral system.
History of the Hindu–Arabic numeral system
Its glyphs are descended from the Indian Brahmi numerals. The full system emerged by the 8th to 9th centuries, and is first described in Al-Khwarizmi's "On the Calculation with Hindu Numerals" (ca. 825), and Al-Kindi's four-volume work "On the Use of the Indian Numerals" (ca. 830). Today the name "Hindu–Arabic numerals" is usually used.
Binary code
The modern binary number system, the basis for binary code, was invented by Gottfried Leibniz in 1689 and appears in his article "Explication de l'Arithmétique Binaire". The full title is translated into English as the "Explanation of the binary arithmetic", which uses only the characters 1 and 0, with some remarks on its usefulness, and on the light it throws on the ancient Chinese figures of Fu Xi." (1703). Leibniz's system uses 0 and 1, like the modern binary numeral system. Leibniz encountered the "I Ching" through French Jesuit Joachim Bouvet and noted with fascination how its hexagrams correspond to the binary numbers from 0 to 111111, and concluded that this mapping was evidence of major Chinese accomplishments in the sort of philosophical mathematics he admired. Leibniz saw the hexagrams as an affirmation of the universality of his own religious belief.
Hindu–Arabic numeral system
Chinese and Japanese finally adopted the Hindu–Arabic numerals in the 19th century, abandoning counting rods.
Egyptian numerals
The system of ancient Egyptian numerals was used in Ancient Egypt from around 3000 BC until the early first millennium AD. It was a system of numeration based on multiples of ten, often rounded off to the higher power, written in hieroglyphs. The Egyptians had no concept of a place-valued system such as the decimal system. The hieratic form of numerals stressed an exact finite series notation, ciphered one to one onto the Egyptian alphabet.
Numerical digit
The modern positional Arabic numeral system was developed by mathematicians in India, and passed on to Muslim mathematicians, along with astronomical tables brought to Baghdad by an Indian ambassador around 773.