1.
Eastern Arabic numerals
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These numbers are known as أرقام هندية in Arabic. They are sometimes also called Indic numerals in English, however, that is sometimes discouraged as it can lead to confusion with Indian numerals, used in Brahmic scripts of India. Each numeral in the Persian variant has a different Unicode point even if it looks identical to the Eastern Arabic numeral counterpart, however the variants used with Urdu, Sindhi and other South Asian languages are not encoded separately from the Persian variants. See U+0660 through U+0669 and U+06F0 through U+06F9, written numerals are arranged with their lowest-value digit to the right, with higher value positions added to the left. That is identical to the arrangement used by Western texts using Hindu-Arabic numerals even though Arabic script is read from right to left. There is no conflict unless numerical layout is necessary, as is the case for arithmetic problems and lists of numbers, Eastern Arabic numerals remain strongly predominant vis-à-vis Western Arabic numerals in many countries to the East of the Arab world, particularly in Iran and Afghanistan. In Pakistan, Western Arabic numerals are more used as a considerable majority of the population is anglophone. Eastern numerals still continue to see use in Urdu publications and newspapers, in North Africa, only Western Arabic numerals are now commonly used. In medieval times, these used a slightly different set
2.
Sinhala numerals
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Sinhalese belongs to the Indo-European language family with its roots deeply associated with Indo-Aryan sub family to which the languages such as Persian and Hindi belong. It is also surmised that Sinhala had evolved from an ancient variant of Apabramsa which is known as ‘Elu’, when tracing history of Elu, it was preceded by Hela or Pali Sihala. The Sinhala script had evolved from Southern Brahmi script from which almost all the Southern Indic Scripts such as Telugu, later Sinhala was influenced by Grantha writing of Southern India. Since 1250 AD, the Sinhala script had remained the same with few changes, although some scholars are of the view that the Brahmi Script arrived with the Buddhism, Mahavamsa speaks of written language even right after the arrival of Vijaya. Archeologists had found pottery fragments in Anuradhapura Sri Lanka with older Brahmi script inscriptions, the earliest Brahmi Script found in India had been dated to 6th Century BC in Tamil Nadu though most of Brahmi writing found in India had been attributed to emperor Ashoka in the 3rd century BC. Sinhala letters are round-shaped and are written left to right. The evolution of the script to the present shapes may have taken place due to writing on Ola leaves, unlike chiseling on a rock, writing on palm leaves has to be more round-shaped to avoid the stylus ripping the Palm leaf while writing on it. When drawing vertical or horizontal lines on Ola leaf, the leaves would have been ripped. Instead a stylistic stop which was known as ‘Kundaliya’ is used, period and commas were later introduced into Sinhala script after the introduction of paper due to the influence of Western languages. In modern Sinhala, Arabic numerals, which were introduced by Portuguese, Dutch and English, is used for writing numbers and it is accepted that Arabic numerals had evolved from Brahmi numerals. This article will touch upon Brahmi numerals, which were found in Sri Lanka. It had been found five different types of numerations were used in the Sinhala language at the time of the invasion of the Kandyan kingdom by the British. Out of the five types of numerations, two sets of numerations were in use in the century mainly for astrological calculations and to express traditional year. The five types or sets of numerals or numerations are listed below, according to Mr. Gunesekera, these numerals were used for ordinary calculations and to express simple numbers. These numerals had separate Symbols for 10,40,50,100,1000 and these numerals were also regarded as Lith Lakunu or ephemeris numbers by W. A. De Silva in his “Catalogue of Palm leaf manuscripts in the library of Colombo Museum”. This set of numerals was known as Sinhala illakkam or Sinhala archaic numerals, Arabic Figures are now universally used. For the benefit of the student, the old numerals are given in the plate opposite,11 clauses had been numbered in Arabic numerals in the English part of the agreement and in parallel Sinhala clauses were numbered in Sinhala archaic numerals. Numbers of lith illakkam look Sinhala letters and vowel modifiers, the number six is known as ‘akma’ in the Lith Illakkam
3.
Tamil numerals
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Traditionally Vattezhuttu characters were used, but now Arabic numerals have become commonplace. Old Tamil possesses a special character for zero and it is read as andru. But yet Modern Tamil renounces the use of its native character, Modern Tamil words for zero include சுழியம் or பூச்சியம். Tamil has a prefix for each number from 1 to 9. For instance, the word for fifty, ஐம்பது is a combination of ஐ, the prefix for nine changes with respect to the succeeding base 10. தொ+ the unvoiced consonant of the succeeding base 10 forms the prefix for nine, for instance,90 is தொ+ண், hence, தொண்ணூறு). These are typically void in the Tamil language except for some Hindu and Christian religious references, example அட்ட இலட்சுமிகள் in a Hindu context, unlike other Indian languages, Tamil has distinct digits for 10,100, and 1000. It also has characters for other number-based aspects of day-to-day life. − − − − − − − − − − − − There are two systems that can be used in the Tamil language, the Tamil system which is as follows. The following are the numbers of the Ancient Tamil Country. Sanskrit based multiples like lakhs are also followed just like other Indian languages and you can transcribe any fraction, by affixing -இல் after the denominator followed by the numerator. For instance, 1/41 can be said as நாற்பத்து ஒன்றில் ஒன்று, the suffixing of the -இல் requires you to change the last consonant of the number to its இ form. For example, மூன்று+இல் becomes மூன்றில், note the உ has been omitted, common fractions have names already allocated to them, hence, these names are often used rather than the above method. Other fractions are, Anu was considered as lowest fraction by ancient Tamils as size of smallest physical object, later, this term went to Sanskrit to refer directly atom. Decimal point is called புள்ளி in Tamil, for example,1.1 would be read as ஒன்று புள்ளி ஒன்று. Percentage is known as விழுக்காடு in Tamil or சதவீதம் and these words are simply added after a number to form percentages. For instance, four percent is நான்கு சதவீதம் or நான்கு விழுக்காடு, percentage symbol is also recognised and used. Ordinal numbers are formed by adding the suffix -ஆம் after the number, as always, when blending two words into one, an unvoiced form of the consonant as the one that the second starts with, is placed in between to blend
4.
Chinese numerals
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Chinese numerals are words and characters used to denote numbers in Chinese. Today speakers of Chinese use three written numeral systems, the system of Arabic numerals used worldwide, and two indigenous systems, the more familiar indigenous system is based on Chinese characters that correspond to numerals in the spoken language. These are shared with languages of the Chinese cultural sphere such as Japanese, Korean. The other indigenous system is the Suzhou numerals, or huama, a positional system and these were once used by Chinese mathematicians, and later in Chinese markets, such as those in Hong Kong before the 1990s, but have been gradually supplanted by Arabic numerals. The Chinese character numeral system consists of the Chinese characters used by the Chinese written language to write spoken numerals, similar to spelling-out numbers in English, it is not an independent system per se. Since it reflects spoken language, it not use the positional system as in Arabic numerals. There are characters representing the numbers zero through nine, and other characters representing larger numbers such as tens, hundreds, thousands, there are two sets of characters for Chinese numerals, one for everyday writing and one for use in commercial or financial contexts known as dàxiě. A forger could easily change the everyday characters 三十 to 五千 just by adding a few strokes and that would not be possible when writing using the financial characters 參拾 and 伍仟. They are also referred to as bankers numerals, anti-fraud numerals, for the same reason, rod numerals were never used in commercial records. T denotes Traditional Chinese characters, S denotes Simplified Chinese characters, in the PLA, some numbers will have altered names when used for clearer radio communications. They are,0, renamed 洞 lit, hole 1, renamed 幺 lit. small 2, renamed 两 lit. Double 7, renamed 拐 lit. cane, kidnap, turn 9, hook For numbers larger than 10,000, similarly to the long and short scales in the West, there have been four systems in ancient and modern usage. The original one, with names for all powers of ten up to the 14th, is ascribed to the Yellow Emperor in the 6th century book by Zhen Luan. To avoid problems arising from the ambiguity, the PRC government never uses this character in official documents, the ROC government in Taiwan uses 兆 to mean 1012 in official documents. Numerals beyond 載 zài come from Buddhist texts in Sanskrit, but are found in ancient texts. Some of the words are still being used today. The following are characters used to denote small order of magnitude in Chinese historically, with the introduction of SI units, some of them have been incorporated as SI prefixes, while the rest have fallen into disuse. In the Peoples Republic of China, the translations for the SI prefixes in 1981 were different from those used today, the Republic of China defined 百萬 as the translation for mega
5.
Ge'ez script
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Geez is a script used as an abugida for several languages of Ethiopia and Eritrea. It originated as an abjad and was first used to write Geez, now the language of the Ethiopian Orthodox Tewahedo Church. In Amharic and Tigrinya, the script is often called fidäl, the Geez script has been adapted to write other, mostly Semitic, languages, particularly Amharic in Ethiopia, and Tigrinya in both Eritrea and Ethiopia. It is also used for Sebatbeit, Meen, and most other languages of Ethiopia, in Eritrea it is used for Tigre, and it has traditionally been used for Blin, a Cushitic language. Tigre, spoken in western and northern Eritrea, is considered to resemble Geez more than do the other derivative languages, some other languages in the Horn of Africa, such as Oromo, used to be written using Geez, but have migrated to Latin-based orthographies. For the representation of sounds, this uses a system that is common among linguists who work on Ethiopian Semitic languages. This differs somewhat from the conventions of the International Phonetic Alphabet, see the articles on the individual languages for information on the pronunciation. The earliest inscriptions of Semitic languages in Eritrea and Ethiopia date to the 9th century BC in Epigraphic South Arabian, after the 7th and 6th centuries BC, however, variants of the script arose, evolving in the direction of the Geez abugida. This evolution can be seen most clearly in evidence from inscriptions in Tigray region in northern Ethiopia, at least one of Wazebas coins from the late 3rd or early 4th century contains a vocalized letter, some 30 or so years before Ezana. It has been argued that the marking pattern of the script reflects a South Asian system. On the other hand, emphatic P̣ait ጰ, a Geez innovation, is a modification of Ṣädai ጸ, while Pesa ፐ is based on Tawe ተ. Thus, there are 24 correspondences of Geez and the South Arabian alphabet, Many of the names are cognate with those of Phoenician. Two alphabets were used to write the Geez language, an abjad and later an abugida. The abjad, used until c.330 AD, had 26 consonantal letters, h, l, ḥ, m, ś, r, s, ḳ, b, t, ḫ, n, ʾ, k, w, ʿ, z, y, d, g, ṭ, p̣, ṣ, ṣ́, f, p Vowels were not indicated. Modern Geez is written left to right. The Geez abugida developed under the influence of Christian scripture by adding obligatory vocalic diacritics to the consonantal letters. The diacritics for the vowels, u, i, a, e, ə, o, were fused with the consonants in a recognizable but slightly irregular way, the original form of the consonant was used when the vowel was ä, the so-called inherent vowel. The resulting forms are shown below in their traditional order, for some consonants, there is an eighth form for the diphthong -wa or -oa, and a ninth for -yä
6.
Roman numerals
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The numeric system represented by Roman numerals originated in ancient Rome and remained the usual way of writing numbers throughout Europe well into the Late Middle Ages. Numbers in this system are represented by combinations of letters from the Latin alphabet, Roman numerals, as used today, are based on seven symbols, The use of Roman numerals continued long after the decline of the Roman Empire. The numbers 1 to 10 are usually expressed in Roman numerals as follows, I, II, III, IV, V, VI, VII, VIII, IX, Numbers are formed by combining symbols and adding the values, so II is two and XIII is thirteen. Symbols are placed left to right in order of value. Named after the year of its release,2014 as MMXIV, the year of the games of the XXII Olympic Winter Games The standard forms described above reflect typical modern usage rather than a universally accepted convention. Usage in ancient Rome varied greatly and remained inconsistent in medieval, Roman inscriptions, especially in official contexts, seem to show a preference for additive forms such as IIII and VIIII instead of subtractive forms such as IV and IX. Both methods appear in documents from the Roman era, even within the same document, double subtractives also occur, such as XIIX or even IIXX instead of XVIII. Sometimes V and L are not used, with such as IIIIII. Such variation and inconsistency continued through the period and into modern times. Clock faces that use Roman numerals normally show IIII for four o’clock but IX for nine o’clock, however, this is far from universal, for example, the clock on the Palace of Westminster in London uses IV. Similarly, at the beginning of the 20th century, different representations of 900 appeared in several inscribed dates. For instance,1910 is shown on Admiralty Arch, London, as MDCCCCX rather than MCMX, although Roman numerals came to be written with letters of the Roman alphabet, they were originally independent symbols. The Etruscans, for example, used
7.
Kharosthi
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The Kharosthi script, also spelled Kharoshthi or Kharoṣṭhī, is an ancient script used in ancient Gandhara to write the Gandhari Prakrit and Sanskrit. It was popular in Central Asia as well, an abugida, it was in use from the middle of the 3rd century BCE until it died out in its homeland around the 3rd century CE. Kharosthi is encoded in the Unicode range U+10A00–U+10A5F, from version 4.1.0, Kharosthi is mostly written right to left, but some inscriptions already show the left to right direction that was to become universal for the later South Asian scripts. Each syllable includes the short /a/ sound by default, with other vowels being indicated by diacritic marks, Kharosthi includes only one standalone vowel sign which is used for initial vowels in words. Other initial vowels use the a character modified by diacritics, using epigraphic evidence, Salomon has established that the vowel order is /a e i o u/, rather than the usual vowel order for Indic scripts /a i u e o/. That is the same as the Semitic vowel order, also, there is no differentiation between long and short vowels in Kharosthi. Both are marked using the same vowel markers, the alphabet was used in Gandharan Buddhism as a mnemonic for remembering a series of verses on the nature of phenomena. In Tantric Buddhism, the list was incorporated into ritual practices, Kharosthi included a set of numerals that are reminiscent of Roman numerals. The symbols were I for the unit, X for four, ੭ for ten, the system is based on an additive and a multiplicative principle, but does not have the subtractive feature used in the Roman number system. Note that the table beside reads right-to-left, just like the Kharosthi abugida itself, the Kharosthi script was deciphered by James Prinsep using the bilingual coins of the Indo-Greek Kingdom. This in turn led to the reading of the Edicts of Ashoka, some of which, scholars are not in agreement as to whether the Kharosthi script evolved gradually, or was the deliberate work of a single inventor. An analysis of the script forms shows a clear dependency on the Aramaic alphabet, however, no intermediate forms have yet been found to confirm this evolutionary model, and rock and coin inscriptions from the 3rd century BCE onward show a unified and standard form. An inscription in Aramaic dating back to the 4th century BC was found in Sirkap, according to Sir John Marshall, this seems to confirm that Kharoshthi was later developed from Aramaic. The manuscripts were donated to the British Library in 1994, the entire set of manuscripts are dated to the 1st century CE, making them the oldest Buddhist manuscripts yet discovered. Kharosthi was added to the Unicode Standard in March,2005 with the release of version 4.1, the Unicode block for Kharosthi is U+10A00–U+10A5F, Brahmi History of Afghanistan History of Pakistan Pre-Islamic scripts in Afghanistan Kaschgar und die Kharoṣṭhī Dani, Ahmad Hassan. Kharoshthi Primer, Lahore Museum Publication Series -16, Lahore,1979 Falk, Schrift im alten Indien, Ein Forschungsbericht mit Anmerkungen, Gunter Narr Verlag,1993 Fussmans, Gérard. Les premiers systèmes décriture en Inde, in Annuaire du Collège de France 1988-1989 Hinüber, der Beginn der Schrift und frühe Schriftlichkeit in Indien, Franz Steiner Verlag,1990 Nasim Khan, M. Ashokan Inscriptions, A Palaeographical Study. Two Dated Kharoshthi Inscriptions from Gandhara, Journal of Asian Civilizations, Vol. XXII, No.1, July 1999, 99-103
8.
Suzhou numerals
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The Suzhou numerals, also known as Suzhou mazi or huama, is a numeral system used in China before the introduction of Arabic numerals. The Suzhou numeral system is the only surviving variation of the rod numeral system, the rod numeral system is a positional numeral system used by the Chinese in mathematics. Suzhou numerals are a variation of the Southern Song rod numerals, Suzhou numerals were used as shorthand in number-intensive areas of commerce such as accounting and bookkeeping. At the same time, standard Chinese numerals were used in formal writing, Suzhou numerals were once popular in Chinese marketplaces, such as those in Hong Kong along with local transportation before the 1990s, but they have gradually been supplanted by Arabic numerals. This is similar to what had happened in Europe with Roman numerals used in ancient and medieval Europe for mathematics, nowadays, the Suzhou numeral system is only used for displaying prices in Chinese markets or on traditional handwritten invoices. In the Suzhou numeral system, special symbols are used for digits instead of the Chinese characters, the digits of the Suzhou numerals are defined between U+3021 and U+3029 in Unicode. An additional three code points starting from U+3038 were added later, the numbers one, two, and three are all represented by vertical bars. This can cause confusion when they next to each other. Standard Chinese ideographs are often used in this situation to avoid ambiguity, for example,21 is written as 〢一 instead of 〢〡 which can be confused with 3. The first character of such sequences is usually represented by the Suzhou numeral, the full numerical notations are written in two lines to indicate numerical value, order of magnitude, and unit of measurement. Following the rod system, the digits of the Suzhou numerals are always written horizontally from left to right. The first line contains the values, in this example. The second line consists of Chinese characters that represents the order of magnitude, in this case 十元 which stands for ten yuan. When put together, it is read as 40.22 yuan. Zero is represented by the character for zero, leading and trailing zeros are unnecessary in this system. This is very similar to the scientific notation for floating point numbers where the significant digits are represented in the mantissa. Also, the unit of measurement, with the first digit indicator, is aligned to the middle of the numbers row. In the Unicode standard version 3.0, these characters are incorrectly named Hangzhou style numerals, in the episode The Blind Banker of the 2010 BBC television series Sherlock, Sherlock Holmes erroneously refers to the number system as Hangzhou instead of the correct Suzhou
9.
Cyrillic numerals
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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, 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. 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 system is an alphabetic system, equivalent to the Ionian numeral system. The order is based on the original Greek alphabet rather than the standard Cyrillic alphabetical order, a separate letter is assigned to each unit, each multiple of ten, and each multiple of one hundred. To distinguish numbers from text, a titlo is drawn over the numbers. Examples, –1706 –7118 To evaluate a Cyrillic number, the values of all the figures are added up, for example, ѰЗ is 700 +7, making 707. If the number is greater than 999, the sign is used to multiply the numbers value, for example, ҂Ѕ is 6000, while ҂Л҂В is parsed as 30,000 +2000. To produce larger numbers, a sign is used to encircle the number being multiplied. Glagolitic numerals are similar to Cyrillic numerals except that values are assigned according to the native alphabetic order of the Glagolitic alphabet. Glyphs for the ones, tens, and hundreds values are combined to form more precise numbers, for example, ⰗⰑⰂ is 500 +80 +3 or 583. As with Cyrillic numerals, the numbers 11 through 19 are typically written with the ones digit before the glyph for 10, for example ⰅⰊ is 6 +10, early Cyrillic alphabet Glagolitic alphabet Relationship of Cyrillic and Glagolitic scripts Greek numerals Combining Cyrillic Millions
10.
Arabic numerals
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In this numeral system, a sequence of digits such as 975 is read as a single number, using the position of the digit in the sequence to interpret its value. The symbol for zero is the key to the effectiveness of the system, the system was adopted by Arab mathematicians in Baghdad and passed on to the Arabs farther west. There is some evidence to suggest that the numerals in their current form developed from Arabic letters in the Maghreb, the current form of the numerals developed in North Africa, distinct in form from the Indian and eastern Arabic numerals. The use of Arabic numerals spread around the world through European trade, books, the term Arabic numerals is ambiguous. It most commonly refers to the widely used in Europe. Arabic numerals is also the name for the entire family of related numerals of Arabic. It may also be intended to mean the numerals used by Arabs and it would be more appropriate to refer to the Arabic numeral system, where the value of a digit in a number depends on its position. The decimal Hindu–Arabic numeral system was developed in India by AD700, the development was gradual, spanning several centuries, but the decisive step was probably provided by Brahmaguptas formulation of zero as a number in AD628. The system was revolutionary by including zero in positional notation, thereby limiting the number of 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. The glyphs most commonly used in conjunction with the Latin script since early modern times are 0123456789. 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 symbol for zero in them, dated back as far as the 6th century AD. Inscriptions in Indonesia and Cambodia dating to AD683 have also been found and their work was principally responsible for the diffusion of the Indian system of numeration in the Middle East and the West. In the 10th century, Middle-Eastern mathematicians extended the decimal system to include fractions. The decimal point notation was introduced by Sind ibn Ali, who wrote the earliest treatise on Arabic numerals. Ghubar numerals themselves are probably of Roman origin, some popular myths have argued that the original forms of these symbols indicated their numeric value through the number of angles they contained, but no evidence exists of any such origin. In 825 Al-Khwārizmī wrote a treatise in Arabic, On the Calculation with Hindu Numerals, Algoritmi, the translators rendition of the authors name, gave rise to the word algorithm
11.
Counting rods
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Counting rods are small bars, typically 3–14 cm long, that were used by mathematicians for calculation in ancient China, Japan, Korea, and Vietnam. They are placed horizontally or vertically to represent any integer or rational number. The written forms based on them are called rod numerals and they are a true positional numeral system with digits for 1–9 and a blank for 0, from the Warring states period to the 16th century. Counting rods were used by ancient Chinese for more two thousand years. In 1954, forty-odd counting rods of the Warring States period were found in Zuǒjiāgōngshān Chu Grave No.15 in Changsha, in 1973, archeologists unearthed a number of wood scripts from a Han dynasty tomb in Hubei. On one of the scripts was written, “当利二月定算”. This is one of the earliest examples of using counting rod numerals in writing, in 1976, a bundle of Western Han counting rods made of bones was unearthed from Qianyang County in Shaanxi. The use of counting rods must predate it, Laozi said a good calculator doesnt use counting rods, the Book of Han recorded, they calculate with bamboo, diameter one fen, length six cun, arranged into a hexagonal bundle of two hundred seventy one pieces. At first calculating rods were round in section, but by the time of the Sui dynasty triangular rods were used to represent positive numbers. After the abacus flourished, counting rods were abandoned except in Japan, counting rods represent digits by the number of rods, and the perpendicular rod represents five. To avoid confusion, vertical and horizontal forms are alternately used, generally, vertical rod numbers are used for the position for the units, hundreds, ten thousands, etc. while horizontal rod numbers are used for the tens, thousands, hundred thousands etc. It is written in Sunzi Suanjing that one is vertical, ten is horizontal, red rods represent positive numbers and black rods represent negative numbers. Ancient Chinese clearly understood negative numbers and zero, though they had no symbol for the latter, later, a go stone was sometimes used to represent zero. This alternation of vertical and horizontal rod numeral form is important to understanding written transcription of rod numerals on manuscripts correctly. In the same manuscript,405 was transcribed as, with a space in between for obvious reasons, and could in no way be interpreted as 45. In other words, transcribed rod numerals may not be positional, the value of a number depends on its physical position on the counting board. A9 at the rightmost position on the stands for 9. Moving the batch of rods representing 9 to the one position gives 9 or 90
