1.
Maya civilization
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The Maya civilization developed in an area that encompasses southeastern Mexico, all of Guatemala and Belize, and the western portions of Honduras and El Salvador. The Archaic period, prior to 2000 BC, saw the first developments in agriculture, the first Maya cities developed around 750 BC, and by 500 BC these cities possessed monumental architecture, including large temples with elaborate stucco faĂ§ades. Hieroglyphic writing was being used in the Maya region by the 3rd century BC, in the Late Preclassic a number of large cities developed in the PetĂ©n Basin, and Kaminaljuyu rose to prominence in the Guatemalan Highlands. Beginning around 250 AD, the Classic period is defined as when the Maya were raising sculpted monuments with Long Count dates. This period saw the Maya civilization develop a number of city-states linked by a complex trade network. In the Maya Lowlands two great rivals, Tikal and Calakmul, became powerful, the Classic period also saw the intrusive intervention of the central Mexican city of Teotihuacan in Maya dynastic politics. In the 9th century, there was a political collapse in the central Maya region, resulting in internecine warfare, the abandonment of cities. The Postclassic period saw the rise of Chichen Itza in the north, in the 16th century, the Spanish Empire colonized the Mesoamerican region, and a lengthy series of campaigns saw the fall of NojpetĂ©n, the last Maya city in 1697. Classic period rule was centred on the concept of the divine king, kingship was patrilineal, and power would normally pass to the eldest son. A prospective king was expected to be a successful war leader. Maya politics was dominated by a system of patronage, although the exact political make-up of a kingdom varied from city-state to city-state. By the Late Classic, the aristocracy had greatly increased, resulting in the reduction in the exclusive power of the divine king. Maya cities tended to expand haphazardly, and the city centre would be occupied by ceremonial and administrative complexes, different parts of a city would often be linked by causeways. The principal architecture of the city consisted of palaces, pyramid-temples, ceremonial ballcourts, the Maya elite were literate, and developed a complex system of hieroglyphic writing that was the most advanced in the pre-Columbian Americas. The Maya recorded their history and ritual knowledge in screenfold books, there are also a great many examples of Maya text found on stelae and ceramics. The Maya developed a complex series of interlocking ritual calendars. As a part of their religion, the Maya practised human sacrifice, the Maya civilization developed within the Mesoamerican cultural area, which covers a region that spreads from northern Mexico southwards into Central America. Mesoamerica was one of six cradles of civilization worldwide, the Mesoamerican area gave rise to a series of cultural developments that included complex societies, agriculture, cities, monumental architecture, writing, and calendrical systems
2.
Vigesimal
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The vigesimal or base 20 numeral system is based on twenty. In a vigesimal system, twenty individual numerals are used. One modern method of finding the extra needed symbols is to write ten as the letter A20, to write nineteen as J20, and this is similar to the common computer-science practice of writing hexadecimal numerals over 9 with the letters AâF. Another method skips over the letter I, in order to avoid confusion between I20 as eighteen and one, so that the number eighteen is written as J20, the number twenty is written as 1020. According to this notation,2020 means forty in decimal = + D020 means two hundred and sixty in decimal = +10020 means four hundred in decimal = + +, in the rest of this article below, numbers are expressed in decimal notation, unless specified otherwise. For example,10 means ten,20 means twenty, in decimal, dividing by three twice only gives one digit periods because 9 is the number below ten. 21, however, the adjacent to 20 that is divisible by 3, is not divisible by 9. Ninths in vigesimal have six-digit periods, the prime factorization of twenty is 22 Ă5, so it is not a perfect power. However, its part,5, is congruent to 1. Thus, according to Artins conjecture on primitive roots, vigesimal has infinitely many cyclic primes, but the fraction of primes that are cyclic is not necessarily ~37. 395%. An UnrealScript program that computes the lengths of recurring periods of various fractions in a set of bases found that, of the first 15,456 primes. In many European languages,20 is used as a base, vigesimal systems are common in Africa, for example in Yoruba. OgĂșn,20, is the basic numeric block, ogĂłjĂŹ,40, =20 multiplied by 2. Ogota,60, =20 multiplied by 3, ogorin,80, =20 multiplied by 4. Ogorun,100, =20 multiplied by 5, twenty was a base in the Maya and Aztec number systems. The Maya used the names for the powers of twenty, kal, bak, pic, calab, kinchil. See also Maya numerals and Maya calendar, Mayan languages, Yucatec, the Aztec called them, cempoalli, centzontli, cenxiquipilli, cempoalxiquipilli, centzonxiquipilli and cempoaltzonxiquipilli. Note that the ce prefix at the beginning means one and is replaced with the number to get the names of other multiples of the power
3.
Positional notation
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Positional notation or place-value notation is a method of representing or encoding numbers. Positional notation is distinguished from other notations for its use of the symbol for the different orders of magnitude. This greatly simplified arithmetic, leading to the spread of the notation across the world. With the use of a point, the notation can be extended to include fractions. The HinduâArabic numeral system, base-10, is the most commonly used system in the world today for most calculations, today, the base-10 system, which is likely motivated by counting with the ten fingers, is ubiquitous. Other bases have been used in the past however, and some continue to be used today, for example, the Babylonian numeral system, credited as the first positional numeral system, was base-60, but it lacked a real 0 value. Zero was indicated by a space between sexagesimal numerals, by 300 BC, a punctuation symbol was co-opted as a placeholder in the same Babylonian system. In a tablet unearthed at Kish, the scribe BĂȘl-bĂąn-aplu wrote his zeros with three hooks, rather than two slanted wedges, the Babylonian placeholder was not a true zero because it was not used alone. Nor was it used at the end of a number, thus numbers like 2 and 120,3 and 180,4 and 240, looked the same because the larger numbers lacked a final sexagesimal placeholder. Counting rods and most abacuses have been used to represent numbers in a numeral system. This approach required no memorization of tables and could produce practical results quickly, for four centuries there was strong disagreement between those who believed in adopting the positional system in writing numbers and those who wanted to stay with the additive-system-plus-abacus. Although electronic calculators have largely replaced the abacus, the continues to be used in Japan. After the French Revolution, the new French government promoted the extension of the decimal system, some of those pro-decimal effortsâsuch as decimal time and the decimal calendarâwere unsuccessful. Other French pro-decimal effortsâcurrency decimalisation and the metrication of weights and measuresâspread widely out of France to almost the whole world. According to Joseph Needham and Lam Lay Yong, decimal fractions were first developed and used by the Chinese in the 1st century BC, the written Chinese decimal fractions were non-positional. However, counting rod fractions were positional, the Jewish mathematician Immanuel Bonfils used decimal fractions around 1350, anticipating Simon Stevin, but did not develop any notation to represent them. A forerunner of modern European decimal notation was introduced by Simon Stevin in the 16th century. A key argument against the system was its susceptibility to easy fraud by simply putting a number at the beginning or end of a quantity, thereby changing 100 into 5100
4.
Numeral system
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A numeral system is a writing system for expressing numbers, that is, a mathematical notation for representing numbers of a given set, using digits or other symbols in a consistent manner. It can be seen as the context that allows the symbols 11 to be interpreted as the symbol for three, the decimal symbol for eleven, or a symbol for other numbers in different bases. The number the numeral represents is called its value, ideally, a numeral system will, Represent a useful set of numbers Give every number represented a unique representation Reflect the algebraic and arithmetic structure of the numbers. For example, the decimal representation of whole numbers gives every nonzero whole number a unique representation as a finite sequence of digits. Etc. all of which have the same meaning except for some scientific, such systems are, however, not the topic of this article. The most commonly used system of numerals is the HinduâArabic numeral system, two Indian mathematicians are credited with developing it. Aryabhata of Kusumapura developed the notation in the 5th century. The numeral system and the concept, developed by the Hindus in India, slowly spread to other surrounding countries due to their commercial. The Arabs adopted and modified it, even today, the Arabs call the numerals which they use Rakam Al-Hind or the Hindu numeral system. The Arabs translated Hindu texts on numerology and spread them to the world due to their trade links with them. The Western world modified them and called them the Arabic numerals, hence the current western numeral system is the modified version of the Hindu numeral system developed in India. It also exhibits a great similarity to the SanskritâDevanagari notation, which is used in India. The simplest numeral system is the numeral system, in which every natural number is represented by a corresponding number of symbols. If the symbol / is chosen, for example, then the seven would be represented by ///////. Tally marks represent one such system still in common use, the unary system is only useful for small numbers, although it plays an important role in theoretical computer science. Elias gamma coding, which is used in data compression. The unary notation can be abbreviated by introducing different symbols for new values. The ancient Egyptian numeral system was of type, and the Roman numeral system was a modification of this idea
5.
Zero number
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0 is both a number and the numerical digit used to represent that number in numerals. The number 0 fulfills a role in mathematics as the additive identity of the integers, real numbers. As a digit,0 is used as a placeholder in place value systems, names for the number 0 in English include zero, nought or naught, nil, orâin contexts where at least one adjacent digit distinguishes it from the letter Oâoh or o. Informal or slang terms for zero include zilch and zip, ought and aught, as well as cipher, have also been used historically. The word zero came into the English language via French zĂ©ro from Italian zero, in pre-Islamic time the word áčŁifr had the meaning empty. Sifr evolved to mean zero when it was used to translate ĆĆ«nya from India, the first known English use of zero was in 1598. The Italian mathematician Fibonacci, who grew up in North Africa and is credited with introducing the system to Europe. This became zefiro in Italian, and was contracted to zero in Venetian. The Italian word zefiro was already in existence and may have influenced the spelling when transcribing Arabic áčŁifr, modern usage There are different words used for the number or concept of zero depending on the context. For the simple notion of lacking, the words nothing and none are often used, sometimes the words nought, naught and aught are used. Several sports have specific words for zero, such as nil in football, love in tennis and it is often called oh in the context of telephone numbers. Slang words for zero include zip, zilch, nada, duck egg and goose egg are also slang for zero. Ancient Egyptian numerals were base 10 and they used hieroglyphs for the digits and were not positional. By 1740 BC, the Egyptians had a symbol for zero in accounting texts. The symbol nfr, meaning beautiful, was used to indicate the base level in drawings of tombs and pyramids. By the middle of the 2nd millennium BC, the Babylonian mathematics had a sophisticated sexagesimal positional numeral system, the lack of a positional value was indicated by a space between sexagesimal numerals. By 300 BC, a symbol was co-opted as a placeholder in the same Babylonian system. In a tablet unearthed at Kish, the scribe BĂȘl-bĂąn-aplu wrote his zeros with three hooks, rather than two slanted wedges, the Babylonian placeholder was not a true zero because it was not used alone
6.
Turtle shell
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It is constructed of modified bony elements such as the ribs, parts of the pelvis and other bones found in most reptiles. The bone of the consists of both skeletal and dermal bone, showing that the complete enclosure of the shell probably evolved by including dermal armor into the rib cage. Hence understanding the structure of the shell in living species gives us comparable material with fossils, the turtle shell is made up of numerous bony elements, generally named after similar bones in other vertebrates, and a series of keratinous scutes which are also uniquely named. Some of those bones that make the top of the shell, carapace, the ventral surface is called the plastron. These are joined by a called the bridge. The actual suture between the bridge and the plastron is called the anterior bridge strut, in Pleurodires the posterior pelvis is also part of the carapace, fully fused with it. This is not the case in Cryptodires which have a floating pelvis, the anterior bridge strut and posterior bridge strut are part of the plastron, on the carapace are the sutures into which they insert, known as the Bridge carapace suture. The bones of the shell are named for standard vertebrate elements, as such the carapace is made up of 8 pleurals on each side, these are a combination of the ribs and fused dermal bone. Outside of this at the anterior of the shell is the single nuchal bone, at the posterior of the shell is the pygal bone and in front of this nested behind the eighth pleurals is the suprapygal. Between each of the pleurals are a series of neural bones, beneath the neural bone is the Neural arch which forms the upper half of the encasement for the spinal chord. Below this the rest of the vertebral column, some species of turtles have some extra bones called mesoplastra, which are located between the carapace and plastron in the bridge area. They are present in most Pelomedusid turtles, the skeletal elements of the plastron are also largely in pairs. Anteriorly there are two epiplastra, with the hyoplastra behind them and these make up the front half of the plastron and the hyoplastron contains the anterior bridge strut. The posterior half is made up of two hypoplastra and the rear is a pair of xiphiplastra, overlying the boney elements are a series of scutes, which are made of keratin and are a lot like horn or nail tissue. In the center of the carapace are 5 vertebral scutes and out from these are 4 pairs of costal scutes, around the edge of the shell are 12 pairs of marginal scutes. All these scutes are aligned so that for the most part the sutures between the bones are in the middle of the scutes above. At the anterior of the shell there may be a cervical scute however the presence or absence of this scute is highly variable, on the plastron there are two gular scutes at the front, followed by a pair of pectorals, then abdominals, femorals and lastly anals. A particular variation is the Pleurodiran turtles have an intergular scute between the gulars at the front, giving them a total of 13 plastral scutes, compared to the 12 in all Cryptodiran turtles
7.
1 (number)
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1, is a number, a numeral, and the name of the glyph representing that number. It represents a single entity, the unit of counting or measurement, for example, a line segment of unit length is a line segment of length 1. It is also the first of the series of natural numbers. The word one can be used as a noun, an adjective and it comes from the English word an, which comes from the Proto-Germanic root *ainaz. The Proto-Germanic root *ainaz comes from the Proto-Indo-European root *oi-no-, compare the Proto-Germanic root *ainaz to Old Frisian an, Gothic ains, Danish een, Dutch een, German eins and Old Norse einn. Compare the Proto-Indo-European root *oi-no- to Greek oinos, Latin unus, Old Persian aivam, Old Church Slavonic -inu and ino-, Lithuanian vienas, Old Irish oin, One, sometimes referred to as unity, is the first non-zero natural number. It is thus the integer before two and after zero, and the first positive odd number, any number multiplied by one is that number, as one is the identity for multiplication. As a result,1 is its own factorial, its own square, its own cube, One is also the result of the empty product, as any number multiplied by one is itself. It is also the natural number that is neither composite nor prime with respect to division. The Gupta wrote it as a line, and the Nagari sometimes added a small circle on the left. The Nepali also rotated it to the right but kept the circle small and this eventually became the top serif in the modern numeral, but the occasional short horizontal line at the bottom probably originates from similarity with the Roman numeral I. Where the 1 is written with an upstroke, the number 7 has a horizontal stroke through the vertical line. While the shape of the 1 character has an ascender in most modern typefaces, in typefaces with text figures, many older typewriters do not have a separate symbol for 1 and use the lowercase letter l instead. It is possible to find cases when the uppercase J is used,1 cannot be used as the base of a positional numeral system, as the only digit that would be permitted in such a system would be 0. Since the base 1 exponential function always equals 1, its inverse does not exist, there are two ways to write the real number 1 as a recurring decimal, as 1.000. and as 0.999. There is only one way to represent the real number 1 as a Dedekind cut, in a multiplicative group or monoid, the identity element is sometimes denoted 1, but e is also traditional. However,1 is especially common for the identity of a ring. When such a ring has characteristic n not equal to 0,1 is the first figurate number of every kind, such as triangular number, pentagonal number and centered hexagonal number, to name just a few
8.
5 (number)
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5 is a number, numeral, and glyph. It is the number following 4 and preceding 6. Five is the prime number. Because it can be written as 221 +1, five is classified as a Fermat prime, therefore a regular polygon with 5 sides is constructible with compass and unmarked straightedge. 5 is the third Sophie Germain prime, the first safe prime, the third Catalan number, Five is the first Wilson prime and the third factorial prime, also an alternating factorial. Five is the first good prime and it is an Eisenstein prime with no imaginary part and real part of the form 3n â1. It is also the number that is part of more than one pair of twin primes. Five is conjectured to be the only odd number and if this is the case then five will be the only odd prime number that is not the base of an aliquot tree. Five is also the only prime that is the sum of two primes, namely 2 and 3. The number 5 is the fifth Fibonacci number, being 2 plus 3,5 is also a Pell number and a Markov number, appearing in solutions to the Markov Diophantine equation. Whereas 5 is unique in the Fibonacci sequence, in the Perrin sequence 5 is both the fifth and sixth Perrin numbers,5 is the length of the hypotenuse of the smallest integer-sided right triangle. In bases 10 and 20,5 is a 1-automorphic number,5 and 6 form a RuthâAaron pair under either definition. There are five solutions to ZnĂĄms problem of length 6 and this is related to the fact that the symmetric group Sn is a solvable group for n â€4 and not solvable for n â„5. While all graphs with 4 or fewer vertices are planar, there exists a graph with 5 vertices which is not planar, K5, Five is also the number of Platonic solids. A polygon with five sides is a pentagon, figurate numbers representing pentagons are called pentagonal numbers. Five is also a square pyramidal number, Five is the only prime number to end in the digit 5, because all other numbers written with a 5 in the ones-place under the decimal system are multiples of five. As a consequence of this,5 is in base 10 a 1-automorphic number, vulgar fractions with 5 or 2 in the denominator do not yield infinite decimal expansions, unlike expansions with all other prime denominators, because they are prime factors of ten, the base. When written in the system, all multiples of 5 will end in either 5 or 0
9.
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 HinduâArabic 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-KhwÄrizmÄ« 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
10.
Eastern Arabic numerals
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These numbers are known as ŰŁŰ±ÙŰ§Ù
ÙÙŰŻÙŰ© 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-Ă -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
11.
Indian numerals
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Indian numerals are the symbols representing numbers in India. These numerals are used in the context of the decimal HinduâArabic numeral system. Below is a list of the Indian numerals in their modern Devanagari form, the corresponding Hindu-Arabic equivalents, their Hindi and Sanskrit pronunciation, since Sanskrit is an Indo-European language, it is obvious that the words for numerals closely resemble those of Greek and Latin. The word Shunya for zero was translated into Arabic as Ű”ÙŰ± sifr, meaning nothing which became the zero in many European languages from Medieval Latin. The five Indian languages that have adapted the Devanagari script to their use also naturally employ the numeral symbols above, of course, for numerals in Tamil language see Tamil numerals. For numerals in Telugu language see Telugu numerals, Tamil and Malayalam scripts also have distinct forms for 10,100,1000 numbers, àŻ°, àŻ±, àŻČand à”°, à”±, à”Č respectively in tamil and scripts. A decimal place system has been traced back to ca.500 in India, before that epoch, the Brahmi numeral system was in use, that system did not encompass the concept of the place-value of numbers. Instead, Brahmi numerals included additional symbols for the tens, as well as symbols for hundred. The Indian place-system numerals spread to neighboring Persia, where they were picked up by the conquering Arabs, in 662, Severus Sebokht - a Nestorian bishop living in Syria wrote, I will omit all discussion of the science of the Indians. Of their subtle discoveries in astronomy â discoveries that are more ingenious than those of the Greeks, I wish only to say that this computation is done by means of nine signs. But it is in Khmer numerals of modern Cambodia where the first extant material evidence of zero as a numerical figure, as it was from the Arabs that the Europeans learned this system, the Europeans called them Arabic numerals, the Arabs refer to their numerals as Indian numerals. In academic circles they are called the HinduâArabic or IndoâArabic numerals, but what was the net achievement in the field of reckoning, the earliest art practiced by man. An inflexible numeration so crude as to progress well nigh impossible. Man used these devices for thousands of years without contributing an important idea to the system. Even when compared with the growth of ideas during the Dark Ages. When viewed in light, the achievements of the unknown Hindu. Sanskrit Siddham Numbers Karl Menninger, Number Words and Number Symbols - A Cultural History of Numbers ISBN 0-486-27096-3 David Eugene Smith and Louis Charles Karpinski, The Hindu-Arabic Numerals
12.
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 âEluâ, 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 âKundaliyaâ 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 âCatalogue of Palm leaf manuscripts in the library of Colombo Museumâ. 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 âakmaâ in the Lith Illakkam
13.
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 àźàŻàźŽàźżàźŻàźźàŻ or àźȘàŻàźàŻàźàźżàźŻàźźàŻ. Tamil has a prefix for each number from 1 to 9. For instance, the word for fifty, àźàźźàŻàźȘàź€àŻ is a combination of àź, the prefix for nine changes with respect to the succeeding base 10. àź€àŻ+ the unvoiced consonant of the succeeding base 10 forms the prefix for nine, for instance,90 is àź€àŻ+àźŁàŻ, hence, àź€àŻàźŁàŻàźŁàŻàź±àŻ). These are typically void in the Tamil language except for some Hindu and Christian religious references, example àź
àźàŻàź àźàźČàźàŻàźàŻàźźàźżàźàźłàŻ 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. â â â â â â â â â â â â 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 -àźàźČàŻ after the denominator followed by the numerator. For instance, 1/41 can be said as àźšàźŸàź±àŻàźȘàź€àŻàź€àŻ àźàź©àŻàź±àźżàźČàŻ àźàź©àŻàź±àŻ, the suffixing of the -àźàźČàŻ requires you to change the last consonant of the number to its àź form. For example, àźźàŻàź©àŻàź±àŻ+àźàźČàŻ becomes àźźàŻàź©àŻàź±àźżàźČàŻ, note the àź 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 àźȘàŻàźłàŻàźłàźż in Tamil, for example,1.1 would be read as àźàź©àŻàź±àŻ àźȘàŻàźłàŻàźłàźż àźàź©àŻàź±àŻ. Percentage is known as àź”àźżàźŽàŻàźàŻàźàźŸàźàŻ in Tamil or àźàź€àź”àŻàź€àźźàŻ and these words are simply added after a number to form percentages. For instance, four percent is àźšàźŸàź©àŻàźàŻ àźàź€àź”àŻàź€àźźàŻ or àźšàźŸàź©àŻàźàŻ àź”àźżàźŽàŻàźàŻàźàźŸàźàŻ, percentage symbol is also recognised and used. Ordinal numbers are formed by adding the suffix -àźàźźàŻ 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
14.
Balinese numerals
â
The Balinese language has an elaborate decimal numeral system. The numerals 1â10 have basic, combining, and independent forms, the combining forms are used to form higher numbers. In some cases there is more than one word for a numeral, reflecting the Balinese register system, final orthographic -a is a schwa. * A less productive combining form of a-1 is sa- and it, ulung-, and sangang- are from Javanese. Dasa 10 is from Sankrit dĂ©sa, like English, Balinese has compound forms for the teens and tens, however, it also has a series of compound tweens, 21â29. The teens are based on a root *-welas, the tweens on -likur, hyphens are not used in the orthography, but have been added to the table below to clarify their derivation. The high-register combining forms kalih-2 and tigang-3 are used with -likur, -dasa, and higher numerals, the teens are from Javanese, where the -olas forms are regular, apart from pele-kutus 18, which is suppletive. Sa-laĂ©25, and se-ket 50 are also suppletive, and cognate with Javanese sÉlawĂ©25, there are additional numerals pasasur ~ sasur 35 and se-timahan ~ se-timan 45, and a compound telung-benang for 75. The unit combining forms are combined with atus 100, atak 200, amas 400, tali 1000, laksa 10,000, keti 100,000, in addition, there is karobelah 150, lebak 175, and sepa for 1600. At least karobelah has a cognate in Javanese, ro-bÉlah, where ro- is the form for two
15.
Burmese numerals
â
Burmese numerals are a set of numerals traditionally used in the Burmese language, although the Arabic numerals are also used. Burmese numerals follow the Hindu-Arabic numeral system used in the rest of the world. 1 Burmese for zero comes from Sanskrit ĆĆ«nya.2 Can be abbreviated to IPA, in list contexts, spoken Burmese has innate pronunciation rules that govern numbers when they are combined with another word, be it a numerical place or a measure word. Other suffixes such as áá±áŹááș, áá±áŹááșáž, ááááșáž, and áááșáž all shift to, for six and eight, no pronunciation shift occurs. These pronunciation shifts are exclusively confined to spoken Burmese and are not spelt any differently,1 Shifts to voiced consonant following three, four, five, and nine. Ten to nineteen are almost always expressed without including áá
áș, another pronunciation rule shifts numerical place name from the low tone to the creaky tone. Number places from 10 up to 107 has increment of 101, beyond those Number places, larger number places have increment of 107. 1014 up to 10140 has increment of 107, numbers in the hundreds place, shift from ááŹ to ááŹá·, except for numbers divisible by 100. Numbers in the place, shift from áá±áŹááș to áá±áŹáá·áș. Hence, a number like 301 is pronounced, while 300 is pronounced, the digits of a number are expressed in order of decreasing digits place. When a number is used as an adjective, the word order is. However, for numbers, the word order is flipped to. The exception to rule is the number 10, which follows the standard word order. Ordinal numbers, from first to tenth, are Burmese pronunciations of their Pali equivalents and they are prefixed to the noun. Beyond that, cardinal numbers can be raised to the ordinal by suffixing the particle ááŒá±áŹááș to the number in the order, number + measure word + ááŒá±áŹááș. Colloquially, decimal numbers are formed by saying ááá where the separator is located. For example,10.1 is áááș ááá áá
áș, half is expressed primarily by áá
áșáááș, although áááșáááș, áĄááœáČ and áĄááŒááșáž are also used. Quarter is expressed with áĄá
áááș or áá
áșá
áááș, other fractional numbers are verbally expressed as follows, denominator + ááŻá¶ + numerator + ááŻá¶
16.
Dzongkha numerals
â
Dzongkha, the national language of Bhutan, has two numeral systems, one vigesimal, and a modern decimal system. The vigesimal system remains in robust use, ten is an auxiliary base, the teens are formed with ten and the numerals 1â9. *When it appears on its own, ten is usually said cu-tÊ°ĂŁm a full ten, in combinations it is simply cu. Factors of 20 are formed from kÊ°e, intermediate factors of ten are formed with pÉÊ±e-da half to,400 ÉČiÉu is the next unit, ÉČiÉu ciË400, ÉČiÉu ÉČi 800, etc. Higher powers are 8000 kÊ°ecÊ°e and jĂŁËcÊ°e 160,000, the decimal system is the same as the vigesimal system up to 19. Then decades, however, are formed as unitâten, as in Chinese,20 is reported to be ÉČiÉu, the vigesimal numeral 400, this may be lexical interference for the expected *ÉČi-cu. Mazaudon & Lacito,2002, Les principes de construction du nombre dans les langues tibeto-birmanes, in FranĂ§ois, ed
17.
Gujarati numerals
â
Gujarati numerals is the numeral system of the Gujarati script of South Asia, which is a derivative of Devanagari numerals. It is the numeral system of Gujarat, India. It is also recognized in India and as a minor script in Pakistan. The following table shows Gujarati numbers and the Gujarati word for each of them in various scripts, Gujarati script Gurmukhi numerals Devanagari alphabet
18.
Javanese numerals
â
The Javanese language has a decimal numeral system with distinct words for the tweens from 21 to 29, called likuran. The basic numerals 1â10 have independent and combining forms, the latter derived via a suffix -ng, the combining forms are used to form the tens, hundreds, thousands, and millions. The numerals 1â5 and 10 have distinct high-register and low register forms, the halus forms are listed below in italics. Like English, Javanese has compound forms for the teens, however, it also has a series of compound tweens, the teens are based on a root -las, the tweens on -likur, and the tens are formed by the combining forms. Hyphens are not used in the orthography, but have added to the table below to clarify their derivation. Final orthographic -a tends to in many dialects, as does any preceding a, parallel to the tens are the hundreds, the thousands, and the millions, except that the compounds of five and six are formed with limang- and nem-. The names of the Old Javanese numerals were derived from their names in the Sanskrit language, balinese numerals, a related but yet more complex numeral system
19.
Khmer numerals
â
Khmer numerals are the numerals used in the Khmer language. They have been in use since at least the early 7th century, with the earliest known use being on a stele dated to AD604 found in Prasat Bayang, Cambodia, having been derived from the Hindu numerals, modern Khmer numerals also represent a decimal positional notation system. It is the script with the first extant material evidence of zero as a figure, dating its use back to the seventh century. However, Old Khmer, or Angkorian Khmer, also possessed separate symbols for the numbers 10,20 and this inconsistency with its decimal system suggests that spoken Angkorian Khmer used a vigesimal system. For example,6 is formed from 5 plus 1, with the exception of the number 0, which stems from Sanskrit, the etymology of the Khmer numbers from 1 to 5 is of proto-MonâKhmer origin. For details of the various alternative romanization systems, see Romanization of Khmer, some authors may alternatively mark as the pronunciation for the word two, and either or for the word three. In neighbouring Thailand the number three is thought to bring good luck, however, in Cambodia, taking a picture with three people in it is considered bad luck, as it is believed that the person situated in the middle will die an early death. As mentioned above, the numbers from 6 to 9 may be constructed by adding any number between 1 and 4 to the base number 5, so that 7 is literally constructed as 5 plus 2. Beyond that, Khmer uses a base, so that 14 is constructed as 10 plus 4, rather than 2 times 5 plus 4. In constructions from 6 to 9 that use 5 as a base, /pram/ may alternatively be pronounced, giving and this is especially true in dialects which elide /r/, but not necessarily restricted to them, as the pattern also follows Khmers minor syllable pattern. The numbers from thirty to ninety in Khmer bear many resemblances to both the modern Thai and Cantonese numbers, informally, a speaker may choose to omit the final and the number is still understood. For example, it is possible to say instead of the full, Language Comparisons, Words in parenthesis indicate literary pronunciations, while words preceded with an asterisk mark are non-productive. The standard Khmer numbers starting from one hundred are as follows, Although ááœááááá· is most commonly used to mean ten million, in some areas this is also colloquially used to refer to one billion. In order to avoid confusion, sometimes ááááá¶á is used to mean ten million, along with ááœááááá¶á for one hundred million, different Cambodian dialects may also employ different base number constructions to form greater numbers above one thousand. As a result of prolonged literary influence from both the Sanskrit and Pali languages, Khmer may occasionally use borrowed words for counting. One reason for the decline of numbers is that a Khmer nationalism movement. The Khmer Rouge also attempted to cleanse the language by removing all words which were considered politically incorrect, Khmer ordinal numbers are formed by placing the word ááž in front of a cardinal number. This is similar to the use of àžàž”àč thi in Thai and it is generally assumed that the Angkorian and pre-Angkorian numbers also represented a dual base system, with both base 5 and base 20 in use
20.
Lao alphabet
â
Lao script, or Akson Lao, is the primary script used to write the Lao language and other minority languages in Laos. It was also used to write the Isan language, but was replaced by the Thai script and it has 27 consonants,7 consonantal ligatures,33 vowels, and 4 tone marks. Akson Lao is a system to the Thai script, with which it shares many similarities. However, Lao has fewer characters and is formed in a curvilinear fashion than Thai. Lao is traditionally written from left to right, Lao is considered an abugida, in which certain implied vowels are unwritten. However, due to spelling reforms by the communist Lao Peoples Revolutionary Party, despite this, most Lao outside of Laos, and many inside Laos, continue to write according to former spelling standards, so vernacular Lao functions as a pure abugida. For example, the old spelling of àșȘà»àș„àș”àșĄ to hold a ceremony, vowels can be written above, below, in front of, or behind consonants, with some vowel combinations written before, over and after. Spaces for separating words and punctuation were traditionally not used, but a space is used, the letters have no majuscule or minuscule differentiation. The Lao script was standardized in the Mekong River valley after the various Tai principalities of the region were merged under Lan Xang in the 14th century. This script, sometimes known as Tai Noi, has changed little since its inception and continued use in the Lao-speaking regions of modern-day Laos, conversely, the Thai alphabet continued to evolve, but the scripts still share similarities. This script was derived locally from the Khmer script of Angkor with additional influence from Mon, traditionally, only secular literature were written with the Lao alphabet. Religious literature was written in Tua Tham, a Mon-based script that is still used for the Tai KhĂŒn, Tai Lue. Mystical, magical, and some literature was written in a modified version of the Khmer alphabet. Essentially Thai and Lao are almost typographic variants of other just as in the Javanese and Balinese scripts. The Lao and Thai alphabets share the same roots, but Lao has fewer characters and is written in a curvilinear fashion than Thai. However this is apparent today due to the communist party simplifying the spelling to be phonetic. There is speculation that the Lao and Thai script both derive from a common script due to the similarities between the scripts. When examining older forms of Thai scripts, many letters are almost identical to the Lao alphabet, some minority languages use separate writing systems, The Hmong have adopted the Roman Alphabet
21.
Thai numerals
â
The Thai language lacks grammatical number. A count is expressed in the form of an uninflected noun followed by a number. In Thai, counting is kannap, the classifier, laksananam Variations to this pattern do occur, a partial list of Thai words that also classify nouns can be found in Wiktionary category, Thai classifiers. Thai sĆ«n is written as oval 0 when using Arabic numerals, but a small circle àč when using traditional numerals and it is from Sanskrit ĆĆ«nya, as are the alternate names for numbers one to four given below, but not the counting 1. Thai names for N +1 and the regular digits 2 through 9 as shown in the table, below, resemble those in Chinese varieties as spoken in Southern China, Thai and Lao words for numerals are almost identical, however, the numerical digits vary somewhat in shape. Shown below is a comparison between three languages using Cantonese and Minnan characters and pronunciations, the Thai transliteration uses the Royal Thai General System of Transcription. Sanskrit lakh designates the place value of a digit, which are named for the powers of ten, the place is lak nuai, tens place, lak sip, hundreds place, lak roi. The number one following any multiple of sip becomes et, the number ten is the same as Minnan ć. Numbers from twenty to twenty nine begin with yi sip, names of the lak sip for 30 to 90, and for the lak of 100,1000,10,000,100,000 and million, are almost identical to those of the like Khmer numerals. For the numbers twenty-one through twenty-nine, the part signifying twenty, yi sip, see the alternate numbers section below. The hundreds are formed by combining roi with the tens and ones values, for example, two hundred and thirty-two is song roi sam sip song. The words roi, phan, muen, and saen should occur with a preceding numeral, nueng never precedes sip, so song roi nueng sip is incorrect. Native speakers will sometimes use roi nueng with different tones on nueng to distinguish one hundred from one hundred, however, such distinction is often not made, and ambiguity may follow. To resolve this problem, if the number 101 is intended, numbers above a million are constructed by prefixing lan with a multiplier. For example, ten million is sip lan, and a trillion is lan lan, colloquially, decimal numbers are formed by saying chut where the decimal separator is located. For example,1.01 is nueng chut sun nueng, fractional numbers are formed by placing nai between the numerator and denominator or using x suan y to clearly indicate. For example, â
is nueng nai sam or nueng suan sam, the word set can be omitted. The word khrueng is used for half and it precedes the measure word if used alone, but it follows the measure word when used with another number
22.
Chinese numerals
â
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 dĂ xiÄ. A forger could easily change the everyday characters äžć to äșć just by adding a few strokes and that would not be possible when writing using the financial characters ćæŸ and äŒä». 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 æŽ lit, hole 1, renamed ćčș lit. small 2, renamed äž€ lit. Double 7, renamed æ 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 ć
to mean 1012 in official documents. Numerals beyond èŒ zĂ i 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 çŸèŹ as the translation for mega
23.
Suzhou numerals
â
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 ăąäž instead of ăąăĄ 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 ćć
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
24.
Japanese numerals
â
The system of Japanese numerals is the system of number names used in the Japanese language. The Japanese numerals in writing are based on the Chinese numerals. Two sets of pronunciations for the numerals exist in Japanese, one is based on Sino-Japanese readings of the Chinese characters, there are two ways of writing the numbers in Japanese, in Hindu-Arabic numerals or in Chinese numerals. The Hindu-Arabic numerals are often used in horizontal writing. Numerals with multiple On readings use the Go-on and Kan-on variants respectively, * The special reading ă maru is also found. It may be used when reading individual digits of a number one after another. A popular example is the famous 109 store in Shibuya, Tokyo which is read as ichi-maru-kyĆ« and this usage of maru for numerical 0 is similar to reading numeral 0 in English as oh. However, as a number, it is written as 0 or rei. Additionally, two and five are pronounced with a vowel in phone numbers Starting at äž, numbers begin with äž if no digit would otherwise precede. That is,100 is just çŸ hyaku, and 1000 is just ć sen and this differs from Chinese as numbers begin with äž if no digit would otherwise precede starting at çŸ. And, if ć sen directly precedes the name of powers of myriad, äž ichi is normally attached before ć sen and that is,10,000,000 is normally read as äžćäž issenman. But if ć sen does not directly precede the name of powers of myriad or if numbers are lower than 2,000 and that is,15,000,000 is read as ćäșçŸäž sengohyakuman or äžćäșçŸäž issengohyakuman, and 1,500 as ćäșçŸ sengohyaku or äžćäșçŸ issengohyaku. The numbers 4 and 9 are considered unlucky in Japanese,4, pronounced shi, is a homophone for death,9, the number 13 is sometimes considered unlucky, though this is a carryover from Western tradition. On the contrary, numbers 7 and sometimes 8 are considered lucky in Japanese, in modern Japanese, cardinal numbers are given the on readings except 4 and 7, which are called yon and nana respectively. Alternate readings are used in names, day-of-month names. For instance, the decimal fraction 4.79 is always read yon-ten nana kyĆ«, though April, July, and September are called shi-gatsu, shichi-gatsu, the on readings are also used when shouting out headcounts. Intermediate numbers are made by combining elements, Tens from 20 to 90 are -jĆ« as in äșć to äčć. Hundreds from 200 to 900 are -hyaku, thousands from 2000 to 9000 are -sen
25.
Korean numerals
â
The Korean language has two regularly used sets of numerals, a native Korean system and Sino-Korean system. For both native and Sino- Korean numerals, the teens are represented by a combination of tens, for instance,15 would be sib-o, but not usually il-sib-o in the Sino-Korean system, and yeol-daseot in native Korean. Twenty through ninety are likewise represented in this manner in the Sino-Korean system, while Native Korean has its own unique set of words. The grouping of large numbers in Korean follow the Chinese tradition of myriads rather than thousands, the Sino-Korean system is nearly entirely based on the Chinese numerals. The distinction between the two systems is very important. Everything that can be counted will use one of the two systems, but seldom both, Sino-Korean words are sometimes used to mark ordinal usage, yeol beon means ten times while sip beon means number ten. When denoting the age of a person, one will usually use sal for the native Korean numerals, for example, seumul-daseot sal and i-sib-o se both mean twenty-five-year-old. See also East Asian age reckoning, the Sino-Korean numerals are used to denote the minute of time. For example, sam-sib-o bun means __,35 or thirty-five minutes, the native Korean numerals are used for the hours in the 12-hour system and for the hours 0,00 to 12,00 in the 24-hour system. The hours 13,00 to 24,00 in the 24-hour system are denoted using both the native Korean numerals and the Sino-Korean numerals. For example, se si means 03,00 or 3,00 a. m. /p. m. for counting above 100, Sino-Korean words are used, sometimes in combination,101 can be baek-hana or baeg-il. The usual liaison and consonant-tensing rules apply, so for example, ìììŹìŻ yesun-yeoseot is pronounced like, beon, ho, cha, and hoe are always used with Sino-Korean or Arabic ordinal numerals. For example, Yihoseon is Line Number Two in a subway system. 906íž is Apt #906 in a mailing address,906 without ho is not used in spoken Korean to imply apartment number or office suite number. The special prefix je is usually used in combination with suffixes to designate a specific event in sequential things such as the Olympics, in commerce or the financial sector, some hanja for each Sino-Korean numbers are replaced by alternative ones to prevent ambiguity or retouching. For verbally communicating number sequences such as numbers, ID numbers, etc. especially over the phone. For the same reason, military transmissions are known to use mixed native Korean and Sino-Korean numerals, note 1, ^ Korean assimilation rules apply as if the underlying form were ìë„ |sip. ryuk|, giving sim-nyuk instead of the expected sib-yuk. Note 2, ^ ^ ^ ^ ^ These names are considered archaic, note 3, ^ ^ ^ ^ ^ ^ ^ The numbers higher than 1020 are not usually used
26.
Vietnamese numerals
â
Historically Vietnamese has two sets of numbers, one is etymologically native Vietnamese, the other uses Sino-Vietnamese vocabulary. In the modern language the native Vietnamese vocabulary is used for both everyday counting and mathematical purposes, the Sino-Vietnamese vocabulary is used only in fixed expressions or in Sino-Vietnamese words. This is somewhat analogous to the way in which Latin and Greek numerals are used in modern English, Sino-Vietnamese words are also used for units of ten thousand or above, where native vocabulary was lacking. Among the languages of the Chinese cultural sphere, Japanese and Korean both use two systems, one native and one Chinese-based. The Chinese-based vocabulary is the one in common use, in Vietnamese, on the other hand, the Chinese-based system is not in everyday use. Numbers from 1 to 1000 are expressed using native Vietnamese vocabulary, in the modern Vietnamese writing system, numbers are written in the romanized script quá»c ngá»Ż or Arabic numerals. Prior to the 20th century Vietnam officially used Classical Chinese as a written language, for non-official purposes Vietnamese also had a writing system known as HĂĄn-NĂŽm. Under this system, Sino-Vietnamese numbers were written in HĂĄn tá»±, basic features of the Vietnamese numbering system include the following, Unlike other sinoxenic numbering systems, Vietnamese separates place values in thousands rather than myriads. The Sino-Vietnamese numbers are not in frequent use in modern Vietnamese, number values for these words follow usage in Ancient China, with each numeral increasing tenfold in digit value, ć being the number for 105, ć
for 106, et cetera. As a result, the value of triá»u differs from modern Chinese ć
, outside of fixed Sino-Vietnamese expressions, Sino-Vietnamese words are usually used in combination with native Vietnamese words. For instance, mÆ°á»i triá»u combines native mÆ°á»i and Sino-Vietnamese triá»u, the following table is an overview of the basic Vietnamese numeric figures, provided in both Native and Sino-Viet forms. For each number, the form that is commonly used is highlighted. Where there are differences between the Hanoi and Saigon dialects of Vietnamese, readings between each are differentiated below within the notes, when the number 1 appears after 20 in the unit digit, the pronunciation changes to má»t. When the number 4 appears after 20 in the digit, it is more common to use Sino-Viet tÆ°ïŒć. When the number 5 appears after 10 in the unit digit, when mÆ°á»i appears after 20, the pronunciation changes to mÆ°ÆĄi. Vietnamese ordinal numbers are preceded by the prefix thá»©, which is a Sino-Viet word which corresponds to æŹĄ. For the ordinal numbers of one and four, the Sino-Viet readings nháș„tïŒäž and tÆ°ïŒć are more commonly used, in all other cases, the native Vietnamese number is used. Chinese numerals Japanese numerals Korean numerals
27.
Counting rods
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Counting rods are small bars, typically 3â14 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 1â9 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 ZuÇjiÄgĆngshÄn 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, âćœć©äșæćźçźâ. 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
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Abjad numerals
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The Abjad numerals are a decimal numeral system in which the 28 letters of the Arabic alphabet are assigned numerical values. They have been used in the Arabic-speaking world since before the century when Arabic numerals were adopted. In modern Arabic, the word abjadÄ«yah means alphabet in general, in the Abjad system, the first letter of the Arabic alphabet, alif, is used to represent 1, the second letter, bÄÊŸ, is used to represent 2, etc. Individual letters also represent 10s and 100s, yÄÊŸ for 10, kÄf for 20, qÄf for 100, the word abjad itself derives from the first four letters in the Phoenician alphabet, Aramaic alphabet, Hebrew alphabet and other scripts for Semitic languages. These older alphabets contained only 22 letters, stopping at taw, the Arabic Abjad system continues at this point with letters not found in other alphabets, áčŻÄÊŸ=500, etc. The Abjad order of the Arabic alphabet has two different variants. Loss of samekh was compensated for by the split of shin Ś© into two independent Arabic letters, ŰŽ and ïș±, which moved up to take the place of samekh. The most common Abjad sequence, read right to left, is, This is commonly vocalized as follows. Before the introduction of the HinduâArabic numeral system, the numbers were used for all mathematical purposes. In modern Arabic, they are used for numbering outlines, items in lists. In English, points of information are sometimes referred to as A, B, and C, the abjad numbers are also used to assign numerical values to Arabic words for purposes of numerology. The common Islamic phrase ŰšŰłÙ
Ű§ÙÙÙ Ű§ÙŰ±ŰÙ
Ù Ű§ÙŰ±ŰÙÙ
bismillÄh al-Raáž„mÄn al-Raáž„Ä«m has a value of 786. The name AllÄh Ű§ÙÙÙ by itself has the value 66, a few of the numerical values are different in the alternative Abjad order. For four Persian letters these values are used, The Abjad numerals are equivalent to the earlier Hebrew numerals up to 400, the Hebrew numeral system is known as Gematria and is used in Kabbalistic texts and numerology. Like the Abjad order, it is used in times for numbering outlines and points of information. The Greek numerals differ in a number of ways from the Abjad ones, the Greek language system of letters-as-numbers is called isopsephy
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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, â1706 â7118 To evaluate a Cyrillic number, the values of all the figures are added up, for example, Ń°Đ is 700 +7, making 707. If the number is greater than 999, the sign is used to multiply the numbers value, for example, ÒĐ
is 6000, while ÒĐÒĐ 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, â°â°â° 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 â°
â° is 6 +10, early Cyrillic alphabet Glagolitic alphabet Relationship of Cyrillic and Glagolitic scripts Greek numerals Combining Cyrillic Millions
30.
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 fidĂ€l, 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 PÌŁait á°, a Geez innovation, is a modification of áčąĂ€dai áž, while Pesa á is based on Tawe á°. 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, áž„, m, Ć, r, s, ážł, b, t, áž«, n, ÊŸ, k, w, Êż, z, y, d, g, áč, pÌŁ, áčŁ, áčŁÌ, 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, É, 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 Ă€, 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 -yĂ€
31.
Georgian numerals
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The Georgian numerals are the system of number names used in Georgian, a language spoken in the country of Georgia. The Georgian numerals from 30 to 99 are constructed using a system, similar to the scheme used in Basque, French for numbers 80 through 99. An older method for writing numerals exists in which most of letters of the Georgian alphabet are assigned a numeric value. The Georgian cardinal numerals up to ten are primitives, as are the words for 20 and 100, other cardinal numbers are formed from these primitives via a mixture of decimal and vigesimal structural principles. The following chart shows the forms of the primitive numbers. Except for rva and tskhra, these words are all consonant-final stems, numbers from 11 to 19 are formed from 1 through 9, respectively, by prefixing t and adding meti. In some cases, the prefixed t coalesces with the consonant of the root word to form a single consonant. Numbers between 20 and 99 use a vigesimal system. g, the hundreds are formed by linking 2,3. 10 directly to the word for 100,1000 is expressed as atasi, and multiples of 1000 are expressed using atasi â so, for example,2000 is ori atasi. The final i is dropped when a number is added to a multiple of 100. The Georgian numeral system is a system of representing numbers using letters of the Georgian alphabet, numerical values in this system are obtained by simple addition of the component numerals, which are written greatest-to-least from left to right. *Both letters áł and áŁ are equal to 400 in numerical value and these letters have no numerical value
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Greek numerals
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Greek numerals are a system of writing numbers using the letters of the Greek alphabet. These alphabetic numerals are known as Ionic or Ionian numerals, Milesian numerals. In modern Greece, they are used for ordinal numbers. For ordinary cardinal numbers, however, Greece uses Arabic numerals, attic numerals, which were later adopted as the basis for Roman numerals, were the first alphabetic set. They were acrophonic, derived from the first letters of the names of the numbers represented and they ran =1, =5, =10, =100, =1000, and =10000. 50,500,5000, and 50000 were represented by the letter with minuscule powers of ten written in the top right corner, the same system was used outside of Attica, but the symbols varied with the local alphabets, in Boeotia, was 1000. The present system probably developed around Miletus in Ionia, 19th-century classicists placed its development in the 3rd century BC, the occasion of its first widespread use. The present system uses the 24 letters adopted by Euclid as well as three Phoenician and Ionic ones that were not carried over, digamma, koppa, and sampi. The position of characters within the numbering system imply that the first two were still in use while the third was not. Greek numerals are decimal, based on powers of 10, the units from 1 to 9 are assigned to the first nine letters of the old Ionic alphabet from alpha to theta. Each multiple of one hundred from 100 to 900 was then assigned its own separate letter as well and this alphabetic system operates on the additive principle in which the numeric values of the letters are added together to obtain the total. For example,241 was represented as, in ancient and medieval manuscripts, these numerals were eventually distinguished from letters using overbars, Î±, ÎČ, Îł, etc. In medieval manuscripts of the Book of Revelation, the number of the Beast 666 is written as ÏÎŸÏ, although the Greek alphabet began with only majuscule forms, surviving papyrus manuscripts from Egypt show that uncial and cursive minuscule forms began early. These new letter forms sometimes replaced the ones, especially in the case of the obscure numerals. The old Q-shaped koppa began to be broken up and simplified, the numeral for 6 changed several times. During antiquity, the letter form of digamma came to be avoided in favor of a special numerical one. By the Byzantine era, the letter was known as episemon and this eventually merged with the sigma-tau ligature stigma. In modern Greek, a number of changes have been made
33.
Hebrew numerals
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The system of Hebrew numerals is a quasi-decimal alphabetic numeral system using the letters of the Hebrew alphabet. The system was adapted from that of the Greek numerals in the late 2nd century BC, the current numeral system is also known as the Hebrew alphabetic numerals to contrast with earlier systems of writing numerals used in classical antiquity. The Greek system was adopted in Hellenistic Judaism and had been in use in Greece since about the 5th century BC, in this system, there is no notation for zero, and the numeric values for individual letters are added together. Each unit is assigned a letter, each tens a separate letter. The later hundreds are represented by the sum of two or three letters representing the first four hundreds, to represent numbers from 1,000 to 999,999, the same letters are reused to serve as thousands, tens of thousands, and hundreds of thousands. In Israel today, the system of Arabic numerals is used in almost all cases. The Hebrew numerals are used only in cases, such as when using the Hebrew calendar, or numbering a list. Numbers in Hebrew from zero to one million, Hebrew alphabet are used to a limited extent to represent numbers, widely used on calendars. In other situations Arabic numerals are used, cardinal and ordinal numbers must agree in gender with the noun they are describing. If there is no such noun, the form is used. For ordinal numbers greater than ten the cardinal is used and numbers above the value 20 have no gender, note, For ordinal numbers greater than 10, cardinal numbers are used instead. Note, For numbers greater than 20, gender does not apply, cardinal and ordinal numbers must agree in gender with the noun they are describing. If there is no such noun, the form is used. Ordinal numbers must also agree in number and definite status like other adjectives, the cardinal number precedes the noun, except for the number one which succeeds it. The number two is special - shnayim and shtayim become shney and shtey when followed by the noun they count, for ordinal numbers greater than ten the cardinal is used. The Hebrew numeric system operates on the principle in which the numeric values of the letters are added together to form the total. For example,177 is represented as Ś§ŚąŚ which corresponds to 100 +70 +7 =177, mathematically, this type of system requires 27 letters. In practice the last letter, tav is used in combination with itself and/or other letters from kof onwards, to numbers from 500
34.
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 oâclock but IX for nine oâclock, 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
35.
Attic numerals
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Attic numerals were used by the ancient Greeks, possibly from the 7th century BC. They were also known as Herodianic numerals because they were first described in a 2nd-century manuscript by Herodian. They are also known as acrophonic numerals because the symbols derive from the first letters of the words that the symbols represent, five, ten, hundred, thousand and ten thousand. The use of Î for 100 reflects the date of this numbering system. It wasnt until Aristophanes of Byzantium introduced the various accent markings during the Hellenistic period that the spiritus asper began to represent /h/, thus the word for a hundred would originally have been written ÎÎÎÎÎ€ÎÎ, as compared to the now more familiar spelling áŒÎșÎ±ÏÏÎœ. In modern Greek, the /h/ phoneme has disappeared altogether, unlike the more familiar Modern Roman numeral system, the Attic system contains only additive forms. Thus, the number 4 is written ÎÎÎÎ, not ÎÎ , the numerals representing 50,500, and 5,000 were composites of pi and a tiny version of the applicable power of ten. For example, is five times one thousand, specific numeral symbols were used to represent one drachma, to represent talents and staters, to represent ten mnas and to represent one half and one quarter. Attic numerals in Unicode Etruscan numerals
36.
Babylonian numerals
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Babylonian numerals were written in cuneiform, using a wedge-tipped reed stylus to make a mark on a soft clay tablet which would be exposed in the sun to harden to create a permanent record. The Babylonians, who were famous for their observations and calculations. Neither of the predecessors was a positional system and 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 attests to a relation with the Sumerian system. The Babylonian system is credited as being the first known positional numeral system and this was an extremely important development, because non-place-value systems require unique symbols to represent each power of a base, which can make calculations more difficult. Only two symbols were used to notate the 59 non-zero digits and these symbols and their values were combined to form a digit in a sign-value notation quite similar to that of Roman numerals, for example, the combination represented the digit for 23. A space was left to indicate a place value, similar to the modern-day zero. Babylonians later devised a sign to represent this empty place and they lacked a symbol to serve the function of radix point, so the place of the units had to be inferred from context, could have represented 23 or 23Ă60 or 23Ă60Ă60 or 23/60, etc. A common theory is that 60, a highly composite number, was chosen due to its prime factorization, 2Ă2Ă3Ă5, which makes it divisible by 1,2,3,4,5,6,10,12,15,20. Integers and fractions were represented identically â a radix point was not written, the Babylonians did not technically have a digit for, nor a concept of, the number zero. Although they understood the idea of nothingness, it was not seen as a numberâmerely the lack of a number, what the Babylonians had instead was a space to mark the nonexistence of a digit in a certain place value. Babylon Babylonia History of zero Numeral system Menninger, Karl W. Number Words and Number Symbols, Number, From Ancient Civilisations to the Computer. CESCNC - a handy and easy-to use numeral converter
37.
Brahmi numerals
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The Brahmi numerals are a numeral system attested from the 3rd century BCE. They are the direct ancestors of the modern Indian and HinduâArabic numerals. However, they were 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, there were also symbols for 100 and 1000 which were combined in ligatures with the units to signify 200,300,2000,3000, etc. In the oldest inscriptions,4 is a +, reminiscent of the X of neighboring KharoáčŁáčhÄ«, however, the other unit numerals appear to be arbitrary symbols in even the oldest inscriptions. Likewise, the units for the tens are not obviously related to other or to the units. With a similar writing instrument, the forms of such groups of strokes could easily be broadly similar as well. Another possibility is that the numerals were acrophonic, like the Attic numerals, and based on the KharoáčŁáčhÄ« alphabet. For instance, chatur 4 early on took a Â„ shape much like the Kharosthi letter ch, panca 5 looks remarkably like Kharosthi p, and so on through shat 6, sapta 7, however, there are problems of timing and lack of records. The full set of numerals is not attested until the 1st-2nd century CE,400 years after Ashoka, both suggestions, that the numerals derive from tallies or that theyre alphabetic, are purely speculative at this point, with little evidence to decide between them. Brahmi script Georges Ifrah, The Universal History of Numbers, From Prehistory to the Invention of the Computer, translated by David Bellos, Sophie Wood, pub. Karl Menninger, Number Words and Number Symbols - A Cultural History of Numbers ISBN 0-486-27096-3 David Eugene Smith and Louis Charles Karpinski, The Hindu-Arabic Numerals
38.
Chuvash numerals
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Chuvash numerals is an ancient numeral system from the Old Turkic script the Chuvash people used. Those numerals originate from finger numeration and they look like Roman numerals, but larger numerals stay at the right side. It was possible to carve those numerals on wood, in some cases numerals were preserved until the beginning of 20th century
39.
Egyptian numerals
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The system of ancient Egyptian numerals was used in Ancient Egypt around 3000 BC until the early first millennium AD. It was a system of numeration based on the scale of ten, often rounded off to the power, written in hieroglyphs. The hieratic form of numerals stressed an exact finite series notation, the Ancient Egyptian system used bases of ten. The following hieroglyphics were used to denote powers of ten, Multiples of these values were expressed by repeating the symbol as many times as needed, for instance, a stone carving from Karnak shows the number 4622 as Egyptian hieroglyphs could be written in both directions. The symbol nfr, meaning beautiful, was used to indicate the base level in drawings of tombs and pyramids. Rational numbers could also be expressed, but only as sums of fractions, i. e. sums of reciprocals of positive integers, except for â2â3. The hieroglyph indicating a fraction looked like a mouth, which meant part, Fractions were written with this fractional solidus, i. e. the numerator 1, and the positive denominator below. As with most modern day languages, the ancient Egyptian language could also write out numerals as words phonetically, just like one can write thirty instead of 30 in English. The word, for instance, was written as while the numeral was This was, however, uncommon for most numbers other than one, instances of numerals written in hieratic can be found as far back as the Early Dynastic Period. The Old Kingdom Abusir Papyri are an important corpus of texts that utilize hieratic numerals. A large number like 9999 could thus be written only four signsâcombining the signs for 9000,900,90. Boyer saw the new hieratic numerals as ciphered, mapping one number onto one Egyptian letter for the first time in human history, greeks adopted the new system, mapping their counting numbers onto two of their alphabets, the Doric and Ionian. In the oldest hieratic texts the individual numerals were written in a ciphered relationship to the Egyptian alphabet. But during the Old Kingdom a series of standardized writings had developed for sign-groups containing more than one numeral, however, repetition of the same numeral for each place-value was not allowed in the hieratic script. As the hieratic writing system developed over time, these sign-groups were further simplified for quick writing, two famous mathematical papyri using hieratic script are the Moscow Mathematical Papyrus and the Rhind Mathematical Papyrus. The majuscule letter A in some reconstructed forms means that the quality of that remains uncertain, Ancient Egypt Egyptian language Egyptian mathematics Allen. Middle Egyptian, An Introduction to the Language and Culture of Hieroglyphs, Egyptian Grammar, Being an Introduction to the Study of Hieroglyphs. Hieratische PalĂ€ographie, Die aegyptische Buchschrift in ihrer Entwicklung von der FĂŒnften Dynastie bis zur rĂ¶mischen Kaiserzeit, Introduction Egyptian numerals Numbers and dates http, //egyptianmath. blogspot. com
40.
Etruscan numerals
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The Etruscan numerals were used by the ancient Etruscans. The system was adapted from the Greek Attic numerals and formed the inspiration for the later Roman numerals via the Old Italic script, there is very little surviving evidence of these numerals. Examples are known of the symbols for numbers, but it is unknown which symbol represents which number. Thanks to the written out on the Tuscania dice, there is agreement that zal, ci, huÎž. The assignment depends on whether the numbers on opposite faces of Etruscan dice add up to seven, some dice found did not show this proposed pattern. An aspect of the Etruscan numeral system is that some numbers, so 17 is not written *semÏ-Ćar as users of the Hindu-Arabic numerals might reason. One instead finds ci-em zaÎžrum, literally three from twenty, the numbers 17,18 and 19 are all written in this way. The general agreement among Etruscologists nowadays is the following, Archaeological evidence strongly supports the correspondence 4/huth and 6/sa. In the same necropolis, in the Tomb of the Anina, which contains six burial places, an inscription reads, sa suthi cherichunce, however, other scholars disagree with this attribution. In this connection, in October 2011, Artioli and colleagues presented evidence from 93 Etruscan dice allowing the firm attribution of the numeral 6 to the graphical value huth and 4 to sa. In 2006, S. A. Yatsemirsky presented evidence that zar = Ćar meant â12â while halÏ meant â10â, according to his interpretation, the attested form huÎžzar was used for âsixteenâ, not âfourteenâ, assuming huÎž meant four. Much debate has been carried out about a possible Indo-European origin of the Etruscan cardinals, in the words of Larissa Bonfante, What these numerals show, beyond any shadow of a doubt, is the non-Indo-European nature of the Etruscan language
41.
Kaktovik Inupiaq numerals
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Inuit, like other Eskimo languages, uses a vigesimal counting system. Inuit counting has sub-bases at 5,10, and 15, arabic numerals, consisting of 10 distinct digits are not adequate to represent a base-20 system. The numeral system has helped to revive counting in Inuit, which had been falling into disuse among Inuit speakers due to the prevalence of the system in schools. The picture below shows the numerals 1â19 and then 0, twenty is written with a one and a zero, forty with a two and a zero, and four hundred with a one and two zeros. The corresponding spoken forms are, In Greenlandic Inuit language
42.
Kharosthi
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The Kharosthi script, also spelled Kharoshthi or KharoáčŁáčhÄ«, 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+10A00âU+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, à© 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+10A00âU+10A5F, Brahmi History of Afghanistan History of Pakistan Pre-Islamic scripts in Afghanistan Kaschgar und die KharoáčŁáčhÄ« 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, GĂ©rard. Les premiers systĂšmes dĂ©criture en Inde, in Annuaire du CollĂšge de France 1988-1989 HinĂŒber, der Beginn der Schrift und frĂŒhe 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