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Hindu–Arabic Numeral System
The HINDU–ARABIC NUMERAL SYSTEM (also called the ARABIC NUMERAL SYSTEM or HINDU NUMERAL SYSTEM) a positional decimal numeral system , is the most common system for the symbolic representation of numbers in the world. It was invented between the 1st and 4th centuries by Indian mathematicians . The system was adopted in Arabic
Arabic
mathematics by the 9th century. Influential were the books of Muḥammad ibn Mūsā al-Khwārizmī (On the Calculation with Hindu
Hindu
Numerals, c.825) and Al-Kindi
Al-Kindi
(On the Use of the Hindu
Hindu
Numerals, c.830). The system later spread to medieval Europe
Europe
by the High Middle Ages
High Middle Ages
. The system is based upon ten (originally nine) different glyphs . The symbols (glyphs) used to represent the system are in principle independent of the system itself
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Dzongkha Numerals
Dzongkha , the national language of Bhutan
Bhutan
, has two numeral systems, one vigesimal (base 20), 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 1–9. VIGESIMAL 1 ciː 11 cu-ci 2 ˈɲiː 12 cu-ɲi 3 sum 13 cu-sum 4 ʑi 14 cu-ʑi 5 ˈŋa 15 ce-ŋa 6 ɖʱuː 16 cu-ɖu 7 dyn 17 cup-dỹ 8 ɡeː 18 cop-ɡe 9 ɡuː 19 cy-ɡu 10 cu-tʰãm* 20 kʰe ciː*When it appears on its own, 'ten' is usually said cu-tʰãm 'a full ten'. In combinations it is simply cu. Factors of 20 are formed from kʰe
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Brahmi Numerals
The BRAHMI NUMERALS are a numeral system attested from the 3rd century BCE (somewhat later in the case of most of the tens). They are the direct graphic ancestors of the modern Indian and Hindu–Arabic numerals . However, they were conceptually distinct from these later systems, as they were not used as a positional system with a zero . Rather, there were separate numerals for each of the tens (10, 20, 30, etc.). There were also symbols for 100 and 1000 which were combined in ligatures with the units to signify 200, 300, 2000, 3000, etc. ORIGINSThe source of the first three numerals seems clear: they are collections of 1, 2, and 3 strokes, in Ashoka 's era vertical I, II, III like Roman numerals
Roman numerals
, but soon becoming horizontal like the modern Chinese numerals . In the oldest inscriptions, 4 is a +, reminiscent of the X of neighboring Kharoṣṭhī , and perhaps a representation of 4 lines or 4 directions
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Egyptian Numerals
The system of ancient EGYPTIAN NUMERALS was used in Ancient Egypt from around 3000 BC until the early first millennium AD. It was a system of numeration based on multiples of ten, often rounded off to the higher power, written in hieroglyphs . The Egyptians had no concept of a place-valued system such as the decimal system . The hieratic form of numerals stressed an exact finite series notation, ciphered one to one onto the Egyptian alphabet
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Etruscan Numerals
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
Roman numerals
via the Old Italic script . ETRUSCAN ARABIC SYMBOL * OLD ITALIC θu 1 𐌠 maχ 5 𐌡 śar 10 𐌢 muvalχ 50 𐌣 ? 100 or C 𐌟There is very little surviving evidence of these numerals. Examples are known of the symbols for larger numbers, but it is unknown which symbol represents which number. Thanks to the numbers written out on the Tuscania
Tuscania
dice , there is agreement that zal, ci, huθ and śa are the numbers up to six (besides 1 and 5). The assignment depends on whether the numbers on opposite faces of Etruscan dice add up to seven, like nowadays. Some dice found did not show this proposed pattern
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Babylonian Numerals
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 astronomical observations and calculations (aided by their invention of the abacus ), used a sexagesimal (base-60) positional numeral system inherited from either the Sumerian or the Eblaite civilizations. Neither of the predecessors was a positional system (having a convention for which ‘end’ of the numeral represented the units). CONTENTS * 1 Origin * 2 Characters * 3 Zero * 4 See also * 5 Notes * 6 Bibliography * 7 External links ORIGINThis system first appeared around 2000 BC; its structure reflects the decimal lexical numerals of Semitic languages
Semitic languages
rather than Sumerian lexical numbers
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Inuit Numerals
Inuit , like other Eskimo languages (and Celtic and Mayan languages as well), uses a vigesimal counting system. Inuit counting has sub-bases at 5, 10, and 15. Arabic numerals
Arabic numerals
, consisting of 10 distinct digits (0-9) are not adequate to represent a base-20 system. Students from Kaktovik, Alaska , came up with the KAKTOVIK INUPIAQ NUMERALS, which has since gained wide use among Alaskan Iñupiaq , and is slowly gaining ground in other countries where dialects of the Inuit language are spoken. 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 base-10 system in schools. The picture below shows the numerals 1–19 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
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Aegean Numerals
AEGEAN NUMBERS was the numeral system used by the Minoan and Mycenaean civilizations. They are attested in several Aegean scripts ( Linear A , Linear B
Linear B
). They may have survived in the Cypro-Minoan script , where a single sign with "100" value is attested so far on a large clay tablet from Enkomi
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Cyrillic Numerals
CYRILLIC NUMERALS are a numeral system derived from the Cyrillic script , developed in the First Bulgarian Empire
First Bulgarian Empire
in the late 10th century. It was used in the First Bulgarian Empire
First Bulgarian Empire
and by South and East Slavic peoples
Slavic peoples
. The system was used in Russia as late as the early 18th century, when Peter the Great replaced it with Arabic numerals as part of his civil script reform initiative. Cyrillic numbers played a role in Peter the Great's currency reform plans, too, with silver wire kopecks issued after 1696 and mechanically minted coins issued between 1700 and 1722 inscribed with the date using Cyrillic numerals. By 1725, Russian Imperial coins had transitioned to Arabic numerals. The Cyrillic numerals
Cyrillic numerals
may still be found in books written in the Church Slavonic language
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Georgian Numerals
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 base-20 system, similar to the scheme used in Basque , French for numbers 80 through 99, or the notion of the score in English. The symbols for numbers in modern Georgian texts are the same Arabic numerals used in English, except that the comma is used as the decimal separator , and digits in large numbers are divided into groups of three using spaces or periods (full stops). An older method for writing numerals exists in which most of letters of the Georgian alphabet (including some obsolete letters) are each assigned a numeric value
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Greek Numerals
GREEK NUMERALS, also known as IONIC, IONIAN, MILESIAN, or ALEXANDRIAN NUMERALS, are a system of writing numbers using the letters of the Greek alphabet . In modern Greece
Greece
, they are still used for ordinal numbers and in contexts similar to those in which Roman numerals
Roman numerals
are still used elsewhere in the West. For ordinary cardinal numbers , however, Greece
Greece
uses Arabic numerals
Arabic numerals
. CONTENTS * 1 History * 2 Description * 3 Table * 4 Higher numbers * 5 Zero * 6 See also * 7 References * 8 External links HISTORYThe Minoan and Mycenaean civilizations ' Linear A and Linear B alphabets used a different system, called Aegean numerals
Aegean numerals
, which included specialized symbols for numbers: 𐄇 = 1, 𐄐 = 10, 𐄙 = 100, 𐄢 = 1000, and 𐄫 = 10000
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Hebrew Numerals
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
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. These systems were inherited from usage in the Aramaic and Phoenician scripts, attested from c. 800 BC in the so-called Samaria ostraca and sometimes known as Hebrew-Aramaic numerals, ultimately derived from the Egyptian Hieratic numerals . The Greek system was adopted in Hellenistic Judaism
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
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Maya Numerals
The MAYA NUMERAL SYSTEM is a vigesimal (base-20) positional notation used in the Maya civilization to represent numbers. The numerals are made up of three symbols; zero (shell shape, with the plastron uppermost), one (a dot) and five (a bar). For example, thirteen is written as three dots in a horizontal row above two horizontal lines stacked above each other. 400s 20s 1s 33 429 5125 Numbers after 19 were written vertically in powers of twenty. For example, thirty-three would be written as one dot above three dots, which are in turn atop two lines. The first dot represents "one twenty" or "1×20", which is added to three dots and two bars, or thirteen. Therefore, (1×20) + 13 = 33. Upon reaching 202 or 400, another row is started (203 or 8000, then 204 or 160,000, and so on). The number 429 would be written as one dot above one dot above four dots and a bar, or (1×202) + (1×201) + 9 = 429
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Muisca Numerals
MUISCA NUMERALS were the numeric notation system used by the Muisca , one of the four advanced civilizations of the Americas
Americas
before the Spanish conquest of the Muisca . Just like the Mayas , the Muisca had a vigesimal numerical system, based on multiples of twenty (Chibcha : gueta). The Muisca numerals
Muisca numerals
were based on counting with fingers and toes. They had specific numbers from one to ten, yet for the numbers between eleven and nineteen they used "foot one" (11) to "foot nine" (19). The number 20 was the 'perfect' number for the Muisca which is visible in their calendar . To calculate higher numbers than 20 they used multiples of their 'perfect' number; gue-muyhica would be "20 times 4", so 80. To describe "50" they used "20 times 2 plus 10"; gue-bosa asaqui ubchihica, transcripted from guêboʒhas aſaqɣ hubchìhicâ
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Quaternary Numeral System
QUATERNARY is the base -4 numeral system . It uses the digits 0, 1, 2 and 3 to represent any real number . Four is the largest number within the subitizing range and one of two numbers that is both a square and a highly composite number (the other being 36), making quaternary a convenient choice for a base at this scale. Despite being twice as large, its radix economy is equal to that of binary. However, it fares no better in the localization of prime numbers (the next best being the primorial base six, senary ). Quaternary shares with all fixed-radix numeral systems many properties, such as the ability to represent any real number with a canonical representation (almost unique) and the characteristics of the representations of rational numbers and irrational numbers . See decimal and binary for a discussion of these properties
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Quinary
QUINARY (BASE -5 or PENTAL ) is a numeral system with five as the base. A possible origination of a quinary system is that there are five fingers on either hand . In the quinary place system, five numerals, from 0 to 4 , are used to represent any real number . According to this method, five is written as 10, twenty-five is written as 100 and sixty is written as 220. As five is a prime number, only the reciprocals of the powers of five terminate, although its location between two highly composite numbers (4 and 6 ) guarantees that many recurring fractions have relatively short periods. Today, the main usage of base 5 is as a biquinary system, which is decimal using five as a sub-base . Another example of a sub-base system, is sexagesimal , base 60, which used 10 as a sub-base. Each quinary digit has log25 (approx. 2.32) bits of information
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