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Arabic Numerals
ARABIC NUMERALS, also called HINDU–ARABIC NUMERALS are the ten digits : 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, based on the Hindu–Arabic numeral system , the most common system for the symbolic representation of numbers in the world today. 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, which was developed by ancient mathematicians in the Indian subcontinent around AD 500. The system was adopted by Arabic
Arabic
mathematicians in Baghdad
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
Arabic
letters in the Maghreb
Maghreb
, the western region of the Arab world
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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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Sans-serif
In typography and lettering, a SANS-SERIF, SANS SERIF, GOTHIC, or simply SANS letterform is one that does not have extending features called "serifs " at the end of strokes. Sans-serif
Sans-serif
fonts tend to have less line width variation than serif fonts. In most print, they are often used for headings rather than for body text. They are often used to convey simplicity and modernity or minimalism. Sans-serif
Sans-serif
fonts have become the most prevalent for display of text on computer screens. On lower-resolution digital displays, fine details like serifs may disappear or appear too large. The term comes from the French word sans, meaning "without" and "serif" of uncertain origin, possibly from the Dutch word schreef meaning "line" or pen-stroke. Before the term "sans-serif" became common in English typography, a number of other terms had been used
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Positional Notation
POSITIONAL NOTATION or PLACE-VALUE NOTATION is a method of representing or encoding numbers . Positional notation
Positional notation
is distinguished from other notations (such as Roman numerals
Roman numerals
) for its use of the same symbol for the different orders of magnitude (for example, the "ones place", "tens place", "hundreds place"). This greatly simplified arithmetic , leading to the rapid spread of the notation across the world. With the use of a radix point (decimal point in base-10), the notation can be extended to include fractions and the numeric expansions of real numbers . The Babylonian numeral system , base-60, was the first positional system developed, and its influence is present today in the way time and angles are counted in tallies related to 60, like 60 minutes in an hour, 360 degrees in a circle
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Āryabhaṭa Numeration
The ĀRYABHAṭA NUMERATION is a system of numerals based on Sanskrit phonemes . It was introduced in the early 6th century in India by Āryabhaṭa , in the first chapter titled Gītika Padam of his Aryabhatiya . It attributes a numerical value to each syllable of the form consonant+vowel possible in Sanskrit phonology , from ka = 1 up to hau = 1018 . CONTENTS * 1 History * 2 Example * 3 Numeral table * 4 See also * 5 References HISTORYThe basis of this number system is mentioned in the second stanza of the first chapter of Aryabhatiya . The Varga (Group/Class) letters ka to ma are to be placed in the varga (square) places (1st, 100th, 10000th, etc.) and Avarga letters like ya, ra, la .. have to be placed in Avarga places (10th, 1000th, 100000th, etc.). The Varga letters kak to ma have value from 1, 2, 3 .. up to 25 and Avarga letters ya to ha have value 30, 40, 50.. up to 100
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Korean Numerals
The Korean language
Korean language
has two regularly used sets of numerals , a native Korean system and Sino-Korean system. CONTENTS * 1 Construction * 2 Numerals (Cardinal) * 3 Pronunciation * 4 Constant suffixes used in Sino-Korean ordinal numerals * 5 Substitution for disambiguation * 6 Notes * 7 References * 8 See also CONSTRUCTIONFor both native and Sino- KOREAN NUMERALS, the teens (11 through 19) are represented by a combination of tens and the ones places. For instance, 15 would be sib-o (십오; 十五), but not usually il-sib-o in the Sino-Korean system, and yeol-daseot (열다섯) in native Korean. Twenty through ninety are likewise represented in this place-holding manner in the Sino-Korean system, while Native Korean has its own unique set of words, as can be seen in the chart below. The grouping of large numbers in Korean follow the Chinese tradition of myriads (10000) rather than thousands (1000)
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Radix
In mathematical numeral systems , the RADIX or BASE is the number of unique digits , including zero, used to represent numbers in a positional numeral system . For example, for the decimal system (the most common system in use today) the radix is ten, because it uses the ten digits from 0 through 9. In any standard positional numeral system, a number is conventionally written as (x)y with x as the string of digits and y as its base, although for base ten the subscript is usually assumed (and omitted, together with the pair of parentheses ), as it is the most common way to express value . For example, (100)dec = 100 (in the decimal system) represents the number one hundred, while (100)2 (in the binary system with base 2) represents the number four. CONTENTS * 1 Etymology * 2 In numeral systems * 3 See also * 4 References * 5 External links ETYMOLOGY Radix
Radix
is a Latin word for "root"
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Prehistoric Numerals
Counting
Counting
in prehistory was first assisted by using body parts, primarily the fingers . This is reflected in the etymology of certain number names , such as in the names of ten and hundred in the Proto-Indo-European numerals , both containing the root *dḱ also seen in the word for "finger" (Latin digitus, cognate to English toe). Early systems of counting using tally marks appear in the Upper Paleolithic . The first more complex systems develop in the Ancient Near East together with the development of early writing out of proto-writing systems
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Counting Rods
COUNTING RODS (traditional Chinese : 籌; simplified Chinese : 筹; pinyin : chóu; Japanese : 算木; rōmaji : sangi) are small bars, typically 3–14 cm long, that were used by mathematicians for calculation in ancient China
China
, Japan
Japan
, Korea
Korea
, and Vietnam
Vietnam
. They are placed either horizontally or vertically to represent any integer or rational number . The written forms based on them are called ROD NUMERALS
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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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Kharosthi Numerals
Egyptian hieroglyphs
Egyptian hieroglyphs
32 c. BCE * Hieratic
Hieratic
32 c. BCE * Demotic 7 c. BCE * Meroitic 3 c. BCE* Proto-Sinaitic 19 c. BCE * Ugaritic 15 c. BCE* Epigraphic South Arabian 9 c. BCE * Ge’ez 5–6 c. BCE* Phoenician 12 c. BCE * Paleo-Hebrew 10 c. BCE * Samaritan 6 c. BCE* Libyco-Berber 3 c. BCE * Tifinagh * Paleohispanic (semi-syllabic) 7 c. BCE* Aramaic 8 c. BCE * Kharoṣṭhī 4 c. BCE* Brāhmī 4 c. BCE * Brahmic family
Brahmic family
(see) * E.g. Tibetan 7 c. CE * Hangul
Hangul
(core letters only) 1443* Devanagari 13 c. CE * Canadian syllabics 1840 * Hebrew 3 c. BCE* Pahlavi 3 c. BCE * Avestan 4 c. CE * Palmyrene 2 c. BCE* Syriac 2 c. BCE * Nabataean 2 c. BCE * Arabic 4 c. CE * N\'Ko 1949 CE* Sogdian 2 c. BCE * Orkhon (old Turkic) 6 c
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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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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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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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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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Attic Numerals
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. See Greek numerals
Greek numerals
and acrophony . DECIMAL SYMBOL GREEK NUMERAL IPA 1 Ι – – 5 Π πέντε 10 Δ δέκα 100 Η ἑκατόν 1000 Χ χίλιοι / χιλιάς 10000 Μ μύριονThe use of Η for 100 reflects the early date of this numbering system: Η (Eta ) in the early Attic alphabet represented the sound /h/. In later, "classical" Greek, with the adoption of the Ionic alphabet throughout the majority of Greece, the letter eta had come to represent the long e sound while the rough aspiration was no longer marked
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