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Encyclopedia > Vigesimal
Numeral systems

List of numeral system topics A numeral is a symbol or group of symbols that represents a number. ... This is a list of numeral system topics, by Wikipedia page. ...

Hindu-Arabic system Abjad
Armenian
Babylonian
Brahmi
Chinese
Cyrillic
Egyptian
Etruscan
Ge'ez
Greek Hebrew
Japanese
Khmer
Korean
Mayan
Roman

D'ni (fictitious)
Positional systems
with various bases:

2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 20, 24, 26, 27, 30, 32, 36, 60, 64 The system of Hindu-Arabic numerals is a positional decimal numeral system that evolved from the Brahmi numeral system in ancient India, from the 9th century documented to have used a positional notation including a zero symbol. ... // Origins The Hindu-Arabic numeral system originated from the Hindu numeral system, which is a pure place value system, that requires a zero. ... Various symbol sets are used to represent numbers in the Hindu-Arabic numeral system, all of which evolved from the Brahmi numerals. ... Numerals sans serif Arabic numerals, also known as Hindu-Arabic numerals, Indian numerals, Hindu numerals, European numerals, and Western numerals, are the most common symbolic representation of numbers around the world. ... The Eastern Arabic numerals (also called Eastern Arabic numerals, Arabic-Indic numerals, Arabic Eastern Numerals) are the symbols (glyphs) used to represent the Hindu-Arabic numeral system in conjunction with the Arabic alphabet in Egypt, Iran, Pakistan and parts of India, and also in the no longer used Ottoman Turkish... India has produced many numeral systems. ... The Abjad numerals are a numeral system which was used in the Arabic-speaking world prior to the use of the Arabic numerals (which are actually of Indian origin). ... 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 Brahmi numerals are an indigenous Indian numeral system attested from the 3rd century BCE (somewhat later in the case of most of the tens). ... Cyrillic numerals was a numbering system derived from the Cyrillic alphabet, used by South and East Slavic peoples. ... The Etruscan numerals were used by the ancient Etruscans. ... Note: This article contains special characters. ... Attic numerals were used by 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 Herodianus. ... Ionian numerals were used by the ancient Greeks, possibly before the 7th century BC. They are also known by the names Milesian numerals or Alexandrian numerals. ... The system of Hebrew numerals is a quasi-decimal alphabetic numeral system using the letters of the Hebrew alphabet. ... Khmer numerals are the numerals used in the Khmer language of Cambodia. ... Mayan numerals. ... The system of Roman numerals is a numeral system originating in ancient Rome, and was adapted from Etruscan numerals. ... Myst franchise Games Myst Riven Myst III: Exile Myst IV: Revelation Myst V: End of Ages Uru: Ages Beyond Myst Ages of: Myst Riven Myst III: Exile Myst IV: Revelation Uru Novels Myst: The Book of Atrus   Tiana   Dni Comic Books #0   #1 Miscellaneous Dni Ages   The... Positional notation is a system in which each position has a value represented by a unique symbol or character. ... In mathematics, the base or radix is the number of various unique symbols (digits), including zero, that a positional numeral system uses to represent numbers in a given counting system. ... The binary numeral system (base 2 numerals) represents numeric values using two symbols, typically 0 and 1. ... Ternary or trinary is the base-3 numeral system. ... Quaternary is the base four numeral system. ... Quinary (base-5) is a numeral system with five as the base. ... A senary numeral system is a base-six numeral system. ... The septenary numeral system is the base seven number system, and uses the digits 0-6. ... The octal numeral system is the base-8 number system, and uses the digits 0 to 7. ... Nonary is a base 9 numeral system, typically using the digits 0-8, but not the digit 9. ... The decimal (base ten or occasionally denary) numeral system has ten as its base. ... The undecimal (base-11) positional notation system is based on the number eleven, rather than ten as in decimal or eight in octal and so on. ... A duodecimal multiplication table The duodecimal (also known as base-12 or dozenal) system is a numeral system using twelve as its base. ... Base-13, tridecimal, or tredecimal is a nonstandard positional numeral system with thirteen as its base. ... In mathematics and computer science, base-16, hexadecimal, or simply hex, is a numeral system with a radix or base of 16 usually written using the symbols 0–9 and A–F or a–f. ... As there are 24 hours in a day a numbering system based upon 24, and as the base 12 is convenient here some examples of the base 24 (quadrovigesimal) system. ... A Hexavigesimal numeral system has a base of twenty-six. ... A Septemvigesimal numeral system has a base of twenty-seven. ... Base 30 or trigesimal is a positional numeral system using 30 as the radix. ... Base32 is a derivation of Base64 with the following additional properties: The resulting character set is all uppercase, which can often be beneficial when using a case-sensitive filesystem. ... Base 36 refers to a positional numeral system using 36 as the radix. ... The sexagesimal (base-sixty) is a numeral system with sixty as the base. ... Base 64 literally means a positional numeral system using a base of 64. ...

Non-standard systems:

1, -2, Signed-digit, Non-adjacent, -3, Balanced ternary, mixed, Factoradic, Fibonacci coding, bijective, 2i, φ Non-standard positional numeral systems are numeral systems that may be denoted positional systems, but that deviate in one way or another from the following description of standard positional system: In a standard positional numeral system, the base b is a positive integer, and b different glyphs are used to... The unary numeral system is the simplest numeral system to represent natural numbers: in order to represent a number N, an arbitrarily chosen symbol is repeated N times. ... Negabinary (radix -2) is a fairly obscure numeral system used in the experimental Polish computers SKRZAT 1 and BINEG in 1950. ... Signed-digit representation of numbers indicates that values can be prefixed with a − (minus) sign to indicate that they are negative. ... The non-adjacent form (NAF) of a number is a unique signed-digit representation. ... Negaternary is a numeral system in which numbers are written as sums of successive powers of -3. ... Balanced Ternary (aka Signary) is a method of numeric representation which expands on binary and is similar to trinary. ... Mixed radix numeral systems are more general than the usual ones in that the numerical base may vary from position to position. ... The factorial based radix or factoradic is a factorial based mixed radix numeral scheme: radix: 5! 4! 3! 2! 1! decimal: 120 24 6 2 1 In this numbering system, the rightmost digit may be 0 or 1, the next 0, 1, or 2, and so on. ... The Fibonacci code is a universal code which encodes positive integers into binary code words. ... Bijective numeration is any numeral system that establishes a bijection between the set of non-negative integers and the set of finite strings over a finite set of digits. ... The quater-imaginary numeral system was first proposed by Donald Knuth in 1955, in a submission to a high-school science talent search. ... Golden ratio base refers to the use of the golden ratio, the irrational number ≈1. ...

edit

The vigesimal or base-20 numeral system is based on twenty (in the same way in which the ordinary decimal numeral system is based on ten). Twenty is the sum of all fingers and toes on unmutated human hands and feet, and is the product of five and four. In mathematics, the base or radix is the number of various unique symbols (digits), including zero, that a positional numeral system uses to represent numbers in a given counting system. ... 20 (twenty) is the natural number following 19 and preceding 21. ... 20 (twenty) is the natural number following 19 and preceding 21. ... Fingers of the human left hand The finger is any of the digits of the hand in humans and other species such as the great apes. ... 5 (five) is a number, numeral, and glyph. ... 4 (four) is a number, numeral, and glyph. ...

Contents


Places

In a vigesimal place system, twenty individual numerals (or digit symbols) are used, ten more than in the usual decimal system. One modern method of finding the extra needed symbols is to write ten as the letter A20 (the 20 means base 20), to write nineteen as J20, and the numbers between with the corresponding letters of the alphabet. (This is an extension of the common practice of writing hexadecimal numerals over 9 with the letters "A-F".) Another method skips over the letter "I", in order to avoid confusion between I20 as eighteen and 1 (one), so that the number eighteen is written as J20, and nineteen is written as K20. The number twenty is written as 1020. Digit may refer to: A finger or a toe Numerical digit, as used in mathematics or computer science Digit (unit), an ancient meterological unit Digit (magazine), an Indian information technology magazine This is a disambiguation page: a list of articles associated with the same title. ... 10 (ten) is an even natural number following 9 and preceding 11. ... 19 (nineteen) is the natural number following 18 and preceding 20. ... 18 (eighteen) is the natural number following 17 and preceding 19. ... Look up one in Wiktionary, the free dictionary. ...


According to this notation, 2020 means forty (= two times twenty), DA20 means two hundred seventy (= thirteen times twenty plus ten), 10020 means four hundred (= twenty times twenty). In the rest of this article below, numbers are expressed in decimal notation, unless specified otherwise. For example, 10 means ten, 20 means twenty. 40 (forty) is the natural number following 39 and preceding 41. ... Four hundred is the natural number following three hundred ninety-nine and preceding four hundred one. ... 10 (ten) is an even natural number following 9 and preceding 11. ... 20 (twenty) is the natural number following 19 and preceding 21. ...


Usage

In many languages, especially in Europe, 20 is a base, at least with respect to the linguistic structure of the names of certain numbers (though a thoroughgoing consistent vigesimal system, based on the powers 20, 400, 8000 etc., is not generally used). Europe is conventionally considered one of the seven continents of Earth which, in this case, is more a cultural and political distinction than a physiographic one, leading to some dispute as to Europes actual borders. ... 20 (twenty) is the natural number following 19 and preceding 21. ...


In Europe

According to German linguist Theo Vennemann, the vigesimal system in Europe is of Basque (Vasconic) origin and spread from the Vasconic languages to other European tongues, such as many Celtic languages, French and Danish. Theo Vennemann genannt Nierfeld (May 27, 1937 - ) is a German linguist known best for his work on historical linguistics. ... Basque (in Basque: Euskara) is the language spoken by the Basque people who inhabit the Pyrenees in North-Central Spain and the adjoining region of South-Western France. ... The Celtic languages are the languages descended from Proto-Celtic, or Common Celtic, spoken by ancient and modern Celts alike. ...


However according to Menninger the vigesimal system originated with the Normans and spread through them to Western Europe; as Celtic languages often use vigesimal counting systems, some believe that this theory is unlikely, however. The Celtic languages are the languages descended from Proto-Celtic, or Common Celtic, spoken by ancient and modern Celts alike. ...

  • Twenty (vingt) is used as a base number in the French language names of numbers from 80 to 99. So for example, quatre-vingts means 4 times 20, i.e. is the French word for 80, and soixante quinze (literally "sixty-fifteen") means 75.
  • Twenty (tyve) is used as a base number in the Danish language names of numbers from 50 to 99. For example, Tres (short for tresindstyve) means 3 times 20, i.e. 60. For details, see Danish numerals.
  • Twenty (ugain) is used as a base number in the Welsh language, although in the latter part of the twentieth century a decimal counting system has come to be preferred (particularly in the South), with the vigesimal system becoming 'traditional' and more popular in North Welsh. Deugain means 2 times 20 i.e. 40, trigain means 3 times 20 i.e. 60. Prior to the currency decimalisation in 1971, papur chwigain (6 times 20 paper) was the nickname for the 10 shilling (= 120 pence) note.
  • Twenty (fiche) is used in an older counting system in Irish Gaelic, though most people nowadays use a decimal system, and this is what is taught in schools. Thirty is fiche is deag, literally twenty and ten. Forty is dhá fhichid, literally two twenties. Trichid is sixty (three twenties) and ceithre fichid is eighty (literally four twenties).
  • Twenty (njëzet) is used as a base number in the Albanian language. The word for 40 (dyzet) means two times 20.
  • Twenty (hogei) is used as a base number in the Basque language for numbers up to 100 (ehun). The words for 40 (berrogei), 60 (hirurogei) and 80 (laurogei) mean "two-score", "three-score" and "four-score", respectively. The number 75 is called hirurogeita hamabost, lit. "three-score-and ten-five".
  • In English, counting by the score has been used historically, as in the famous opening of the Gettysburg Address "Four score and seven years ago…", meaning eighty-seven (87) years ago. This method has fallen into disuse, however.

French (français, langue française) is one of the most important Romance languages, outnumbered in speakers only by Spanish and Portuguese. ... 80 (eighty) is the natural number following 79 and preceding 81. ... Danish (dansk) belongs to the North Germanic languages (also called Scandinavian languages), a sub-group of the Germanic branch of the Indo-European languages. ... 60 (sixty) is the natural number following 59 and preceding 61. ... Danish (dansk) belongs to the North Germanic languages (also called Scandinavian languages), a sub-group of the Germanic branch of the Indo-European languages. ... Welsh redirects here, and this article describes the Welsh language. ... (19th century - 20th century - 21st century - more centuries) Decades: 1900s 1910s 1920s 1930s 1940s 1950s 1960s 1970s 1980s 1990s The 20th century lasted from 1901 to 2000 in the Gregorian calendar (often from (1900 to 1999 in common usage). ... Welsh redirects here, and this article describes the Welsh language. ... Welsh redirects here, and this article describes the Welsh language. ... 40 (forty) is the natural number following 39 and preceding 41. ... 120 (one hundred twenty in American English; one hundred and twenty in British English) is the natural number following 119 and preceding 121. ... Note: This page contains phonetic information presented in the International Phonetic Alphabet (IPA) using Unicode. ... Albanian (gjuha shqipe //) is a language spoken by over 6 million people, primarily in Albania, Kosovo, and the Republic of Macedonia but also in other parts of the Balkans, along the eastern coast of Italy and in Sicily, as well as by emigrant groups in Scandinavia, Germany, Greece, Italy, the... Basque (in Basque: Euskara) is the language spoken by the Basque people who inhabit the Pyrenees in North-Central Spain and the adjoining region of South-Western France. ... Score can mean one of several things: Look up score in Wiktionary, the free dictionary. ... The shilling (or informally: bob) was an English coin first issued in 1548 for Henry VIII, although arguably the testoon issued about 1487 for Henry VII was the first English shilling. ... UKP redirects here. ... Hundred weight or hundredweight is a unit of measurement for mass in both the system of measurement used in the United Kingdom and Ireland (and previously throughout the British Commonwealth), and in the system used in the United States. ... The word ton or tonne is derived from the Old English tunne, and ultimately from the Old French tonne, and referred originally to a large cask with a capacity of 252 wine gallons, which holds approximately 2100 pounds of water. ... The English language is a West Germanic language that originates in England. ... Score can mean one of several things: Look up score in Wiktionary, the free dictionary. ... The only known photo of Abraham Lincoln at Gettysburg (seated, center), taken about noon, just after Lincoln arrived and some three hours before he spoke. ... 87 is the natural number following 86 and preceding 88. ...

Outside Europe

  • Twenty (otsi) is used as a base number in the Georgian language. For example, 31 (otsdatertmeti) literally means, twenty-and-eleven. 67 (samotsdashvidi) is said as, “three-twenty-and-seven”.
  • In East Asia, the Ainu language also uses a counting system that is based around the number 20. “hotnep” is 20, “wanpe etu hotnep” (ten more until two twenties) is 30, “tu hotnep” (two twenties) is 40, “ashikne hotnep” (five twenties) is 100. Subtraction is also heavily used, e.g. “shinepesanpe” (one more until ten) is 9.
  • Twenty was a base in the Maya and Aztec number systems. The Maya used the following names for the powers of twenty: kal (20), bak (202 = 400), pic (203 = 8,000), calab (204 = 160,000), kinchil (205 = 3,200,000) and alau (206 = 64,000,000). See also Maya numerals and Maya calendar, Mayan languages, Yucatec. The Aztec called them: cempoalli (1 × 20), centzontli (1 × 400), cenxiquipilli (1 × 8,000), cempoalxiquipilli (1 × 20 × 8,000 = 160,000), centzonxiquipilli (1 × 400 × 8,000 = 3,200,000) and cempoaltzonxiquipilli (1 × 20 × 400 × 8,000 = 64,000,000). Note that the ce(n/m) prefix at the beginning means "one" (as in "one hundred" and "one thousand") and is replaced with the corresponding number to get the names of other multiples of the power. For example, ome (2) × poalli (20) = ompoalli (40), ome (2) × tzontli (400) = ontzontli (800). Note also that the -li in poalli (and xiquipilli) and the -tli in tzontli are grammatical noun suffixes that are appended only at the end of the word; thus poalli, tzontli and xiquipilli compound together as poaltzonxiquipilli (instead of *poallitzontlixiquipilli). (See also Nahuatl language.)

Georgian (ქართული ენა, kartuli ena) is the official language of Georgia, a republic in the Caucasus. ... 31 (thirty-one) is the natural number following 30 and preceding 32. ... 67 is the natural number following 66 and preceding 68. ... Geographic scope of East Asia East Asia is a subregion of Asia that can be defined in either geographical or cultural terms. ... The Ainu language (Ainu: アイヌ イタㇰ, aynu itak; Japanese: アイヌ語, ainu-go) is spoken by the Ainu ethnic group on the northern Japanese island of Hokkaido. ... 30 (thirty) is the natural number following 29 and preceding 31. ... 100 (one hundred) (the Roman numeral is C for centum) is the natural number following 99 and preceding 101. ... The Maya civilization is a historical Mesoamerican civilization, which extended throughout the northern Central American region which includes the present-day nations of Guatemala, Belize, western Honduras and El Salvador, as well as the southern Mexican states of Chiapas, Tabasco, and the Yucatán peninsula states of Quintana Roo, Campeche... The Aztecs were a Mesoamerican people of central Mexico in the 14th, 15th and 16th centuries. ... Mayan numerals. ... The Maya calendar is actually a system of distinct calendars and almanacs used by the Maya civilization of pre-Columbian Mesoamerica. ... Mayan languages constitute a language family of related languages which are spoken in Mesoamerica, from southeastern Mexico to northern Central America, and as far south as Honduras. ... Yucatec Maya is a Maya language spoken in the Yucatan Peninsula, northern Belize and parts of Guatemala. ... Nahuatl (pronounced in two syllables, NA-watl ) is a term applied to some members of the Aztecan or Nahuan sub-branch of the Uto-Aztecan language family, indigenous to central Mexico. ...

Related observations

  • Among multiples of 10, 20 is described in a special way in some languages. For example, the Spanish words treinta (30) and cuarenta (40) consist of "tre(3)+inta (10 times)", "cuar(4)+enta (10 times)", but the word veinte (20) is not presently connected to any word meaning "two" (although, historically, it is[1]). Similarly, in Semitic languages such as Arabic and Hebrew, the numbers 30, 40 ... 90 are expressed by morphologically plural forms of the words for the numbers 3, 4 ... 9, but the number 20 is expressed by a morphologically plural form of the word for 10.
  • In some languages, the names of the two-digit numbers from 11 to 19 consist of one word, but the names of the two-digit numbers from 21 on consist of two words. So for example, the English words eleven (11), twelve (12), thirteen (13) etc., as opposed to twenty-one (21), twenty-two (22), twenty-three (23), etc. In a number of other languages (such as Hebrew), the names of the numbers from 11-19 contain two words, but one of these words is a special "teen" form which is different from the ordinary form of the word for the number 10, and may in fact be only found in these names of the numbers 11-19.

Multiple is a comic book superhero in the Marvel Comics universe. ... 10 (ten) is an even natural number following 9 and preceding 11. ... 30 (thirty) is the natural number following 29 and preceding 31. ... Events Roman Empire Caligula embarks on a campaign to conquer Britain, and fails miserably. ... 20 (twenty) is the natural number following 19 and preceding 21. ... 14th century BC diplomatic letter in Akkadian, found in Tell Amarna. ... 11 (eleven) is the natural number following 10 and preceding 12. ... 19 (nineteen) is the natural number following 18 and preceding 20. ... 21 (twenty-one) is the natural number following 20 and preceding 22. ... 11 (eleven) is the natural number following 10 and preceding 12. ... 12 (twelve) is the natural number following 11 and preceding 13. ... See also Thirteen, a 2003 movie, 13 an album by British band Blur, Thirteen an album by Teenage Fanclub. ... 21 (twenty-one) is the natural number following 20 and preceding 22. ... 22 (twenty-two) is the natural number following 21 and preceding 23. ... 23 (twenty-three) is the natural number following 22 and preceding 24. ... Hebrew (עִבְרִית ‘Ivrit) is a Semitic language of the Afro-Asiatic language family spoken by more than seven million people in Israel with significant communities in the West Bank, the United States, and Jewish communities around the world. ...

Further reading

  • Karl Menninger: Number words and number symbols: a cultural history of numbers; translated by Paul Broneer from the revised German edition. Cambridge, Mass.: M.I.T. Press, 1969 (also available in paperback: New York: Dover, 1992 ISBN 0-486-27096-3)
  • Levi Leonard Conant: The Number Concept: Its Origin and Development; New York, New York: MacMillon & Co, 1931. Project Gutenberg EBook

Notes

  1.   The diachronic view is like this. Spanish: veinte < Latin: vīgintī, the IE etymology of which (view) connects it to the roots meaning '2' and 10'. (The etymological databases of the Tower of Babel project are referred here.)

  Results from FactBites:
 
Omniglot - the blog » Counting in twenties (863 words)
The word vigesimal comes from the Latin vīgēsimus, which is a variant of vīcēsimus (twentieth) and influenced by viginti (twenty).
The vigesimal system is also used in the other Celtic languages and in a number of other languages, at least to some extent.
The number from 16-19 in the Welsh vigesimal system are unusual: 16 = un ar bymtheg (one on fifteen), 17 = dau ar bymtheg (two on fifteen), 18 = deunaw (two nines), and 19 = pedwar ar bymtheg (four on fifteen).
  More results at FactBites »

 
 

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