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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
• History
• Symbol sets:
Armenian
Babylonian
Brahmi
Chinese
Cyrillic
Egyptian
Etruscan
Ge'ez
Greek Hebrew
Japanese
Khmer
Korean
Mayan
Roman

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

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 â‰ˆ1. ...

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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

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.

### 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 (áƒ¥áƒáƒ áƒ—áƒ£áƒšáƒ˜ áƒ”áƒœáƒ, 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: ã‚¢ã‚¤ãƒŒ ã‚¤ã‚¿ã‡°, aynu itak; Japanese: ã‚¢ã‚¤ãƒŒèªž, 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 YucatÃ¡n 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 (×¢Ö´×‘Ö°×¨Ö´×™×ª â€˜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. ...

• 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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