A vigesimal () or base-20 (base-score) numeral system is based on
twenty
Twenty or 20 may refer to:
* 20 (number), the natural number following 19 and preceding 21
* one of the years 20 BC, AD 20, 1920, 2020
Music
Albums
* ''20'' (2nd Chapter of Acts album), 1992
* ''20'' (Cunter album), 2011
* ''20'' (Dr ...
(in the same way in which the
decimal numeral system
The decimal numeral system (also called the base-ten positional numeral system and denary or decanary) is the standard system for denoting integer and non-integer numbers. It is the extension to non-integer numbers of the Hindu–Arabic numeral ...
is based on
ten). ''
Vigesimal
vigesimal () or base-20 (base-score) numeral system is based on twenty (in the same way in which the decimal numeral system is based on ten). '' Vigesimal'' is derived from the Latin adjective '' vicesimus'', meaning 'twentieth'.
Places
In ...
'' is derived from the Latin adjective ''
vicesimus'', meaning 'twentieth'.
Places
In a vigesimal
place
Place may refer to:
Geography
* Place (United States Census Bureau), defined as any concentration of population
** Census-designated place, a populated area lacking its own Municipality, municipal government
* "Place", a type of street or road ...
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 (the
20 means
base ), to write
nineteen as , and the numbers between with the corresponding letters of the alphabet. This is similar to the common
computer-science practice of writing
hexadecimal
In mathematics and computing, the hexadecimal (also base-16 or simply hex) numeral system is a positional numeral system that represents numbers using a radix (base) of 16. Unlike the decimal system representing numbers using 10 symbols, hexa ...
numerals over 9 with the letters "A–F". Another less common method skips over the letter "I", in order to avoid confusion between I
20 as
eighteen and
one, so that the number eighteen is written as J
20, and nineteen is written as K
20. The number twenty is written as .
According to this notation:
: is equivalent to
forty
40 (forty) is the natural number following 39 and preceding 41.
Though the word is related to "four" (4), the spelling "forty" replaced "fourty" in the course of the 17th century and is now the standard form.
In mathematics
*Forty is a compo ...
in decimal =
: is equivalent to
two hundred and sixty in decimal =
: is equivalent to
four hundred
400 (four hundred) is the natural number following 399 and preceding 401.
Mathematical properties
400 is the square of 20. 400 is the sum of the powers of 7 from 0 to 3, thus making it a repdigit in base 7 (1111).
A circle is divided into ...
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
Twenty or 20 may refer to:
* 20 (number), the natural number following 19 and preceding 21
* one of the years 20 BC, AD 20, 1920, 2020
Music
Albums
* ''20'' (2nd Chapter of Acts album), 1992
* ''20'' (Cunter album), 2011
* ''20'' (Dr ...
. Numbers in vigesimal notation use the convention that I means eighteen and J means nineteen.
Fractions
As 20 is divisible by two and five and is adjacent to 21, the product of three and seven, thus covering the first four prime numbers, many vigesimal fractions have simple representations, whether terminating or recurring (although thirds are more complicated than in decimal, repeating two digits instead of one). In decimal, dividing by three twice (ninths) only gives one digit periods ( = 0.1111.... for instance) because 9 is the number below ten. 21, however, the number adjacent to 20 that is divisible by 3, is not divisible by 9. Ninths in vigesimal have six-digit periods. As 20 has the same prime factors as 10 (two and five), a fraction will terminate in decimal
if and only if
In logic and related fields such as mathematics and philosophy, "if and only if" (shortened as "iff") is a biconditional logical connective between statements, where either both statements are true or both are false.
The connective is bicondi ...
it terminates in vigesimal.
Cyclic numbers
The prime factorization of twenty is 2
2 × 5, so it is not a
perfect power
In mathematics, a perfect power is a natural number that is a product of equal natural factors, or, in other words, an integer that can be expressed as a square or a higher integer power of another integer greater than one. More formally, ''n'' ...
. However, its squarefree part, 5, is congruent to 1 (mod 4). Thus, according to
Artin's conjecture on primitive roots
In number theory, Artin's conjecture on primitive roots states that a given integer ''a'' that is neither a square number nor −1 is a primitive root modulo infinitely many primes ''p''. The conjecture also ascribes an asymptotic density to the ...
, vigesimal has infinitely many
cyclic
Cycle, cycles, or cyclic may refer to:
Anthropology and social sciences
* Cyclic history, a theory of history
* Cyclical theory, a theory of American political history associated with Arthur Schlesinger, Sr.
* Social cycle, various cycles in soc ...
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 given set of bases found that, of the first 15,456 primes, ~39.344% are cyclic in vigesimal.
Real numbers
Use
In many European languages,
20 is used as 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).
Africa
Vigesimal systems are common in Africa, for example in
Yoruba
The Yoruba people (, , ) are a West African ethnic group that mainly inhabit parts of Nigeria, Benin, and Togo. The areas of these countries primarily inhabited by Yoruba are often collectively referred to as Yorubaland. The Yoruba constitute ...
. While the Yoruba number system may be regarded as a vigesimal system, it is complex.
Americas
* Twenty is a base in the
Maya
Maya may refer to:
Civilizations
* Maya peoples, of southern Mexico and northern Central America
** Maya civilization, the historical civilization of the Maya peoples
** Maya language, the languages of the Maya peoples
* Maya (Ethiopia), a populat ...
and
Aztec
The Aztecs () were a Mesoamerican culture that flourished in central Mexico in the post-classic period from 1300 to 1521. The Aztec people included different Indigenous peoples of Mexico, ethnic groups of central Mexico, particularly those g ...
number systems. The Maya use the following names for the powers of twenty: (20), (20
2 = 400), (20
3 = 8,000), (20
4 = 160,000), (20
5 = 3,200,000) and (20
6 = 64,000,000). See
Maya numerals
The Mayan numeral system was the system to represent numbers and calendar dates in the Maya civilization. It was a vigesimal (base-20) positional numeral system. The numerals are made up of three symbols; zero (a shell), one (a dot) and fiv ...
and
Maya calendar
The Maya calendar is a system of calendars used in pre-Columbian Mesoamerica and in many modern communities in the Guatemalan highlands, Veracruz, Oaxaca and Chiapas, Mexico.
The essentials of the Maya calendar are based upon a system which had ...
,
Nahuatl language
Nahuatl (; ), Aztec, or Mexicano is a language or, by some definitions, a group of languages of the Uto-Aztecan languages, Uto-Aztecan language family. Varieties of Nahuatl are spoken by about Nahuas, Nahua peoples, most of whom live mainly in ...
.
![InupiaqNumbers](https://upload.wikimedia.org/wikipedia/commons/1/1f/InupiaqNumbers.gif)
* The
Inuit-Yupik-Unangax languages have base-20 number systems. In 1994, Inuit students in
Kaktovik, Alaska
Kaktovik (; ik, Qaaktuġvik, ) is a City (Alaska), city in North Slope Borough, Alaska, North Slope Borough, Alaska, United States. The population was 283 at the 2020 United States census, 2020 census.
History
Until the late nineteenth century ...
, came up with the base-20
Kaktovik numerals
The Kaktovik numerals or Kaktovik Iñupiaq numerals are a base-20 system of numerical digits created by Alaskan Iñupiat. They are visually Iconicity, iconic, with shapes that indicate the number being represented.
The Iñupiaq language#Nume ...
to better represent their language. Before this invention led to a revival, the Inuit numerals had been falling out of use.
Asia
*
Dzongkha
Dzongkha (; ) is a Sino-Tibetan language that is the official and national language of Bhutan. It is written using the Tibetan script.
The word means "the language of the fortress", from ' "fortress" and ' "language". , Dzongkha had 171,080 n ...
, the national language of
Bhutan
Bhutan (; dz, འབྲུག་ཡུལ་, Druk Yul ), officially the Kingdom of Bhutan,), is a landlocked country in South Asia. It is situated in the Eastern Himalayas, between China in the north and India in the south. A mountainous ...
, has a full vigesimal system, with numerals for the powers of 20, 400, 8,000 and 160,000.
*
Atong, a language spoken in the South Garo Hills of Meghalaya state, Northeast India, and adjacent areas in Bangladesh, has a full vigesimal system that is nowadays considered archaic.
* In
Santali, a
Munda language
The Munda languages are a group of closely related languages spoken by about nine million people in India and Bangladesh. Historically, they have been called the Kolarian languages. They constitute a branch of the Austroasiatic language family ...
of
India
India, officially the Republic of India (Hindi: ), is a country in South Asia. It is the seventh-largest country by area, the second-most populous country, and the most populous democracy in the world. Bounded by the Indian Ocean on the so ...
, "fifty" is expressed by the phrase ''bār isī gäl'', literally "two twenty ten." Likewise, in
Didei, another Munda language spoken in India, complex numerals are decimal to 19 and decimal-vigesimal to 399.
* The
Burushaski
Burushaski (; ) is a language isolate spoken by Burusho people, who reside almost entirely in northern Gilgit-Baltistan, Pakistan, with a few hundred speakers in northern Jammu and Kashmir, India. In Pakistan, Burushaski is spoken by people in ...
number system is base-20. For example, 20 altar, 40 alto-altar (2 times 20), 60 iski-altar (3 times 20) etc.
* In
East Asia
East Asia is the eastern region of Asia, which is defined in both geographical and ethno-cultural terms. The modern states of East Asia include China, Japan, Mongolia, North Korea, South Korea, and Taiwan. China, North Korea, South Korea and ...
, the
Ainu language
Ainu (, ), or more precisely Hokkaido Ainu, is a language spoken by a few elderly members of the Ainu people on the northern Japanese island of Hokkaido. It is a member of the Ainu language family, itself considered a language family isolate ...
also uses a counting system that is based around the number 20. "" is 20, "" (ten more until two twenties) is
30, "" (two twenties) is 40, "" (five twenties) is
100. Subtraction is also heavily used, e.g. "" (one more until ten) is 9.
* The
Chukchi language
Chukchi , also known as Chukot, is a Chukotko-Kamchatkan languages, Chukotko–Kamchatkan language spoken by the Chukchi people in the easternmost extremity of Siberia, mainly in Chukotka Autonomous Okrug. The language is closely related to Koryak ...
has a vigesimal numeral system.
Oceania
There is some evidence of base-20 usage in the
Māori language
Māori (), or ('the Māori language'), also known as ('the language'), is an Eastern Polynesian language spoken by the Māori people, the indigenous population of mainland New Zealand. Closely related to Cook Islands Māori, Tuamotuan, and ...
of New Zealand as seen in the terms ''Te Hokowhitu a Tu'' referring to a war party (literally "the seven 20s of Tu") and ''Tama-hokotahi'', referring to a great warrior ("the one man equal to 20").
Caucasus
In the Central Caucasus a vigesimal system is used by the
Ingush.
Europe
* Twenty () is used as a base number in the
French names of numbers from 70 to 99, except in the French of
Belgium
Belgium, ; french: Belgique ; german: Belgien officially the Kingdom of Belgium, is a country in Northwestern Europe. The country is bordered by the Netherlands to the north, Germany to the east, Luxembourg to the southeast, France to th ...
,
Switzerland
). Swiss law does not designate a ''capital'' as such, but the federal parliament and government are installed in Bern, while other federal institutions, such as the federal courts, are in other cities (Bellinzona, Lausanne, Luzern, Neuchâtel ...
, the
Democratic Republic of the Congo
The Democratic Republic of the Congo (french: République démocratique du Congo (RDC), colloquially "La RDC" ), informally Congo-Kinshasa, DR Congo, the DRC, the DROC, or the Congo, and formerly and also colloquially Zaire, is a country in ...
,
Rwanda
Rwanda (; rw, u Rwanda ), officially the Republic of Rwanda, is a landlocked country in the Great Rift Valley of Central Africa, where the African Great Lakes region and Southeast Africa converge. Located a few degrees south of the Equator ...
, the
Aosta Valley
, Valdostan or Valdotainian it, Valdostano (man) it, Valdostana (woman)french: Valdôtain (man)french: Valdôtaine (woman)
, population_note =
, population_blank1_title = Official languages
, population_blank1 = Italian French
...
and the
Channel Islands
The Channel Islands ( nrf, Îles d'la Manche; french: îles Anglo-Normandes or ''îles de la Manche'') are an archipelago in the English Channel, off the French coast of Normandy. They include two Crown Dependencies: the Bailiwick of Jersey, ...
. For example, , the French word for "
80", literally means "four-twenties"; ''soixante-dix'', the word for "
70", is literally "sixty-ten"; ("
75") is literally "sixty-fifteen"; ''quatre-vingt-sept'' ("
87") is literally "four-twenties-seven"; ''quatre-vingt-dix'' ("
90") is literally "four-twenties-ten"; and ''quatre-vingt-seize'' ("
96") is literally "four-twenties-sixteen". However, in the French of Belgium, Switzerland, the Democratic Republic of the Congo, Rwanda, the Aosta Valley, and the Channel Islands, the numbers 70 and 90 generally have the names ''septante'' and ''nonante''. Therefore, the year 1996 is "mille neuf cent quatre-vingt-seize" in Parisian French, but it is "mille neuf cent nonante-six" in Belgian French. In Switzerland, "80" can be ''quatre-vingts'' (Geneva, Neuchâtel, Jura) or ''huitante'' (Vaud, Valais, Fribourg).
* Twenty () is used as a base number in the
Danish
Danish may refer to:
* Something of, from, or related to the country of Denmark
People
* A national or citizen of Denmark, also called a "Dane," see Demographics of Denmark
* Culture of Denmark
* Danish people or Danes, people with a Danish a ...
names of tens from 50 to 90. For example, (short for ) means 3 times 20, i.e.
60. However, Danish numerals are not vigesimal since it is only the names of some of the tens that are etymologically formed in a vigesimal way. In contrast with e.g. French ''quatre-vingt-seize'', the units only go from zero to nine between each ten which is a defining trait of a decimal system. For details, see
Danish numerals.
* Twenty () is used as a base number in the
Breton
Breton most often refers to:
*anything associated with Brittany, and generally
** Breton people
** Breton language, a Southwestern Brittonic Celtic language of the Indo-European language family, spoken in Brittany
** Breton (horse), a breed
**Ga ...
names of numbers from 40 to 49 and from 60 to 99. For example, means 2 times 20, i.e.
40, and (literally "three-six and four-twenty") means 3×6 + 4×20, i.e. 98. However, 30 is and not * ("ten and twenty"), and 50 is ("half-hundred").
* Twenty () is used as a base number in
Welsh
Welsh may refer to:
Related to Wales
* Welsh, referring or related to Wales
* Welsh language, a Brittonic Celtic language spoken in Wales
* Welsh people
People
* Welsh (surname)
* Sometimes used as a synonym for the ancient Britons (Celtic peop ...
from numbers up to 50 () and from 60 to 100 (), although since the 1940s a decimal counting system has come to be preferred. However, the vigesimal system exclusively is used for ordinal numbers and is still required in telling the time, money, and with weights and measures. means 'two twenties' i.e. 40, means 'three twenties' i.e. 60, etc. means 57 (two on fifteen and twenty). Prior to its withdrawal from circulation, (note of sixscore) was the nickname for the ten-shilling (120 pence) note; due to 120 pence = half a pound the term continues to be used to mean 50 pence in modern Welsh and phrases like ('50p piece') is also not uncommon.
* Twenty () is traditionally used as a base number in
Scottish Gaelic
Scottish Gaelic ( gd, Gàidhlig ), also known as Scots Gaelic and Gaelic, is a Goidelic language (in the Celtic branch of the Indo-European language family) native to the Gaels of Scotland. As a Goidelic language, Scottish Gaelic, as well as ...
, with or being 30 (ten over twenty, or twenty and ten), 40 (two twenties), 50 (two twenty and ten) / 50 (half a hundred), 60 (three twenties) and so on up to 180 (nine twenties). Nowadays a decimal system is taught in schools, but the vigesimal system is still used by many, particularly older speakers.
* Twenty () is traditionally used as a base number in
Manx Gaelic
Manx ( or , pronounced or ), also known as Manx Gaelic, is a Gaelic language of the insular Celtic branch of the Celtic language family, itself a branch of the Indo-European language family. Manx is the historical language of the Manx peo ...
, with being 30 (ten and twenty), 40 (two twenties), 50 (ten and two twenties), 60 (three twenty) and so on. A decimal system also exists, using the following tens: jeih (ten), feed (twenty), treead (thirty), daeed (forty), queigad (fifty), sheyad (sixty), shiagtad (seventy, hoghtad (eighty) and nuyad (ninety).
* Twenty () is used as a base number in
Albanian
Albanian may refer to:
*Pertaining to Albania in Southeast Europe; in particular:
**Albanians, an ethnic group native to the Balkans
**Albanian language
**Albanian culture
**Demographics of Albania, includes other ethnic groups within the country ...
. The word for 40 () means "two times 20". The
Arbëreshë Arbën/Arbër, from which derived Arbënesh/Arbëresh originally meant all Albanians, until the 18th century. Today it is used for different groups of Albanian origin, including:
* Arbër (given name), an Albanian masculine given name
* Arbëresh ...
in Italy may use 'trizetë' for 60. Formerly, 'katërzetë' was also used for 80. Today
Cham Albanians
Cham Albanians or Chams ( sq, Çamë; el, Τσάμηδες, ''Tsámidhes''), are a sub-group of Albanians who originally resided in the western part of the region of Epirus in northwestern Greece, an area known among Albanians as Chameria. T ...
in Greece use all zet numbers. Basically, 20 means 1 zet, 40 means 2 zet, 60 means 3 zet and 80 means 4 zet. Albanian is the only language in the Balkans which has retained elements of the vigesimal numeral system side by side with decimal system. The existence of the two systems in Albanian reflect the contribution of Pre-Indo-European people of the Balkans to the formation of the Paleo-Balkan Indo-European tribes and their language.
* Twenty () is used as a base number in
Georgian
Georgian may refer to:
Common meanings
* Anything related to, or originating from Georgia (country)
** Georgians, an indigenous Caucasian ethnic group
** Georgian language, a Kartvelian language spoken by Georgians
**Georgian scripts, three scrip ...
for numbers 30 to 99. For example,
31 () literally means, ''twenty-and-eleven''.
67 () is said as, "three-twenty-and-seven".
* Twenty () is used as a base number in the
Nakh languages
The Nakh languages are a group of languages within Northeast Caucasian family, spoken chiefly by the Chechens and Ingush in the North Caucasus.
Bats is the endangered language of the Bats people, an ethnic minority in Georgia.
The Chechen, In ...
.
* Twenty () is used as a base number in
Basque
Basque may refer to:
* Basques, an ethnic group of Spain and France
* Basque language, their language
Places
* Basque Country (greater region), the homeland of the Basque people with parts in both Spain and France
* Basque Country (autonomous co ...
for numbers up to 100 (). The words for 40 (), 60 () and 80 () mean "two-score", "three-score" and "four-score", respectively. For example, the number 75 is called , lit. "three-score-and ten-five". The Basque nationalist
Sabino Arana
Sabino Policarpo Arana Goiri (in Spanish), Sabin Polikarpo Arana Goiri (in Basque), or Arana ta Goiri'taŕ Sabin (self-styled) (26 January 1865 – 25 November 1903), was a Basque writer and the founder of the Basque Nationalist Party (PNV) ...
proposed a vigesimal digit system to match the spoken language,
[''Artículos publicados en la 1.ª época de "Euzkadi" : revista de Ciencias, Bellas Artes y Letras de Bilbao por Arana-Goiri'taŕ Sabin'': 1901, Artículos publicados en la 1 época de "Euskadi" : revista de Ciencias, Bellas Artes y Letras de Bilbao por Arana-Goiri'ttarr Sabin : 1901, ]Sabino Arana
Sabino Policarpo Arana Goiri (in Spanish), Sabin Polikarpo Arana Goiri (in Basque), or Arana ta Goiri'taŕ Sabin (self-styled) (26 January 1865 – 25 November 1903), was a Basque writer and the founder of the Basque Nationalist Party (PNV) ...
, 1908, Bilbao, Eléxpuru Hermanos
102–112
/ref> and, as an alternative, a reform of the spoken language to make it decimal,[''Artículos ...'', Sabino Arana]
112–118
/ref> but both are mostly forgotten.[''Efemérides Vascas y Reforma d ela Numeración Euzkérica'', ]Sabino Arana
Sabino Policarpo Arana Goiri (in Spanish), Sabin Polikarpo Arana Goiri (in Basque), or Arana ta Goiri'taŕ Sabin (self-styled) (26 January 1865 – 25 November 1903), was a Basque writer and the founder of the Basque Nationalist Party (PNV) ...
, Biblioteca de la Gran Enciclopedia Vasca, Bilbao, 1969. Extracted from the magazine '' Euskal-Erria'', 1880 and 1881.
* Twenty (''dwisti'' or ''dwujsti'') is used as a base number in the Resian dialect
The Resian dialect or simply Resian (self-designation Standard , Bila , Osoanë , Solbica ; sl, rezijansko narečje , ; ) is a distinct variety in the South Slavic continuum, generally considered a Slovene dialect spoken in the Resia Valley, P ...
of Slovenian
Slovene or Slovenian may refer to:
* Something of, from, or related to Slovenia, a country in Central Europe
* Slovene language, a South Slavic language mainly spoken in Slovenia
* Slovenes
The Slovenes, also known as Slovenians ( sl, Sloven ...
in Italy
Italy ( it, Italia ), officially the Italian Republic, ) or the Republic of Italy, is a country in Southern Europe. It is located in the middle of the Mediterranean Sea, and its territory largely coincides with the homonymous geographical re ...
's Resia Valley Resia may refer to:
__NOTOC__ Locations in northern Italy South Tyrol
* Resia, a frazione (subdivision) of the village Graun im Vinschgau
* Reschen Pass ( it, Passo di Resia, link=no), a border pass connecting Italy and Austria
* Reschensee, ( it, ...
. 60 is expressed by ''trïkrat dwisti'' (3×20), 70 by ''trïkrat dwisti nu dësat'' (3×20 + 10), 80 by ''štirikrat dwisti'' (4×20) and 90 by ''štirikrat dwisti nu dësat'' (4×20 + 10).[Fran Ramovš, Karakteristika slovenskega narečja v Reziji in: Časopis za slovenski jezik, književnost in zgodovino, no 4, 1928, pages: 107-12]
/ref>
* In the £sd, £sd currency system (used in the United Kingdom
The United Kingdom of Great Britain and Northern Ireland, commonly known as the United Kingdom (UK) or Britain, is a country in Europe, off the north-western coast of the continental mainland. It comprises England, Scotland, Wales and North ...
pre-1971), there were 20 shilling
The shilling is a historical coin, and the name of a unit of modern currencies formerly used in the United Kingdom, Australia, New Zealand, other British Commonwealth countries and Ireland, where they were generally equivalent to 12 pence o ...
s (worth 12 pence each) to the pound. Under the decimal system introduced in 1971 (1 pound equals 100 new pence instead of 240 pence in the old system), the shilling coins still in circulation were re-valued at 5 pence (no more were minted and the shilling coin was demonetised in 1990).
* In the imperial weight system there are twenty hundredweight
The hundredweight (abbreviation: cwt), formerly also known as the centum weight or quintal, is a British imperial and US customary unit of weight or mass. Its value differs between the US and British imperial systems. The two values are distingu ...
in a ton
Ton is the name of any one of several units of measure. It has a long history and has acquired several meanings and uses.
Mainly it describes units of weight. Confusion can arise because ''ton'' can mean
* the long ton, which is 2,240 pounds
...
.
* In English
English usually refers to:
* English language
* English people
English may also refer to:
Peoples, culture, and language
* ''English'', an adjective for something of, from, or related to England
** English national ide ...
, the name of the cardinal number
In mathematics, cardinal numbers, or cardinals for short, are a generalization of the natural numbers used to measure the cardinality (size) of sets. The cardinality of a finite set is a natural number: the number of elements in the set. Th ...
20 is most commonly phrased with the word 'twenty'. Counting by the score has been used historically; for example, the famous opening of the Gettysburg Address
The Gettysburg Address is a Public speaking, speech that President of the United States, U.S. President Abraham Lincoln delivered during the American Civil War at the dedication of the Gettysburg National Cemetery, Soldiers' National Cemetery, ...
, "Four score and seven years ago...", refers to the signing of the Declaration of Independence
A declaration of independence or declaration of statehood or proclamation of independence is an assertion by a polity in a defined territory that it is independent and constitutes a state. Such places are usually declared from part or all of the ...
in 1776, 87 years earlier. In the King James Bible
The King James Version (KJV), also the King James Bible (KJB) and the Authorized Version, is an Bible translations into English, English translation of the Christian Bible for the Church of England, which was commissioned in 1604 and publis ...
, the term 'score' is used over 130 times, though a single score is always expressed as "twenty". 'Score' is still occasionally used to denote groups of 20 analogously to the use of 'dozen
A dozen (commonly abbreviated doz or dz) is a grouping of twelve.
The dozen may be one of the earliest primitive integer groupings, perhaps because there are approximately a dozen cycles of the Moon, or months, in a cycle of the Sun, or year ...
' to quantify groups of 12.
* Other languages have terms similar to 'score', such as Danish
Danish may refer to:
* Something of, from, or related to the country of Denmark
People
* A national or citizen of Denmark, also called a "Dane," see Demographics of Denmark
* Culture of Denmark
* Danish people or Danes, people with a Danish a ...
and Norwegian
Norwegian, Norwayan, or Norsk may refer to:
*Something of, from, or related to Norway, a country in northwestern Europe
*Norwegians, both a nation and an ethnic group native to Norway
*Demographics of Norway
*The Norwegian language, including the ...
''snes
The Super Nintendo Entertainment System (SNES), commonly shortened to Super NES or Super Nintendo, is a 16-bit home video game console developed by Nintendo that was released in 1990 in Japan and South Korea, 1991 in North America, 1992 in Euro ...
''.
* In regions where greater aspects of the Brythonic Celtic languages have survived in modern dialect, sheep enumeration systems that are vigesimal are recalled to the present day. See Yan Tan Tethera
Yan Tan Tethera or yan-tan-tethera is a sheep-counting system traditionally used by shepherds in Northern England and some other parts of Britain. The words are numbers taken from Brythonic Celtic languages such as Cumbric which had died out in ...
.
Software applications
Open Location Code
The Open Location Code (OLC) is a geocode based in a system of regular grids for identifying an area anywhere on the Earth.
It was developed at Google's Zürich engineering office, and released late October 2014. Location codes created by the OL ...
uses a word-safe version of base 20 for its geocodes
A geocode is a code that represents a geographic entity (location or object). It is a unique identifier of the entity, to distinguish it from others in a finite set of geographic entities. In general the ''geocode'' is a human-readable and s ...
. The characters in this alphabet were chosen to avoid accidentally forming words. The developers scored all possible sets of 20 letters in 30 different languages for likelihood of forming words, and chose a set that formed as few recognizable words as possible. The alphabet also is intended to reduce typographical errors by avoiding visually similar digits, and is case-insensitive.
Related observations
* Among multiples of 10, 20 is described in a special way in some languages. For example, the Spanish
Spanish might refer to:
* Items from or related to Spain:
**Spaniards are a nation and ethnic group indigenous to Spain
**Spanish language, spoken in Spain and many Latin American countries
**Spanish cuisine
Other places
* Spanish, Ontario, Cana ...
words ( 30) and (40) consist of " (10 times)", " (10 times)", but the word ( 20) is not presently connected to any word meaning "two" (although historically it is). Similarly, in Semitic languages
The Semitic languages are a branch of the Afroasiatic language family. They are spoken by more than 330 million people across much of West Asia, the Horn of Africa, and latterly North Africa, Malta, West Africa, Chad, and in large immigra ...
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. The Japanese language has a special word (hatachi) for 20 years (of age), and for the 20th day of the month (hatsuka).
* In some languages (e.g. English, Slavic languages
The Slavic languages, also known as the Slavonic languages, are Indo-European languages spoken primarily by the Slavic peoples and their descendants. They are thought to descend from a proto-language called Proto-Slavic, spoken during the Ear ...
and German), 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 French, this is true up to 16. In a number of other languages (such as Hebrew
Hebrew (; ; ) is a Northwest Semitic language of the Afroasiatic language family. Historically, it is one of the spoken languages of the Israelites and their longest-surviving descendants, the Jews and Samaritans. It was largely preserved ...
), the names of the numbers from 11 to 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 it may in fact be only found in these names of the numbers 11–19.
* Cantonese
Cantonese ( zh, t=廣東話, s=广东话, first=t, cy=Gwóngdūng wá) is a language within the Chinese (Sinitic) branch of the Sino-Tibetan languages originating from the city of Guangzhou (historically known as Canton) and its surrounding are ...
[Lau, S. ''A Practical Cantonese English Dictionary'' (1977) The Government Printer] and Wu Chinese
The Wu languages (; Romanization of Wu Chinese, Wu romanization and Romanization of Wu Chinese#IPA, IPA: ''wu6 gniu6'' [] (Shanghainese), ''ng2 gniu6'' [] (Suzhounese), Mandarin pinyin and IPA: ''Wúyǔ'' []) is a major group of Sinitic languag ...
frequently use the single unit (Cantonese ''yàh'', [ hanghainese ''nyae'' or ''ne'', Mandarin ''niàn'') for twenty, in addition to the fully decimal (Cantonese ''yìh sàhp'', Shanghainese ''el sah'', Mandarin ''èr shí'') which literally means "two ten". Equivalents exist for 30 and 40 ( and respectively: Mandarin ''sà'' and ''xì''), but these are more seldom used. This is a historic remnant of a vigesimal system.
* Although Khmer numerals have represented a decimal
The decimal numeral system (also called the base-ten positional numeral system and denary or decanary) is the standard system for denoting integer and non-integer numbers. It is the extension to non-integer numbers of the Hindu–Arabic numeral ...
positional notation
Positional notation (or place-value notation, or positional numeral system) usually denotes the extension to any base of the Hindu–Arabic numeral system (or decimal system). More generally, a positional system is a numeral system in which the ...
system since at least the 7th century, Old Khmer
Old Khmer is the oldest attested stage of the Khmer language, an Austroasiatic language historically and presently spoken across Cambodia, Southern Vietnam, and parts of Thailand and Laos. It is recorded in inscriptions dating from the early 7th c ...
, or Angkorian Khmer, also possessed separate symbols for the numbers 10, 20, and 100. Each multiple of 20 or 100 would require an additional stroke over the character, so the number 47 was constructed using the 20 symbol with an additional upper stroke, followed by the symbol for number 7. This suggests that spoken Angkorian Khmer used a vigesimal system.
* Thai
Thai or THAI may refer to:
* Of or from Thailand, a country in Southeast Asia
** Thai people, the dominant ethnic group of Thailand
** Thai language, a Tai-Kadai language spoken mainly in and around Thailand
*** Thai script
*** Thai (Unicode block ...
uses the term (''yi sip'') for 20. Other multiples of ten consist of the base number, followed by the word for ten, e.g. (''sam sip''), lit. three ten, for thirty. The ''yi'' of ''yi sip'' is different from the number two in other positions, which is สอง (''song''). Nevertheless, ''yi sip'' is a loan word from Chinese.
* Lao similarly forms multiples of ten by putting the base number in front of the word ten, so (''sam sip''), litt. three ten, for thirty. The exception is twenty, for which the word (''xao'') is used. ( ''sao'' is also used in the North-Eastern and Northern dialects of Thai, but not in standard Thai.)
* The Kharosthi numeral system behaves like a partial vigesimal system.
Examples in Mesoamerican languages
Powers of twenty in Yucatec Maya and Nahuatl
Counting in units of twenty
This table shows the Maya numerals
The Mayan numeral system was the system to represent numbers and calendar dates in the Maya civilization. It was a vigesimal (base-20) positional numeral system. The numerals are made up of three symbols; zero (a shell), one (a dot) and fiv ...
and the number names
In linguistics, a numeral (or number word) in the broadest sense is a word or phrase that describes a numerical quantity. Some theories of grammar use the word "numeral" to refer to cardinal numbers that act as a determiner that specify the quan ...
in Yucatec Maya
Yucatec Maya (; referred to by its speakers simply as Maya or as , is one of the 32 Mayan languages of the Mayan language family. Yucatec Maya is spoken in the Yucatán Peninsula and northern Belize. There is also a significant diasporic commu ...
, Nahuatl
Nahuatl (; ), Aztec, or Mexicano is a language or, by some definitions, a group of languages of the Uto-Aztecan language family. Varieties of Nahuatl are spoken by about Nahua peoples, most of whom live mainly in Central Mexico and have smaller ...
in modern orthography and in Classical Nahuatl
Classical Nahuatl (also known simply as Aztec or Nahuatl) is any of the variants of Nahuatl spoken in the Valley of Mexico and central Mexico as a ''lingua franca'' at the time of the 16th-century Spanish conquest of the Aztec Empire. During the s ...
.
Notes
Further reading
*Karl Menninger
Karl Augustus Menninger (July 22, 1893 – July 18, 1990) was an American psychiatrist and a member of the Menninger family of psychiatrists who founded the Menninger Foundation and the Menninger Clinic in Topeka, Kansas.
Biography
Menn ...
: ''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 )
*Levi Leonard Conant: ''The Number Concept: Its Origin and Development''; New York, New York: Macmillan & Co, 1931
Project Gutenberg EBook
{{Authority control
Positional numeral systems