Vigesimal Did You Mean Vigesimal?

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Numeral systems

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D'ni (fictional)
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Unary (1)
Binary (2)
Ternary (3)
Quinary (5)
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Octal (8)
Decimal (10)
Duodecimal (12)
Hexadecimal (16)
Vigesimal (20)
Quadrovigesimal (24)
Hexavigesimal (26)
Septemvigesimal (27)
Hexatridecimal (36)
Sexagesimal (60)

The vigesimal (base-twenty) is a numeral system which is based on twenty. Twenty is the sum of fingers on hands and feet, and is the product of five and four.

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Places

In vigesimal place system, it uses twenty individual numerals. According to this method, ten is written as A, nineteen is written as J, twenty is written as 10. But another, to avoid confusion with I (eighteen) and 1 (one), one skips “I”, and the number eighteen is written as J, nineteen is written as K.

According to this notation, 20 means forty (= two times twenty), DA means two hundred seventy (= thirteen and ten-twentieth times twenty), 100 means four hundred (= twenty times twenty).

Usual vigesimal system is exclusively unit system, which uses ten numerals (from 0 to 9) based on decimal places. (such as a unit “score”.)

Following to this, in this article, places are based on decimal, if there is no notice. For example, 10 means ten, 20 means twenty.

Usage

In many languages, 20 is a base, especially in Europe:

Twenty (vingt) is used as a base number in French. E.g. quatre-vingts means 4 times 20, i.e. 80.

Twenty (tyve) is used as a base number in the Danish language: Tres (short for tresindstyve) means 3 times 20, i.e. 60; firs (short for firsindstyve) means 4 times 20 i.e. 80. halvtreds means (3 － 1/2) times 20, i.e. 50; halvfjerds means (4 － 1/2) times 20, i.e. 70; and halvfems means (5 － 1/2) times 20, i.e. 90.

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 came to be preferred, with the vigesimal system becoming 'traditional'. 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 (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”.

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".

Twenty was the base of 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. 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).

In the old British currency system, there were 20 shillings in a pound.

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.

Among multiples of 10, 20 is described in a special way. For example, Spanish words treinta (30) and cuarenta (40) consist of “tre(3)＋inta (10 times)”, “cuar(4)＋enta (10 times)”, but the word veinte (20) consists of itself.

Two-digit numbers from 11 to 19 consist of one words, but two-digit numbers from 21 consist of two words. Such as English words eleven (11), twelve (12), thirteen (13)… ; twenty-one (21), twenty-two (22), twenty-three (23)….

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.

Origin 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.

However according to Menninger the vigesimal system originated with the Normans and spread through them to Western Europe.

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