Vigesimal System

The system vigesimal (or vigesimal) is a Numbering system using the bases 20. Twenty correspond to the number of fingers and toes which the human being has. One can distinguish the pure vigesimal system, having exclusively for principle base 20, and the partial vigesimal system, resulting from the combination of a base 10 with a base 20.

History

Several vigesimal written numerations are attested in Mésoamérique: that of the Aztec , additive, and that of the scribes Mayas of the traditional time, positional, particularly used to note the dates (known as long account) counted in tun (year of account being worth 360 days). The latter arises under two character sets: the figures of style “not and bars” or the figures of style “céphalomorphe”, each one of these two character sets comprises a figure zero (zero of position).

In Europe, the origin of the vigesimal system is badly known. Some think that it has a pre-indo-European origin, but it was especially spread with the Moyen-âge. It then integrated former French, where one found the forms thus came and say (30), two wines (40), two wines and say , three wines (60), etc an old certificate, “VII vinz will liverez and IIII”, in the Lois of Guillaume 3 , at the 11th century, can let think of an origin Norman.

As of the end of the Middle Ages, it is supplanted by the decimal system (thirty, forty, fifty, sixty), except for the score preceding hundred (eighty, ninety), and of ten before which seems to have a mixed form (seventy).

At the 17th century, under the influence of Vaugelas and Household, the French Academy and the authors of Dictionnaire S adopted the forms seventy , eighty , ninety with the detriment of seventy , octante , ninety . However, the words seventy , octante , ninety appear in all the editions of the Dictionnaire of the French Academy . Still advised by the official Instructions of 1945 to facilitate the training of calculation, they remain known in the use spoken about many areas of the East and the South of France, like in Acadie. They are official in Suisse (like moreover, in this country, huitante for the central cantons) and in Belgium (except, in this country, of octante ).

Uses

Today, one finds of it a use more or less marked in several Langue S, in particular in Europe. But the decimal system generally prevails, because few languages have terms for 400,8000, etc

The vigesimal system is used:

in Basque,
in Breton, competition with a decimal system,
in Danish,
in French in a residual way, in Belgium, with the Canada and in France in the reading of 80 , eighty , or in France in the denomination of the Hospital of Quinze-Vingts, which sheltered 300 beds,
in Gaélique…

Mathematics

In base 20, twenty Chiffre S (or signs graphic) is used, that is to say ten of more than in the usual decimal system. As for any base of numeration higher than 10, the symbols making it possible to represent the figures beyond nine are obtained by using the letters of the Alphabet, on the basis of for ten, and until J for the figure nineteen has. One makes follow the number of ₂₀, because the Indice makes it possible to indicate the base used.

Another method of notation used differs from the preceding one only by the fact that the letter I is jumped, to avoid confusion between I (correspondent with 18 ) and 1 (correspondent with 1 ), thus the figure 18 is written J and quantifies it 19 is written K . As in any numbering system, the number equal to the value of the base is written 10 , in fact, 20 bases 20 of them is written 10 ₂₀.

With this notation, 20₂₀ = 40₁₀ (indeed, 2 × 20 = 40), DA₂₀ = 270₁₀ (indeed, 13 × 20 + 10 = 270), 100₂₀ = 400₁₀ (indeed, 20² = 400).

See too

Numeration

Base (arithmetic)

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