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Vigesimal
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List of numeral systems |
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).
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 A_{20} (the _{20} means base-20), to write nineteen as J_{20}, and the numbers between with the corresponding letters of the alphabet. This is similar to the common computer-science 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 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 10_{20}.
Converting table
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | C | D | E | F | G | H | I | J | 10 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
2 | 4 | 6 | 8 | A | C | E | G | I | 10 | 12 | 14 | 16 | 18 | 1A | 1C | 1E | 1G | 1I | 20 |
3 | 6 | 9 | C | F | I | 11 | 14 | 17 | 1A | 1D | 1G | 1J | 22 | 25 | 28 | 2B | 2E | 2H | 30 |
4 | 8 | C | G | 10 | 14 | 18 | 1C | 1G | 20 | 24 | 28 | 2C | 2G | 30 | 34 | 38 | 3C | 3G | 40 |
5 | A | F | 10 | 15 | 1A | 1F | 20 | 25 | 2A | 2F | 30 | 35 | 3A | 3F | 40 | 45 | 4A | 4F | 50 |
6 | C | I | 14 | 1A | 1G | 22 | 28 | 2E | 30 | 36 | 3C | 3I | 44 | 4A | 4G | 52 | 58 | 5E | 60 |
7 | E | 11 | 18 | 1F | 22 | 29 | 2G | 33 | 3A | 3H | 44 | 4B | 4I | 55 | 5C | 5J | 66 | 6D | 70 |
8 | G | 14 | 1C | 20 | 28 | 2G | 34 | 3C | 40 | 48 | 4G | 54 | 5C | 60 | 68 | 6G | 74 | 7C | 80 |
9 | I | 17 | 1G | 25 | 2E | 33 | 3C | 41 | 4A | 4J | 58 | 5H | 66 | 6F | 74 | 7D | 82 | 8B | 90 |
A | 10 | 1A | 20 | 2A | 30 | 3A | 40 | 4A | 50 | 5A | 60 | 6A | 70 | 7A | 80 | 8A | 90 | 9A | A0 |
B | 12 | 1D | 24 | 2F | 36 | 3H | 48 | 4J | 5A | 61 | 6C | 73 | 7E | 85 | 8G | 97 | 9I | A9 | B0 |
C | 14 | 1G | 28 | 30 | 3C | 44 | 4G | 58 | 60 | 6C | 74 | 7G | 88 | 90 | 9C | A4 | AG | B8 | C0 |
D | 16 | 1J | 2C | 35 | 3I | 4B | 54 | 5H | 6A | 73 | 7G | 89 | 92 | 9F | A8 | B1 | BE | C7 | D0 |
E | 18 | 22 | 2G | 3A | 44 | 4I | 5C | 66 | 70 | 7E | 88 | 92 | 9G | AA | B4 | BI | CC | D6 | E0 |
F | 1A | 25 | 30 | 3F | 4A | 55 | 60 | 6F | 7A | 85 | 90 | 9F | AA | B5 | C0 | CF | DA | E5 | F0 |
G | 1C | 28 | 34 | 40 | 4G | 5C | 68 | 74 | 80 | 8G | 9C | A8 | B4 | C0 | CG | DC | E8 | F4 | G0 |
H | 1E | 2B | 38 | 45 | 52 | 5J | 6G | 7D | 8A | 97 | A4 | B1 | BI | CF | DC | E9 | F6 | G3 | H0 |
I | 1G | 2E | 3C | 4A | 58 | 66 | 74 | 82 | 90 | 9I | AG | BE | CC | DA | E8 | F6 | G4 | H2 | I0 |
J | 1I | 2H | 3G | 4F | 5E | 6D | 7C | 8B | 9A | A9 | B8 | C7 | D6 | E5 | F4 | G3 | H2 | I1 | J0 |
10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 | A0 | B0 | C0 | D0 | E0 | F0 | G0 | H0 | I0 | J0 | 100 |
Decimal | Vigesimal | |
---|---|---|
0 | 0 | |
1 | 1 | |
2 | 2 | |
3 | 3 | |
4 | 4 | |
5 | 5 | |
6 | 6 | |
7 | 7 | |
8 | 8 | |
9 | 9 | |
10 | A | |
11 | B | |
12 | C | |
13 | D | |
14 | E | |
15 | F | |
16 | G | |
17 | H | |
18 | I | J |
19 | J | K |
According to this notation:
- 20_{20} means forty in decimal = {(2 × 20^{1}) + (0 × 20^{0})}
- D0_{20} means two hundred [and] sixty in decimal = {(13 × 20^{1}) + (0 × 20^{0})}
- 100_{20} means four hundred in decimal = {(1 × 20^{2}) + (0 × 20^{1}) + (0 × 20^{0})}.
In the rest of this article below, numbers are expressed in decimal notation, unless specified otherwise. For example, 10 means ten, 20 means twenty.
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). As 20 has the same prime factors as 10 (two and five), any fraction that terminates in decimal will terminate in vigesimal, and any fraction that does not terminate in decimal will not terminate in vigesimal either: the converses of these statements are also true.
In decimal Prime factors of the base: 2, 5 Prime factors of one below the base: 3 Prime factors of one above the base: 11 |
In vigesimal Prime factors of the base: 2, 5 Prime factors of one below the base: J Prime factors of one above the base: 3, 7 | ||||
Fraction | Prime factors of the denominator |
Positional representation | Positional representation | Prime factors of the denominator |
Fraction |
1/2 | 2 | 0.5 | 0.A | 2 | 1/2 |
1/3 | 3 | 0.3333... = 0.3 | 0.6D6D... = 0.6D | 3 | 1/3 |
1/4 | 2 | 0.25 | 0.5 | 2 | 1/4 |
1/5 | 5 | 0.2 | 0.4 | 5 | 1/5 |
1/6 | 2, 3 | 0.16 | 0.36D | 2, 3 | 1/6 |
1/7 | 7 | 0.142857 | 0.2H | 7 | 1/7 |
1/8 | 2 | 0.125 | 0.2A | 2 | 1/8 |
1/9 | 3 | 0.1 | 0.248HFB | 3 | 1/9 |
1/10 | 2, 5 | 0.1 | 0.2 | 2, 5 | 1/A |
1/11 | 11 | 0.09 | 0.1G759 | B | 1/B |
1/12 | 2, 3 | 0.083 | 0.16D | 2, 3 | 1/C |
1/13 | 13 | 0.076923 | 0.1AF7DGI94C63 | D | 1/D |
1/14 | 2, 7 | 0.0714285 | 0.18B | 2, 7 | 1/E |
1/15 | 3, 5 | 0.06 | 0.16D | 3, 5 | 1/F |
1/16 | 2 | 0.0625 | 0.15 | 2 | 1/G |
1/17 | 17 | 0.0588235294117647 | 0.13ABF5HCIG984E27 | H | 1/H |
1/18 | 2, 3 | 0.05 | 0.1248HFB | 2, 3 | 1/I |
1/19 | 19 | 0.052631578947368421 | 0.1 | J | 1/J |
1/20 | 2, 5 | 0.05 | 0.1 | 2, 5 | 1/10 |
Real numbers
Algebraic irrational number | In decimal | In vigesimal |
√2 (the length of the diagonal of a unit square) | 1.41421356237309... | 1.85DE37JGF09H6... |
√3 (the length of the diagonal of a unit cube) | 1.73205080756887... | 1.ECG82BDDF5617... |
√5 (the length of the diagonal of a 1×2 rectangle) | 2.2360679774997... | 2.4E8AHAB3JHGIB... |
φ (phi, the golden ratio = (1+√5)/2 | 1.6180339887498... | 1.C7458F5BJII95... |
Transcendental irrational number | ||
π (pi, the ratio of circumference to diameter) | 3.14159265358979... | 3.2GCEG9GBHJ9D2... |
e (the base of the natural logarithm) | 2.7182818284590452... | 2.E7651H08B0C95... |
γ (the limiting difference between the harmonic series and the natural logarithm) | 0.5772156649015328606... | 0.BAHEA2B19BDIBI... |
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.
Ogún, 20, is the basic numeric block. Ogójì, 40, (Ogún-meji) = 20 multiplied by 2 (èjì). Ogota, 60, (Ogún-mẹ̀ta) = 20 multiplied by 3 (ẹ̀ta). Ogorin, 80, (Ogún-mẹ̀rin) = 20 multiplied by 4 (ẹ̀rin). Ogorun, 100, (Ogún-màrún) = 20 multiplied by 5 (àrún).
16 (Ẹẹ́rìndílógún) = 4 less than 20. 17 (Etadinlogun) = 3 less than 20. 18 (Eejidinlogun) = 2 less than 20. 19 (Okandinlogun) = 1 less than 20. 21 (Okanlelogun) = 1 increment on 20. 22 (Eejilelogun) = 2 increment on 20. 23 (Etalelogun) = 3 increment on 20. 24 (Erinlelogun) = 4 increment on 20. 25 (Aarunlelogun) = 5 increment on 20.
Americas
- 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 (20^{2} = 400), pic (20^{3} = 8,000), calab (20^{4} = 160,000), kinchil (20^{5} = 3,200,000) and alau (20^{6} = 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.)
- The Tlingit people use base 20.
- The Inuit numbering system is base 20.
Asia
- Dzongkha, the national language of Bhutan, has a full vigesimal system, with numerals for the powers of twenty 20, 400, 8,000, and 160,000.
- In Santali, a Munda language of India, "fifty" is expressed by the phrase bār isī gäl, literally "two twenty ten."^{[1]} Likewise, in Didei, another Munda language spoken in India, complex numerals are decimal to 19 and decimal-vigesimal to 399.^{[2]}
- 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.
In Europe
Origins
"Vigesimal" has its roots in the Latin male word vicesimus (in its first or second declension).
Examples
- Twenty (vingt) is used as a base number in the French language names of numbers from 70 to 99, except in the French of Belgium, Switzerland, the Democratic Republic of the Congo, Rwanda, the Aosta Valley and the Channel Islands. For example, quatre-vingts, the French word for "80", literally means "four-twenties"; soixante-dix, the word for "70", is literally "sixty-ten"; soixante-quinze ("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, 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); in the past octante was also in use.
- 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 (ugent) is used as a base number in the Breton language names of numbers from 40 to 49 and from 60 to 99. For example, daou-ugent means 2 times 20, i.e. 40, and triwec'h ha pevar-ugent (literally "three-six and four-twenty") means 3×6 + 4×20, i.e. 98. However, 30 is tregont and not *dek ha ugent ("ten and twenty"), and 50 is hanter-kant ("half-hundred").
- Twenty (ugain) is used as a base number in the Welsh language, although in the latter part of the twentieth century^{[citation needed]} a decimal counting system has come to be preferred (particularly in the South),^{[citation needed]} 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. A vigesimal system (Yan Tan Tethera) for counting sheep has also been recorded in areas of Britain that today are no longer Celtic-speaking.
- Scottish Gaelic traditionally uses a vigesimal system similar to that of traditional Irish, with (fichead) being the word for twenty, deich ar fhichead being 30 (ten over twenty), dà fhichead 40 (two twenties), dà fhichead 's a deich 50 (two twenty and ten), trì fichead 60 (three twenties) and so on up to naoidh fichead 180 (nine twenties). A decimal system is now taught in schools.
- Twenty (njëzet) is used as a base number in the Albanian language. The word for 40 (dyzet) means two times 20 (some Gheg subdialects, however, use 'katërdhetë'). The Arbëreshë in Italy may use 'trizetë' for 60. Formerly, 'katërzetë' was also used for 80. Today Cham Albanians in Greece use all zet numbers. Basically 20 means 1 zet, 40 means 2 zet, 60 means 3 zet and 80 means 4 zet.
- 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 (tqa) is used as a base number in the Nakh languages.
- 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. For example, the number 75 is called hirurogeita hamabost, lit. "three-score-and ten-five". The Basque nationalist Sabino Arana proposed a vigesimal digit system to match the spoken language,^{[3]} and, as an alternative, a reform of the spoken language to make it decimal,^{[4]} but both are mostly forgotten.^{[5]}
- Twenty (dwisti) is used as a base number in the Resian dialect of the Slovenian language in Italy's Resia Valley. 60 is expressed by trïkart dwisti (3×20), 70 by trïkart dwisti nu dësat (3×20 + 10), 80 by štirikrat dwisti (4×20) and 90 by štirikrat dwisti nu dësat (4×20 + 10).
- In the old British currency system (pre-1971), there were 20 shillings (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 in a ton.
- 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. In the Authorised Version of the Bible the term score is used over 130 times although only when prefixed by a number greater than one while a single "score" is always expressed as twenty. The use of the term score to signify multiples of twenty has fallen into disuse in modern English.
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^{[6]}). 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. 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 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), 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 it may in fact be only found in these names of the numbers 11-19.
- Cantonese^{[7]} and Wu Chinese frequently use the single unit 廿 (Cantonese yàh, Shanghainese nyae or ne, Mandarin niàn) for twenty, in addition to the fully decimal 二十 (Cantonese yìh sàhp, Shanghainese el sah, Mandarin èr shí) which literally means "two ten". Equivalents exist for 30 and 40 (卅 and 卌 respectively: Mandarin sà and xì), but these are more seldom used. This is a historic remnant of a vigesimal system.
- Thai uses the term ยี่สิบ (yi sip) for 20. Other multiples of ten consist of the base number, followed by the word for ten, e.g. สามสิบ (sam sip), litt. three ten, for thirty. The yi of yi sip is different from the number two in other positions, which is สอง (song).
- Lao similarly forms multiples of ten by putting the base number in front of the word ten, so ສາມສິບ (sam sip), litt. three ten, for thirty. The exception is twenty, for which the word ຊາວ (xao) is used. (ซาว 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
Powers of Twenty in Yucatec Maya and Nahuatl | |||||||||
---|---|---|---|---|---|---|---|---|---|
Number | English | Maya | Nahuatl (modern orthography) | Classical Nahuatl | Nahuatl root | Aztec pictogram | |||
1 | One | Hun | Se | Ce | Ce | 20px | |||
20 | Twenty | K'áal | Sempouali | Cempohualli (Cempoalli) | Pohualli | 20px | |||
400 | Four hundred | Bak | Sentsontli | Centzontli | Tzontli | 20px | |||
8000 | Eight thousand | Pic | Senxikipili | Cenxiquipilli | Xiquipilli | 20px | |||
160.000 | One hundred sixty thousand | Calab | Sempoualxikipili | Cempohualxiquipilli | Pohualxiquipilli | ||||
3.200.000 | Three million two hundred thousand | Kinchil | Sentsonxikipili | Centzonxiquipilli | Tzonxiquipilli | ||||
64.000.000 | Sixty-four million | Alau | Sempoualtzonxikipili | Cempohualtzonxiquipilli | Pohualtzonxiquipilli |
Counting in units of twenty
This table shows the Maya numerals and the number names in Yucatec Maya, Nahuatl in modern orthography and in Classical Nahuatl.
From one to ten (1 - 10) | |||||||||
---|---|---|---|---|---|---|---|---|---|
1 (one) | 2 (two) | 3 (three) | 4 (four) | 5 (five) | 6 (six) | 7 (seven) | 8 (eight) | 9 (nine) | 10 (ten) |
40px | 40px | 40px | 40px | 40px | 40px | 40px | 40px | 40px | 40px |
Hun | Ka'ah | Óox | Kan | Ho' | Wak | Uk | Waxak | Bolon | Lahun |
Se | Ome | Yeyi | Naui | Makuili | Chikuasen | Chikome | Chikueyi | Chiknaui | Majtlaktli |
Ce | Ome | Yei | Nahui | Macuilli | Chicuace | Chicome | Chicuei | Chicnahui | Matlactli |
From eleven to twenty (11 - 20) | |||||||||
11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
40px | 40px | 40px | 40px | 40px | 40px | 40px | 40px | 40px | 40px 40px |
Buluk | Lahka'a | Óox lahun | Kan lahun | Ho' lahun | Wak lahun | Uk lahun | Waxak lahun | Bolon lahun | Hun k'áal |
Majtlaktli onse | Majtlaktli omome | Majtlaktli omeyi | Majtlaktli onnaui | Kaxtoli | Kaxtoli onse | Kaxtoli omome | Kaxtoli omeyi | Kaxtoli onnaui | Sempouali |
Matlactli huan ce | Matlactli huan ome | Matlactli huan yei | Matlactli huan nahui | Caxtolli | Caxtolli huan ce | Caxtolli huan ome | Caxtolli huan yei | Caxtolli huan nahui | Cempohualli |
From twenty-one to thirty (21 - 30) | |||||||||
21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 |
40px 40px |
40px 40px |
40px 40px |
40px 40px |
40px 40px |
40px 40px |
40px 40px |
40px 40px |
40px 40px |
40px 40px |
Hump'éel katak hun k'áal | Ka'ah katak hun k'áal | Óox katak hun k'áal | Kan katak hun k'áal | Ho' katak hun k'áal | Wak katak hun k'áal | Uk katak hun k'áal | Waxak katak hun k'áal | Bolon katak hun k'áal | Lahun katak hun k'áal |
Sempouali onse | Sempouali omome | Sempouali omeyi | Sempouali onnaui | Sempouali ommakuili | Sempouali onchikuasen | Sempouali onchikome | Sempouali onchikueyi | Sempouali onchiknaui | Sempouali ommajtlaktli |
Cempohualli huan ce | Cempohualli huan ome | Cempohualli huan yei | Cempohualli huan nahui | Cempohualli huan macuilli | Cempohualli huan chicuace | Cempohualli huan chicome | Cempohualli huan chicuei | Cempohualli huan chicnahui | Cempohualli huan matlactli |
From thirty-one to forty (31 - 40) | |||||||||
31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 |
40px 40px |
40px 40px |
40px 40px |
40px 40px |
40px 40px |
40px 40px |
40px 40px |
40px 40px |
40px 40px |
40px 40px |
Buluk katak hun k'áal | Lahka'a katak hun k'áal | Óox lahun katak hun k'áal | Kan lahun katak hun k'áal | Ho' lahun katak hun k'áal | Wak lahun katak hun k'áal | Uk lahun katak hun k'áal | Waxak lahun katak hun k'áal | Bolon lahun katak hun k'áal | Ka' k'áal |
Sempouali ommajtlaktli onse | Sempouali ommajtlaktli omome | Sempouali ommajtlaktli omeyi | Sempouali ommajtlaktli onnaui | Sempouali onkaxtoli | Sempouali onkaxtoli onse | Sempouali onkaxtoli omome | Sempouali onkaxtoli omeyi | Sempouali onkaxtoli onnaui | Ompouali |
Cempohualli huan matlactli huan ce | Cempohualli huan matlactli huan ome | Cempohualli huan matlactli huan yei | Cempohualli huan matlactli huan nahui | Cempohualli huan caxtolli | Cempohualli huan caxtolli huan ce | Cempohualli huan caxtolli huan ome | Cempohualli huan caxtolli huan yei | Cempohualli huan caxtolli huan nahui | Ompohualli |
From twenty to two hundred in steps of twenty (20 - 200) | |||||||||
20 | 40 | 60 | 80 | 100 | 120 | 140 | 160 | 180 | 200 |
40px 40px |
40px 40px |
40px 40px |
40px 40px |
40px 40px |
40px 40px |
40px 40px |
40px 40px |
40px 40px |
40px 40px |
Hun k'áal | Ka' k'áal | Óox k'áal | Kan k'áal | Ho' k'áal | Wak k'áal | Uk k'áal | Waxak k'áal | Bolon k'áal | Lahun k'áal |
Sempouali | Ompouali | Yepouali | Naupouali | Makuilpouali | Chikuasempouali | Chikompouali | Chikuepouali | Chiknaupouali | Majtlakpouali |
Cempohualli | Ompohualli | Yeipohualli | Nauhpohualli | Macuilpohualli | Chicuacepohualli | Chicomepohualli | Chicueipohualli | Chicnahuipohualli | Matlacpohualli |
From two hundred twenty to four hundred in steps of twenty (220 - 400) | |||||||||
220 | 240 | 260 | 280 | 300 | 320 | 340 | 360 | 380 | 400 |
40px 40px |
40px 40px |
40px 40px |
40px 40px |
40px 40px |
40px 40px |
40px 40px |
40px 40px |
40px 40px |
40px 40px 40px |
Buluk k'áal | Lahka'a k'áal | Óox lahun k'áal | Kan lahun k'áal | Ho' lahun k'áal | Wak lahun k'áal | Uk lahun k'áal | Waxak lahun k'áal | Bolon lahun k'áal | Hun bak |
Majtlaktli onse pouali | Majtlaktli omome pouali | Majtlaktli omeyi pouali | Majtlaktli onnaui pouali | Kaxtolpouali | Kaxtolli onse pouali | Kaxtolli omome pouali | Kaxtolli omeyi pouali | Kaxtolli onnaui pouali | Sentsontli |
Matlactli huan ce pohualli | Matlactli huan ome pohualli | Matlactli huan yei pohualli | Matlactli huan nahui pohualli | Caxtolpohualli | Caxtolli huan ce pohualli | Caxtolli huan ome pohualli | Caxtolli huan yei pohualli | Caxtolli huan nahui pohualli | Centzontli |
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
- ^ Gvozdanović, Jadranka. Numeral Types and Changes Worldwide (1999), p.223.
- ^ Chatterjee, Suhas. 1963. On Didei nouns, pronouns, numerals, and demonstratives. Chicago: mimeo., 1963. (cf. Munda Bibliography at the University of Hawaii Department of Linguistics)
- ^ 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, 1908, Bilbao, Eléxpuru Hermanos. 102–112
- ^ Artículos ..., Sabino Arana, 112–118
- ^ Efemérides Vascas y Reforma d ela Numeración Euzkérica, Sabino Arana, Biblioteca de la Gran Enciclopedia Vasca, Bilbao, 1969. Extracted from the magazine Euskal-Erria, 1880 and 1881.
- ^ 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.)
- ^ Lau, S. A Practical Cantonese English Dictionary (1977) The Government Printer