48 quarante-huit. 78 soixante-dix-huit. 19 dix-neuf. 49 quarante-neuf. 79 soixante-dix-neuf. 20 vingt. 50 cinquante. 80 quatre-vingts. 21 vingt et un.
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counting in French 90 is surprising! 0 z”ro 30 trente 60 soixante 90 quatre-vingt-dix 1 un31 trente et un 61 soixante et un 91 quatre-vingt-onze 2 deux 32 trente-deux 62 soixante-deux 3 trois 33 trente-trois 63 soixante-trois 4 quatre 34 trente-quatre 64 soixante-quatre 5 cinq 35 trente-cinq 65 soixante-cinq 6 six 36 trente-six 66 soixante-six 7 sept 37 trente-sept 67 soixante-sept 8 huit 38 trente-huit 68 soixante-huit 9 neuf 39 trente-neuf 69 soixante-neuf 10 dix40 quarante 70 soixante-dix 11 onze 41 quarante et un 71 soixante et onze 12 douze 42 quarante-deux 72 soixante-douze 13 treize 43 quarante-trois 73 soixante-treize 14 quatorze 44 quarante-quatre 74 soixante-quatorze 15 quinze 45 quarante-cinq 75 soixante-quinze 16 seize 46 quarante-six 76 soixante-seize 17 dix-sept 47 quarante-sept 77 soixante-dix-sept 18 dix-huit 48 quarante-huit 78 soixante-dix-huit 19 dix-neuf 49 quarante-neuf 79 soixante-dix-neuf 20 vingt 50 cinquante 80 quatre-vingts 21 vingt et un 51 cinquante et un 81 quatre-vingt-un 22 vingt-deux 52 cinquante-deux 82 quatre-vingt-deux 23 vingt-trois 53 cinquante-trois 83 quatre-vingt-trois 24 vingt-quatre 55 cinquante-quatre 84 quatre-vingt-quatre 25 vingt-cinq 55 cinquante-cinq 85 quatre-vingt-cinq 26 vingt-six 56 cinquante-six 86 quatre-vingt-six 27 vingt-sept 57 cinquante-sept 87 quatre-vingt-sept 28 vingt-huit 58 cinquante-huit 88 quatre-vingt-huit 29 vingt-neuf 59 cinquante-neuf 89 quatre-vingt-neuf 2
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counting in French 90 is surprising! 70 and 80 are too! 0 z”ro 30 trente 60 soixante 90 quatre-vingt-dix 1 un31 trente et un 61 soixante et un 91 quatre-vingt-onze 2 deux 32 trente-deux 62 soixante-deux 3 trois 33 trente-trois 63 soixante-trois 4 quatre 34 trente-quatre 64 soixante-quatre 5 cinq 35 trente-cinq 65 soixante-cinq 6 six 36 trente-six 66 soixante-six 7 sept 37 trente-sept 67 soixante-sept 8 huit 38 trente-huit 68 soixante-huit 9 neuf 39 trente-neuf 69 soixante-neuf 10 dix40 quarante 70 soixante-dix 11 onze 41 quarante et un 71 soixante et onze 12 douze 42 quarante-deux 72 soixante-douze 13 treize 43 quarante-trois 73 soixante-treize 14 quatorze 44 quarante-quatre 74 soixante-quatorze 15 quinze 45 quarante-cinq 75 soixante-quinze 16 seize 46 quarante-six 76 soixante-seize 17 dix-sept 47 quarante-sept 77 soixante-dix-sept 18 dix-huit 48 quarante-huit 78 soixante-dix-huit 19 dix-neuf 49 quarante-neuf 79 soixante-dix-neuf 20 vingt 50 cinquante 80 quatre-vingts 21 vingt et un 51 cinquante et un 81 quatre-vingt-un 22 vingt-deux 52 cinquante-deux 82 quatre-vingt-deux 23 vingt-trois 53 cinquante-trois 83 quatre-vingt-trois 24 vingt-quatre 55 cinquante-quatre 84 quatre-vingt-quatre 25 vingt-cinq 55 cinquante-cinq 85 quatre-vingt-cinq 26 vingt-six 56 cinquante-six 86 quatre-vingt-six 27 vingt-sept 57 cinquante-sept 87 quatre-vingt-sept 28 vingt-huit 58 cinquante-huit 88 quatre-vingt-huit 29 vingt-neuf 59 cinquante-neuf 89 quatre-vingt-neuf trente 30 = 3 ! 10 quarante 40 = 4 ! 10 cinquante 50 = 5 ! 10 soixante 60 = 6 ! 10 soixante-dix 70 = 6 ! 10 +10 quatre-vingts 80 = 4 ! 20 quatre-vingts-dix 90 = 4 ! 20 +10 3
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counting in French different French speakers count differently 102030405060708090DIALECT AREA dix vingt trente quarante cinquante soixante soixante-dix quatre-vingts quatre-vingt-dix Paris dix vingt trente quarante cinquante soixante septante quatre-vingts nonante Belgium dix vingt trente quarante cinquante soixante septante huitante nonante Switzerland dix vingt trente quarante cinquante soixante septante octante nonante Occitania 4
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counting in French southern and eastern French speakers count like Italians 102030405060708090DIALECT AREA dix vingt trente quarante cinquante soixante soixante-dix quatre-vingts quatre-vingt-dix Paris dix vingt trente quarante cinquante soixante septante quatre-vingts nonante Belgium dix vingt trente quarante cinquante soixante septante huitante nonante Switzerland dix vingt trente quarante cinquante soixante septante octante nonante Occitania dieci venti trenta quaranta cinquanta sessanta settanta ottanta novanta Milanquatre-vingts = 4 !20 huitante = 8 !10 octante = 8 !10 ottanta = 8 !10quatre-vingts-dix = 4 !20 +10 nonante = 8 !10 novanta = 8 !105
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the spread from Normandy ¥Comparative linguistic analysis suggests that a Viking pattern of base-20 number words was introduced to Normandy, from where is spread and displaced some Roman base-10 number words. ¥This was a re-introduction, because the pre-Roman Gauls also counted in base-20. ¥We can still find base-20 numerals in modern Welsh ( ugain “20”, deugain “40”, pedwar ugain “80”) and in modern Danish. old base-20 pattern6
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Decimal, vigesimal, quinary, duodecimal, etc. Vigesimal counting in Mayan and Ainu anticipatory vigesimal counting in Q”eqchi! Mayan written spoken phrase meaning of spoken phrase 58kwaqxaqlajuh roxk “aal 18 on the way to 3 !20 (18 of the 3rd 20) 59belelajuh roxkÕaal 19 on the way to 3 !20 (19 of the 3rd 20) 60oxkÕaal 3!2061jun xkaakÕaal 1 on the way to 4 !20 (1 of the 4th 20) 62kwiib xkaakÕaal 2 on the way to 4 !20 (2 of the 4th 20) Historically, the counting systems of the worldÕs languages have been typically based on the numbers 10 (decimal ), 20 (vigesimal ), 5 (quinary ), and 12 (duodecimal ). A base-10 system with subbases 2 and 5 is called biquinary, and a base-20 system with subbases 4 and 5 is called quadquinary. To create complex number words from basic number words, languages use multiplicative, additive, subtractive, and anticipatory strategies. The Mayan languages have perhaps the most famous vigesimal counting systems , and the written Maya numerals are quadquinary. The Ainu language has a vigesimal counting system, but nowadays the Ainu people speak Japanese. Because of influence from English, Spanish, Chinese, and other dominant languages, many languages with original vigesimal counting systems have become or are becoming decimal. 8
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ethnomathematicsstudying the relationships between mathematics and culture Topics studied in ethnomathematics include: systems of counting systems of mapping pastimes and games of skill: board games, string patterns, graphic drawings symmetry in art, aesthetics of proportion, patterns of weaving, tiling patterns musical tunings The mathematics of how different cultures do similar things can be interesting. 9
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