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Societies That Use Numeration Systems with Bases Other Than Ten

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Christie Helton

on 19 July 2013

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Transcript of Societies That Use Numeration Systems with Bases Other Than Ten

Societies That Use Numeration Systems with Bases Other Than Ten
The Dozenal Society of America
The dozenalists claim 12 is the best base mathematically.

The Oksapmin People of New Guinea: Base 27; Body Part Counting
The words for numbers are the words for the 27 body parts they use for counting, starting at the thumb of one hand, going up to the nose, then down the other side of the body to the pinky of the other hand.

Tip^na (thumb): 1
Dopa (wrist): 6
Nata (ear): 12
Tan-nata (opposite ear): 16
Tan-h^th^ta (opposite pinky): 27

This society uses the actual name for each body part to represent each number; 27 numbers represented by 27 body parts.
An Oksapmin woman displaying the traditional 27 body part counting system
Nimbia, Dialect of the Gwandara Language of Nigeria: Base 12

Multiples of 12 are the basic number words around which everything else is built.

Dozenal: Base 12
Most of the world evolved a counting system based on ten, but a system of weights and measures based on twelve.
For the most part, our ancestors counted on their fingers. At the same time, practical people measured in dozens.


the baker sold donuts in collections of twelve
the carpenter divided the ruler into twelve subdivisions
the grocer dealt in dozens and in dozens of dozens or grosses
the pharmacist and the jeweler still use the twelve ounce pound
the minters divided the shilling into twelve pence, etc.
Dozenal: Base 12
"counting in tens is a biological accident."
by using twelve subdivisions, you can use the three most common fractions without having to actually employ fractional notation
For 1⁄2, 1⁄3, and 1⁄4 of a foot are 6, 4, and 3 inches respectively—whole numbers, not fractions!
The Dozenal Society of America advocates a gradual change to dozenal counting.
French Number System
This society uses base-10 counting until 70, at which point it transitions to a mixture with base-20.
The French name their numbers by using the two numbers that add up to to that number.
EX. Vignt-et-un (Twenty and One)
20+1= 21
Vignt-deux (Twenty and Two)
Vignt-trois (Twenty and Three)

The numbers 70 and higher are base-20. The numbers names are determined by addition and multiplication.

EX. Soixante-dix (Seventy)

60+10= 70
Quatre-vignts (Four twenties)

4x20= 80
Quatre-vignt-dix-sept (Four twenties and seventeen)

4x20+10+7 = 97
Babylonian Number System
First Appeared in 3100 B.C.
Written in cuneiform
Used Sexageciamal (Base sixty)
No symbol for zero
Only used two symbols to represent 1-59
Symbol for 1
Symbol for 10
Vigesimal (Base twenty)
Made up of 3 symbols
Shell shape - Zero
Dot - One
Bar - Five
Uses vertical columns for each factor of 20
Mayan Numerals
When counting french numbers, the cases of seventy (70) and ninety (90) divert from the normal. Eleven(11) through nineteen(19) are added to both sixty(60) and eighty(80).
Therefore, seventy(70) is soixante-dix and proceeds as follows:

Soixante-dix: seventy (70)
Soixante-et-onze: seventy-one (71)
Soixatnte-deux: seventy-two (72)
Soixante-treize: seventy-three (73)

Counting with Body Parts
Tzotzil, a Mayan Language spoken in Mexico counts with not only one's body parts but with others too.

For numbers above 20, you refer to the digits of the next full man (vinik). Twenty-one is jun scha'vinik (first digit of the second man), 42 is chib yoxvinik (second digit of the third man), and 70 is lajuneb chanvinik (tenth digit of the fourth man).

Yoruba, a Niger-Congo language spoken in West Africa has a base-20 system. For each 10 numbers you advance, you add for the digits 1-4 and subtract for the digits 5-9.

EX. Fourteen is 10+4
Seventeen is 20-3.
"12 Mind Blowing Number Systems From Other Languages."
Mental Floss. N.p., n.d. Web. 19 July 2013.

"Babylonian Numerals." - Wikipedia, the Free Encyclopedia.
N.p., n.d. Web. 19 July 2013.

"The Dozenal Society of America." The Dozenal Society of
America. N.p., n.d. Web. 19 July 2013.

"Maya Numerals." - Wikipedia, the Free Encyclopedia. N.p.,
n.d. Web. 19 July 2013.

"The Number System of French." The Number System of
French. N.p., n.d. Web. 19 July 2013.
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