Editing Ethnomathematics (section)

===Numerals and naming systems===

====Numerals====

Some of the systems for representing numbers in previous and present cultures are well known. [[Roman numerals]] use a few letters of the alphabet to represent numbers up to the thousands, but are not intended for arbitrarily large numbers and can only represent positive [[integers]]. [[Arabic numerals]] are a family of systems, originating in India and passing to [[Islamic Golden Age|medieval Islamic civilization]], then to Europe, and now standard in global culture—and having undergone many curious changes with time and geography—can represent arbitrarily large numbers and have been adapted to negative numbers, [[fractions]], and [[real numbers]].

Less well known systems include some that are written and can be read today, such as the [[Hebrew numerals|Hebrew]] and [[Greek numerals|Greek]] method of using the letters of the [[alphabet]], in order, for digits 1–9, tens 10–90, and hundreds 100–900.

A completely different system is that of the [[quipu]], which recorded numbers on knotted strings.

Ethnomathematicians are interested in the ways in which numeration systems grew up, as well as their similarities and differences and the reasons for them.  The great variety in ways of representing numbers is especially intriguing.

====Names for numbers====

This means the ways in which number words are formed.<ref>(See Menninger (1934, 1969).) Menninger, Karl (1934), ''Zahlwort und Ziffer''. Revised edition (1958). Göttingen: Vandenhoeck and Ruprecht. (See Menninger (1934, 1969).) Menninger, Karl (1969), ''Number Words and Number Symbols''. Cambridge, Massachusetts: The MIT Press.</ref><ref>Zaslavsky (1973) Zaslavsky, Claudia (1973). ''Africa Counts: Number and Pattern in African Culture''. Third revised ed., 1999. Chicago: Lawrence Hill Books. {{ISBN|1-55652-350-5}}</ref>

=====English=====
For instance, in [[English language|English]], there are four different systems. The units words (one to nine) and ten are special.  The next two are reduced forms of [[Old English language|Anglo-Saxon]] "one left over" and "two left over" (i.e., after counting to ten).  Multiples of ten from "twenty" to "ninety" are formed from the units words, one through nine, by a single pattern.  Thirteen to nineteen are compounded from tens and units words in one way, and the non-multiples of ten from twenty-one to ninety-nine are compounded from tens and units words in a different way.  Larger numbers are also formed on a base of ten and its powers ("[[hundred]]" and "[[thousand]]").  One may suspect this is based on an ancient tradition of [[Finger-counting|finger counting]].  Residues of ancient counting by 20s and 12s are the words "[[Score (number)|score]]", "[[dozen]]", and "gross". (Larger number words like "[[million]]" are not part of the original English system; they are scholarly creations based ultimately on Latin.).  There were historical inconsistencies in the way the term "[[billion]]" was used between American English and British English. These have since been reconciled, and modern English speakers universally refer to 1,000,000,000 as 'one billion'.

=====German=====
The [[German language]] and [[Dutch language|Dutch]] language counts similarly to English, but the unit is placed before the tens in numbers over 20. For example, "26" is "sechsundzwanzig", literally "six and twenty". This system was formerly common in English, as seen in an artifact from the English [[nursery rhyme]] "[[Sing a Song of Sixpence]]": ''Sing a song of sixpence, / a pocket full of rye. / Four and twenty blackbirds, / baked in a pie.'' It persists in some children's songs such as "[https://guidezone.e-guiding.com/jmone_twenty.htm One and Twenty] {{Webarchive|url=https://web.archive.org/web/20190323025144/http://guidezone.e-guiding.com/jmone_twenty.htm |date=2019-03-23 }}."

=====French=====
In the [[French language]] as used in France, one sees some differences. ''Soixante-dix'' (literally, "sixty-ten") is used for "seventy". The words "quatre-vingt" (literally, "four-twenty", or 80) and "quatre-vingt-dix" (literally, "four-twenty ten" 90) are based on 20 ("vingt") instead of 10. [[Swiss French]] and [[Belgian French]] do not use these forms, preferring more standard [[Latin]]ate forms: ''septante'' for 70, ''huitante'' (formerly ''octante'') for 80 (only in Swiss French) and ''nonante'' for 90.<ref>{{cite magazine |title=Bien écrire et parler juste, guide pratique d'expression et de communication |magazine=[[Reader's Digest|Sélection du Reader's Digest]] |page=21 |language=fr }}</ref><ref>{{citation |language=fr |first1=Yves |last1=Cormier |author-link=Yves Cormier |title=Dictionnaire du français acadien |editor=Fides |year=2009 |page=253 |publisher=Fides |isbn=978-2-7621-3010-2 }}.</ref>

=====Welsh=====
Counting in Welsh combines the vigesimal system (counting in twenties) with some other features.{{citation needed|date=March 2020}} The following system is optional for cardinal numbers nowadays, but mandatory for ordinal numbers.

{|class="wikitable"
|+Examples of numbers in Welsh
|-
|14||pedwar ar ddeg||four upon ten
|-
|15||pymtheg||five-ten
|-
|16||un ar bymtheg||one on five-ten
|-
|20||ugain||score
|-
|37||dau ar bymtheg ar hugain||two on five-ten on score
|-
|57||hanner cant a saith||half hundred and seven
|-
|77||dau ar bymtheg a thrigain||two on five-ten and three-score
|-
|99||cant namyn un||hundred less one
|}

=====Chinese=====

Number words in Chinese are assembled from the words for "one" through "nine" and words for powers of ten.

For example, what is in English written out as "twelve thousand three hundred forty five" is "一万二千三百四十五" (simplified) / "一萬二千三百四十五" (traditional) whose characters translate to "one ten-thousand two thousand three hundred four ten five".

=====Mesopotamia=====
In ancient [[Mesopotamia]], the base for constructing numbers was [[Sexagesimal|60]], with 10 used as an intermediate base for numbers below 60.

=====West Africa=====
Many West African languages generally base their number words on a combination of 5 and 20, derived from thinking of a complete hand or a complete set of [[Digit (anatomy)|digits]] comprising both fingers and toes. In fact, in some languages, the words for 5 and 20 refer to these body parts. The words for numbers below 20 are based on 5 and higher numbers combine the lower numbers with multiples and powers of 20.<ref>Zaslavsky, Claudia (1973). ''Africa Counts: Number and Pattern in African Culture''. Third revised ed., 1999. Chicago: Lawrence Hill Books. {{ISBN|1-55652-350-5}}</ref>

====Finger counting====
{{Main|Finger counting}}
Many systems of [[finger counting]] have been, and still are, used in various parts of the world. Most are not as obvious as holding up a number of fingers. The position of fingers may be most important.<ref>(See Zaslavsky (1980) for some finger-counting gestures.)  Zaslavsky, Claudia (1980). ''Count On Your Fingers African Style''. New York: Thomas Y. Crowell. Revised with new illustrations, New York: Black Butterfly Books. {{ISBN|0-86316-250-9}}</ref> One continuing use for finger counting is for people who speak different languages to communicate prices in the marketplace.

In contrast to finger counting, the [[Yuki people]] (indigenous Americans from [[Northern California]]) keep count by using the four spaces between their fingers rather than the fingers themselves.<ref>{{citation
| title=Ethnomathematics: A Multicultural View of Mathematical Ideas
| first=Marcia
| last=Ascher
| year=1994
| publisher=Chapman & Hall
| isbn=0-412-98941-7
}}</ref> This is known as an [[octal]] (base-8) counting system.