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[[Image:maya.svg|thumb|right|Maya numerals]]
{| class="wikitable" style="text-align:center; margin-left:1em; float: right" [[Mayan Numbers/Numerals: Explained in a table]]
|-
|400s
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| {{Horizontal Maya|5}}
|-
| Total(s)
|▼
| 33
| 429
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The '''MayaMayan numeral system''' was the system to represent [[number]]s and [[calendar date]]s in the [[Maya civilization]]. It was a [[vigesimal]] (base-20) [[positional notation|positional]] [[numeral system]]. The numerals are made up of three symbols: [[Zero number#The Americas|zero]] (a [[Oliva reticulata|sea shell]]),<ref>{{Cite web |titlelast=mathematicsBatz -|first=J. WasMucía the|date=March symbol29, post-classical2021 Mayans|title=“Nik” used— toThe representZero zeroin reallyVigesimal derivedMaya fromMathematics a|url=https://baas.aas.org/pub/2021n1i336p03/release/2 depiction of|url-status=live a turtle shell?|archive-url=https://historyarchive.stackexchangetoday/20240910192515/https://baas.comaas.org/questionspub/661622021n1i336p03/was-therelease/2 |archive-symbol-post-classical-mayans-used-to-represent-zero-really-derived-fromdate=September 10, 2024 |access-date=2021-09-October 30, 2024 |website=HistoryBulletin Stackof the ExchangeAAS}}</ref> [[1 (number)|one]] (a dot) and [[5 (number)|five]] (a bar). For example, thirteen is written as three dots in a horizontal row above two horizontal bars; sometimes it is also written as three vertical dots to the left of two vertical bars. With these three symbols, each of the twenty vigesimal digits could be written.
 
Numbers after 19 were written vertically in powers of twenty. The MayaMayan used powers of twenty, just as the [[Hindu–Arabic numeral system]] uses powers of ten.<ref>{{cite web |author=Saxakali |date=1997 |year= |title=Mayan Numerals |url=http://saxakali.com/historymam2.htm|title=Maya Numerals|author=Saxakali|year=1997|archive-url=https://web.archive.org/web/20060714025120/http://www.saxakali.com/historymam2.htm |archive-date=July 14, 2006-07-14 |access-date=2006-07-July 29}}</ref> For example, thirty-three would be written as one dot, above three dots atop two bars. The first dot represents "one twenty" or "1×20", which is added to three dots and two bars, or thirteen. Therefore, (1×20) + 132006 |website= 33. Upon reaching 20<sup>2Saxakali}}</supref> or 400, another row is started (20<sup>3</sup> or 8000, then 20<sup>4</sup> or 160,000, and so on). The number 429 would be written as one dot above one dot above four dots and a bar, or (1×20<sup>2</sup>) + (1×20<sup>1</sup>) + 9 = 429.
 
For example, thirty-three would be written as one dot, above three dots atop two bars. The first dot represents "one twenty" or "1×20", which is added to three dots and two bars, or thirteen. Therefore, (1×20) + 13 = 33.
 
:{| class="mw-collapsible mw-collapsed" style="text-align:center;"
|+Addition (single)
|- style="font-size: 150%;"
| (1×20)
| +
| 13
| =
| 33
|-
| {{Horizontal Maya|1}}
▲|
| {{Horizontal Maya|13}}
|
| {{Horizontal Maya|1}}{{Horizontal Maya|13}}
|}
 
Upon reaching 20<sup>2</sup> or 400, another row is started (20<sup>3</sup> or 8000, then 20<sup>4</sup> or 160,000, and so on). The number 429 would be written as one dot above one dot above four dots and a bar, or (1×20<sup>2</sup>) + (1×20<sup>1</sup>) + 9 = 429.
 
 
:{| class="mw-collapsible mw-collapsed" style="text-align:center;"
|+Addition (multiple)
|- style="font-size: 150%;"
| (1×20<sup>2</sup>)
| +
| (1×20<sup>1</sup>)
| +
| 9
| =
| 429
|-
| {{Horizontal Maya|1}}
|
| {{Horizontal Maya|1}}
|
| {{Horizontal Maya|9}}
|
| {{Horizontal Maya|1}}{{Horizontal Maya|1}}{{Horizontal Maya|9}}
|}
 
Other than the bar and dot notation, Maya numerals were sometimes illustrated by face type glyphs or pictures. The face glyph for a number represents the deity associated with the number. These face number glyphs were rarely used, and are mostly seen on some of the most elaborate monumental carvings.
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| title = Codex Dresdensis - Mscr.Dresd.R.310
| publisher = Saxon State and University Library (SLUB) Dresden
}}</ref> It has been suggested that these pointed, oblong "shellbread" representations are calligraphic variants of the PET logogram, approximately meaning "circular" or "rounded", and perhaps the basis of a derived noun meaning "totality" or "grouping", such that the representations may be an appropriate marker for a number position which has reached its totality.<ref>{{cite web
| url = https://mayadecipherment.com/2012/06/15/the-calligraphic-zero
| title = The Calligraphic Zero
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== Addition and subtraction ==
Adding and subtracting numbers below 20 using MayaMayan numerals is very simple.
[[Addition]] is performed by combining the numeric symbols at each level:<br>
[[Image:Maya add.png|210px]]
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== Origins ==
Several Mesoamerican cultures used similar numerals and base-twenty systems and the [[Mesoamerican Long Count calendar]] requiring the use of zero as a place-holder. The earliest long count date (on [[Chiapa de Corzo Stela 2#Notable finds|Stela 2]] at Chiappa de Corzo, [[Chiapas]]) is from 36 BC.<ref>{{refn|group=lower-alpha|No long count date actually using the number 0 has been found before the 3rd century, but since the long count system would make no sense without some placeholder, and since Mesoamerican glyphs do not typically leave empty spaces, these earlier dates are taken as indirect evidence that the concept of 0 already existed at the time.</ref>}}
 
Since the eight earliest Long Count dates appear outside the Maya homeland,<ref>{{cite book|title=The Olmecs: America's First Civilization|last=Diehl|first=Richard|publisher=Thames & Hudson|year=2004|isbn=0-500-02119-8|location=London|page=[https://archive.org/details/olmecsamericasfi0000dieh/page/186 186]|oclc=56746987|author-link=Richard Diehl|url=https://archive.org/details/olmecsamericasfi0000dieh/page/186}}</ref> it is assumed that the use of zero and the Long Count calendar predated the Maya, and was possibly the invention of the [[Olmec]]. Indeed, many of the earliest Long Count dates were found within the Olmec heartland. However, the Olmec civilization had come to an end by the 4th century BC, several centuries before the earliest known Long Count dates—which suggests that zero was ''not'' an Olmec discovery.
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==See also==
*[[Kaktovik numerals]], a similar system from another culture, created in the late 20th century.
 
== Notes ==
{{reflist|group=lower-alpha}}
 
== References ==
Retrieved from "https://en.wikipedia.org/wiki/Maya_numerals"