Maya numerals: Difference between revisions

{| class="wikitable" style="text-align:center; margin-left:1em; float: right" [[Mayan Numbers/Numerals: Explained in a table]]

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 [[turtle shell|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 (20³ or 8000, then 20⁴ 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 (1×20²) + (1×20¹) + 9 = 429.

Adding and subtracting numbers below 20 using MayaMayan numerals is very simple.

[[File:La Mojarra Estela 1 (Escritura superior).jpg|thumb|266x266px|Detail showing in the right columns glyphs from [[La Mojarra Stela 1]]. The left column uses Maya numerals to show a [[Mesoamerican Long Count calendar|Long Count date]] of 8.5.16.9.7 or 156 CE.]] The "Long Count" portion of the [[Maya calendar]] uses a variation on the strictly vigesimal numerals to show a [[Mesoamerican Long Count calendar|Long Count date]]. In the second position, only the digits up to 17 are used, and the [[positional notation|place value]] of the third position is not 20×20 = 400, as would otherwise be expected, but 18×20 = 360 so that one dot over two zeros signifies 360. Presumably, this is because 360 is roughly the number of days in a [[year]]. (The Maya had however a quite accurate estimation of 365.2422 days for the [[Solar Year|solar year]] at least since the early [[Maya civilization#Classic period|Classic era]].)<ref>{{cite book | title=The Mayans | publisher=Lucent Books, Inc. | author=Kallen, Stuart A. | year=1955 | location=San Diego, CA | pages=[https://archive.org/details/mayans00kall/page/56 56] | isbn=1-56006-757-8 | url-access=registration | url=https://archive.org/details/mayans00kall/page/56 }}</ref> Subsequent positions use all twenty digits and the place values continue as 18×20×20 = 7,200 and 18×20×20×20 = 144,000, etc.

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 ChiapaChiappa 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>}}

{{Commons category|MayaMayan numerals}}