Editing Maya numerals (section)

{{Short description|System used by the ancient Mayan civilization to represent numbers and dates}}
{{stack begin|float=right}}
[[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
| 
| {{Horizontal Maya|1}}
| {{Horizontal Maya|12}}
|- 
| 20s
| {{Horizontal Maya|1}}
| {{Horizontal Maya|1}}
| {{Horizontal Maya|16}}
|-
| 1s
| {{Horizontal Maya|13}}
| {{Horizontal Maya|9}}
| {{Horizontal Maya|5}}
|-
| Total(s)
| 33
| 429
| 5125
|}
{{Table Numeral Systems}}
{{stack end}}

The '''Mayan 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 shell),<ref>{{Cite journal |last=Batz |first=J. Mucía |date=March 29, 2021 |title="Nik" — The Zero in Vigesimal Maya Mathematics |url=https://baas.aas.org/pub/2021n1i336p03/release/2 |url-status=live |archive-url=https://archive.today/20240910192515/https://baas.aas.org/pub/2021n1i336p03/release/2 |archive-date=September 10, 2024 |access-date=October 30, 2024 |website=Bulletin of the AAS|volume=53 |issue=1 }}</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 Mayan used powers of twenty, just as the [[Hindu–Arabic numeral system]] uses powers of ten.<ref>{{cite web |author=Saxakali |date=1997 |title=Mayan Numerals |url=http://saxakali.com/historymam2.htm |archive-url=https://web.archive.org/web/20060714025120/http://www.saxakali.com/historymam2.htm |archive-date=July 14, 2006 |access-date=July 29, 2006 |website=Saxakali}}</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) + 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.

[[File:Dresden_Codex_f8461796.png|thumb|266px|Section of page 43b of the [[Dresden Codex]] showing the different representations of zero.]]

There are different representations of zero in the [[Dresden Codex]], as can be seen at page 43b (which is concerned with the synodic cycle of Mars).<ref>{{cite web
| url = http://digital.slub-dresden.de/id280742827
| title = Codex Dresdensis - Mscr.Dresd.R.310
| publisher = Saxon State and University Library (SLUB) Dresden
}}</ref> It has been suggested that these pointed, oblong "bread" 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
| author = David Stuart
| date = June 15, 2012
| website = Maya Decipherment: Ideas on Maya Writing and Iconography -- Boundary End Archaeological Research Center
| accessdate = Mar 11, 2024
}}</ref>