Maya numerals

The Mayan numeral system was the system to represent

(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.^[1]

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.

(1×20)	+	13	=	33

Upon reaching 20² 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.

(1×202)	+	(1×201)	+	9	=	429

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.

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).^[2] It has been suggested that these pointed, oblong "shell" 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.^[3]

Addition and subtraction

Adding and subtracting numbers below 20 using Mayan numerals is very simple. Addition is performed by combining the numeric symbols at each level:

If five or more dots result from the combination, five dots are removed and replaced by a bar. If four or more bars result, four bars are removed and a dot is added to the next higher row. This also means that the value of 1 bar is 5.

Similarly with

symbol:

If there are not enough dots in a minuend position, a bar is replaced by five dots. If there are not enough bars, a dot is removed from the next higher minuend symbol in the column and four bars are added to the minuend symbol which is being worked on.

Modified vigesimal system in the Maya calendar

solar year at least since the early Classic era.)^[4]

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.

Every known example of large numbers in the Maya system uses this 'modified vigesimal' system, with the third position representing multiples of 18×20. It is reasonable to assume, but not proven by any evidence, that the normal system in use was a pure base-20 system.[5]

Origins

Several Mesoamerican cultures used similar numerals and base-twenty systems and the

Stela 2 at Chiappa de Corzo, Chiapas) is from 36 BC.^[6]

Since the eight earliest Long Count dates appear outside the Maya homeland,

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.

Unicode

Main article: Mayan Numerals (Unicode block)

Mayan numerals codes in Unicode comprise the block 1D2E0 to 1D2F3

Mayan Numerals[1][2] Official Unicode Consortium code chart (PDF)

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

U+1D2Ex

𝋠

𝋡

𝋢

𝋣

𝋤

𝋥

𝋦

𝋧

𝋨

𝋩

𝋪

𝋫

𝋬

𝋭

𝋮

𝋯

U+1D2Fx

𝋰

𝋱

𝋲

𝋳

Notes 1.^ As of Unicode version 15.1 2.^ Grey areas indicate non-assigned code points

See also

• Kaktovik numerals, a similar system from another culture, created in the late 20th century.

References

1. ^ Saxakali (1997). "Mayan Numerals". Archived from the original on 2006-07-14. Retrieved 2006-07-29.
2. ^ "Codex Dresdensis - Mscr.Dresd.R.310". Saxon State and University Library (SLUB) Dresden.
3. ^ David Stuart (June 15, 2012). "The Calligraphic Zero". Maya Decipherment: Ideas on Maya Writing and Iconography -- Boundary End Archaeological Research Center. Retrieved Mar 11, 2024.
4. ISBN 1-56006-757-8
   .
5. ^ Anderson, W. French. “Arithmetic in Maya Numerals.” American Antiquity, vol. 36, no. 1, 1971, pp. 54–63
6. ^ 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.
7. OCLC 56746987
   .

Further reading

• OCLC 15895415
  .
• Díaz Díaz, Ruy (December 2006). "Apuntes sobre la aritmética Maya" (online reproduction). Educere (in Spanish). 10 (35). Táchira, Venezuela:
  OCLC 66480251
  .
• Davidson, Luis J. “The Maya Numerals.” Mathematics in School, vol. 3, no. 4, 1974, pp. 7–7
• OCLC 275252
  .

External links

Wikimedia Commons has media related to Mayan numerals.

• Maya numerals converter - online converter from decimal numeration to Maya numeral notation.
• Anthropomorphic Maya numbers - online story of number representations.
• BabelStone Mayan Numerals - free font for Unicode Mayan numeral characters.