World Library  
Flag as Inappropriate
Email this Article

Maya numerals

Article Id: WHEBN0000019823
Reproduction Date:

Title: Maya numerals  
Author: World Heritage Encyclopedia
Language: English
Subject: List of numeral systems, Non-standard positional numeral systems, Arabic numerals, Decimal, Maya calendar
Collection: Maya Science and Technology, Numeral Systems, Numerals
Publisher: World Heritage Encyclopedia
Publication
Date:
 

Maya numerals

Maya numerals

Maya numerals are a vigesimal (base-twenty) numeral system used by the Pre-Columbian Maya civilization.

The numerals are made up of three symbols; zero (shell shape, with the plastron uppermost), one (a dot) and five (a bar). For example, thirteen is written as three dots in a horizontal row above two horizontal lines stacked above each other.

Contents

  • Numbers above 19 1
  • Zero 2
  • In the calendar 3
  • Notes 4
  • References 5
  • External links 6

Numbers above 19

400s
20s
1s
33 429 5125


Numbers after 19 were written vertically in powers of twenty. For example, thirty-three would be written as one dot above three dots, which are in turn atop two lines. 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. Upon reaching 202 or 400, another row is started. 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. The powers of twenty are numerals, just as the Hindu-Arabic numeral system uses powers of tens.[1]

Other than the bar and dot notation, Maya numerals can be 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 carving.

Addition and subtraction: Adding and subtracting numbers below 20 using Maya 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.

Similarly with subtraction, remove the elements of the subtrahend symbol from the minuend 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.

Zero

The Maya/Mesoamerican Long Count calendar required the use of zero as a place-holder within its vigesimal positional numeral system. A shell glyph -- -- was used as a zero symbol for these Long Count dates, the earliest of which (on Stela 2 at Chiapa de Corzo, Chiapas) has a date of 36 BC.[2]

However, since the eight earliest Long Count dates appear outside the Maya homeland,[3] it is assumed that the use of zero 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.

In the calendar

Detail showing three columns of glyphs from La Mojarra Stela 1. The left column uses Maya numerals to show a Long Count date of 8.5.16.9.7, or 156 CE.

In the "Long Count" portion of the Maya calendar, a variation on the strictly vigesimal numbering is used. The Long Count changes in the third place value; it is not 20×20 = 400, as would otherwise be expected, but 18×20, so that one dot over two zeros signifies 360. This is supposed to be because 360 is roughly the number of days in a year. (Some hypothesize that this was an early approximation to the number of days in the solar year, although the Maya had a quite accurate calculation of 365.2422 days for the solar year at least since the early Classic era.) Subsequent place values return to base-twenty.

In fact, every known example of large numbers 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.

Notes

  1. ^ Saxakali (1997). "Maya Numerals". Archived from the original on 2006-07-14. Retrieved 2006-07-29. 
  2. ^ No long count date actually using the number 0 has been found before the 3rd century BC, 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.
  3. ^ Diehl (2004, p.186).

References

 
Díaz Díaz, Ruy (December 2006). "Apuntes sobre la aritmética Maya" (online reproduction). Educere (in Español) (Táchira, Venezuela:  
 
 

External links

  • Maya Mathematics online converter from decimal numeration to Maya numeral notation.
  • Anthropomorphic Maya numbers online story of number representations.
  • Learn Maya Numbers iPhone app Maya numerals converter.
This article was sourced from Creative Commons Attribution-ShareAlike License; additional terms may apply. World Heritage Encyclopedia content is assembled from numerous content providers, Open Access Publishing, and in compliance with The Fair Access to Science and Technology Research Act (FASTR), Wikimedia Foundation, Inc., Public Library of Science, The Encyclopedia of Life, Open Book Publishers (OBP), PubMed, U.S. National Library of Medicine, National Center for Biotechnology Information, U.S. National Library of Medicine, National Institutes of Health (NIH), U.S. Department of Health & Human Services, and USA.gov, which sources content from all federal, state, local, tribal, and territorial government publication portals (.gov, .mil, .edu). Funding for USA.gov and content contributors is made possible from the U.S. Congress, E-Government Act of 2002.
 
Crowd sourced content that is contributed to World Heritage Encyclopedia is peer reviewed and edited by our editorial staff to ensure quality scholarly research articles.
 
By using this site, you agree to the Terms of Use and Privacy Policy. World Heritage Encyclopedia™ is a registered trademark of the World Public Library Association, a non-profit organization.
 


Copyright © World Library Foundation. All rights reserved. eBooks from Project Gutenberg are sponsored by the World Library Foundation,
a 501c(4) Member's Support Non-Profit Organization, and is NOT affiliated with any governmental agency or department.