Tool to convert to/from Mayan numbers system. The Maya numeral system uses a mix of base 20 (vigesimal) and base 5 (and also 360) numerals

Mayan Numerals - dCode

Tag(s) : Numeral System, History, Symbol Substitution

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Mayan numbers are a numbering system used by the ancient Mayans of Central and South America. The mathematical peculiarity of Maya numeration is the writing of numbers in base 20 (called vicesimal or vigesimal base) contrary to the writing in base 10 usual nowadays.

In the Maya system, numbers consist of simple glyphs/symbols: the dots `.` and the `-` (horizontal) lines. Since they are written in base 20, there are 20 different digits composed of simple glyphs/symbols that can be added: dots `.` associated to value $ 1 $ (units) and horizontal bars `-` associated to value $ 5 $.

__Example:__ The number $ 14 $ (English/hindu-arabic numeral in base 10) is written in Mayan (2 bars and 4 dots: $ 2 \times 5 + 4 \times 1 = 14 $)

__Example:__ $ 0 $ (zero) is noted (originally a shell shape, but some say an egg or an American football/rugby ball)

In the Maya civilization, the writing of numbers is generally vertical (the units are placed under the tens/twenties, under the (four-)hundreds etc.) Beyond 19, base 20 comes into play, and writing requires 2 lines.

__Example:__ $ 26 $ is written (in 2 rows: 1 dot on the first line: $ 1 \times 20 = 20 $ and 1 dot and 1 bar on the second line $ 1 + 5 = 6 $, total $ 20 + 6 = 26 $)

From 360, the writing of Mayan numbers diverges. The written traces show 2 notations, including a specific rule, a *modified vigesimal system* (called long count) particularly when they spoke of dates. The variant takes place at the third tier/line, which then stops at $ 360 $ (base 10).

Converting Mayan numerals to English/Arabic numerals is made by counting dots and bars symbols on each rows and treat it as base 20 writing, before converting it to base 10.

__Example:__ a single row with 2 dots and 3 bars: $ 2 \times 1 + 3 \times 5 = 17 $

__Example:__ A number on two rows with 1 dot then (under) 2 dots: $ 1 \times 20 + 2 \times 1 = 22 $

For numbers that are greater than or equal to 360, be sure to know the variant used (long count).

The dates in Maya are based on the Mesoamerican Long Count calendar. They use the kin, which is 1 day, then the winal which is 20 days, the tun, an 18 winal period which is therefore 360 days, about 1 solar year (365.24 days), then the katun (20 tun = 7200 days = about 20 years), then the baktun (20 katun, 144000 days = about 394 years).

Day 0 seems to match August 11, 3114 BC of our era (precision to be relativised with the Gregorian / Julian calendar chosen)

To write a birthdate or anniversary date in a contemporary way, dCode recommends to use the values of the 3 numbers (day, month, year) written in Maya and separated by a dash `-` or a bar `/` (slash), the year with the font changed to 360.

There are two other calendar variations: the Tzolkin (or Tzolk'in) and the Haab, whose cycles are still slightly different.

Today, for counting, base 10 is used, up to 9, the 10 digits 0,1,2,3,4,5,6,7,8,9 use only one character/symbol /glyph, beyond 9, it is necessary to use 2 symbols/numbers to write 10 (a `1` and a `0`). Similarly, the Mayan numeral uses base 20 to count, so beyond 19 it is necessary to use 2 symbols/glyphs.

It is assumed that men today count in base 10 because they have 10 fingers on their hands. It is likely that the Maya considered a process including the toes, or 20 fingers.

It's mostly unusual and confusing so avoid it. It's a bit like asking the question why not write `10` with a new symbol, like `Ɒ`, some may understand, some may not.

Maya numeration uses generally stacked lines and dots.

The Mayan civilization lived in Central America around -2000 BC as their pyramids testify.

Although there are similarities, the Mayan civilization is different from the Aztecs or the Incas.

Any reference to Mexico, Belize, Guatemala, El Salvador or Honduras (current areas where the Mayans lived) are clues.

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Cite as source (bibliography):

*Mayan Numerals* on dCode.fr [online website], retrieved on 2024-06-16,

- Mayan to Decimal/Arabic Numbers Converter
- Decimal/Arabic to Mayan Numbers Converter
- What are Maya numerals? (Definition)
- How to write Maya numbers?
- How to convert Mayan numbers?
- How to write a date with Mayan numbers? (long count)
- How to count using Mayan numerals?
- Why does maya notation change after 19 (from 20)?
- Why does maya notation use base 20?
- Why is 20 not written with 4 bars?
- How to recognize Mayan numbers?

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https://www.dcode.fr/mayan-numbers

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