Mayan Numerals

Question 1

How to write Maya numbers?

Answer

In Mayan culture, numbers are written in base 20 (called vigesimal base). The 20 Mayan digits are composed of simple glyphs/symbols that can be added: dots . associated to value $ 1 $ (units) and horizontal bars - associated to value $ 5 $. The mayan civilization used a vertical writing for the numbers (units under tens/twenties, under (four-)hundreds, etc.).

Example: The number $ 19 $ (English/hindu-arabic numeral in base 10) is written in Mayan (3 bars and 4 dots: $ 3 \times 5 + 4 \times 1 = 19 $)

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 $)

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

The Mayas seemed to use a specific rule, a modified Vigesimal system, for the third floor when they wrote dates and sometimes for large numbers. Indeed, for dates, the third place always stops at $ 360 $ (base 10). This change on the third floor refers to the following numbers. The reasons for this vigesimal notation (base 20) for dates and large numbers (greater than 360) are not known, and although a majority of the retrieved writings use the modified system, this is not always the case.

Example: In base 20 $ 360 $ is normally written , but in modified base 20, $ 360 $ is written (which equals $ 400 $ in unmodified base 20). In the same way, the number $ 7200 $ is written $ 8000 $.

Question 2

How to convert Mayan numbers?

Answer

Converting Mayan 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 apply the modified vigesimal system if necessary.

Question 3

How to write a date with Mayan numbers?

Answer

The dates in Maya are based on the kin (plural kinob), which is 1 day, then the uinal (plural unialob) which is 20 days, the tun, an 18 uinalob period which is therefore 360 days, about 1 year (365.24 days), then the katun (20 tunob = 7200 days = about 20 years), then the baktun (20 katunob, 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)