Mayan Numerals

Mayan numbers constitute a system of numeration used by the Mayan civilization in Central America, between approximately -2000 and 1500 AD. Their particularity is the use of base 20, called vigesimal (or vicesimal) base where each Mayan number represents a value from 0 to 19.

The Mayan numeral system is additive and positional. In the Mayan system, numbers are composed of simple symbols:

— a dot • represents 1

— a horizontal bar ➖ represents 5

— the symbol represents 0 (originally it was a shell shape, but some say it represents an egg or an American football/rugby ball).

The numbers from 0 to 19 are written by combining these symbols through addition.

Numbers are arranged vertically, with the units at the bottom, then the twenties above, then the hundreds, and so on.

The number $ 26 $ is written on two levels:


The upper level (1 dot) is worth $ 1 \times 20 = 20 $ and the lower level (1 dot and 1 bar) is worth $ 1 + 5 = 6 $, for a total of $ 26 $.

To convert a Mayan number to base 10 (Arabic numerals):

— Identify the number of dots and bars on each level.

— Calculate the value of each level: bottom level: units $ \times 1 $), next level: twenties ($ \times 20 $), next level: $ 20^2 = 400 $ or $ 18 \times 20 = 360 $ depending on the system, etc.

— Add the values obtained.

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.

The first Mayan numbers are:

0(zero)		1		2		3		4
5		6		7		8		9
10		11		12		13		14
15		16		17		18		19
20		21		22		23		24
40		60		80		100

For other Maya numbers (up to 1000, 10000, 100000, 1000000 etc.), use the form above.

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 generally accepted that the Maya chose the base-20 system because they counted using their fingers and toes, which together accounted for 20 extremities.

This vigesimal system also existed among other Mesoamerican peoples and reflects a practical approach to body counting.

The number $ 20 $ therefore represents a change of level: a dot on the top line (worth $ 1 × 20 $) and a zero (shell) on the bottom line.

Writing $ 20 $ with four bars would violate the base-20 place value rule. This notation would be unusual and confusing, so it should be avoided.

It's a bit like asking why not write 10 with a new symbol, like Ɒ; some might understand, others might 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.