Mayan Numeration System

Kelly Phutthavong


The Mayan Numeration System dates back to the fourth century and was approximately 1,000 years more advance than the Europeans at that time. It is not known if this system is still used today; leading to not knowing when the usage had ended.

Basis of the Numeration System

The Mayan Numeration System uses a base number of 20. Which is also can be known by a vigesimal. The symbols they use are dots and lines. The reason they use these symbols are because there may be a connection between the Japanese and certain American tribes (Ortenzi, 1964) which lead them to using those specific symbols. They were the first numerations system to have a symbol for the number zero. They wrote their numbers vertically as opposed to horizontally with the lowest denomination on the bottom. The symbol they use for zero looks like a sea shell. The symbols of a dot represented one and the line represented five. These symbols can be combined to construct 19 digits (0-19).


Addition in the Mayan Numeration involves adding symbols, like in base 10, and carrying it to the next place value when the previous one contains more than it can hold. You simply add lines to lines and dots to dots.

When subtracting we must also look at how many pebbles and sticks we have in each position. But in order to subtract we may need to make some sticks into pebbles.

Multiplication in the Mayan Numeration System is very similar to the Hindu Arabic system. It becomes more difficult once the numbers get bigger.


Division in this numeration system maintains the advantage of non-place-value systems in that it is not necessary at each step to determine the exact number to times the divided can be divided by the divisor.

Below represents the problem 246/6.

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Additional Information

This system is believed to have been used because, since the Mayan's lived in such a warm climate and there was rarely a need to wear shoes, 20 was the total number of fingers and toes, thus making the system workable.

The Mayan’s contributed the 360 day calendar, which they used base 18 when dealing with the calendar — each month contained 20 days within 18 months to a year. Resulting with five days left at the end of the year which was a month in itself that was filled with danger and bad luck to the Mayans. This lead to the Mayans inventing the 365 day calendar which revolved around the solar system.


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