Mayan Arithmetic*

    by Steven Fought

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The Mayan Symbol for Zero

While its value is simple enough, the role of the Mayan symbol is considered one of the greatest achievements of the Mayan civilization.

is the Mayan equivalent of the Arabic zero (0), and it allowed the Mayans to express any whole number quantity using place notation.

People who have used Roman numerals know how frustrating a number system that does not use place notation can be. At first glance, the Roman system seems better; smaller numbers expressed in Roman numerals are simpler than those written in Arabic form. To express the counting numbers between 1 and 9, you need three Roman symbols as opposed to nine Arabic symbols. It is when you travel farther up the number line that the Roman system becomes complicated. Each larger quantity (X, L, C, M, etc.) needs a different symbol.

The Arabic system never needs more symbols than the ten it starts with. The value of a particular symbol depends not only on what it is, but also where it is. When you see the number 34, you assume that each unit in the right place is worth 1 and each unit in the left place is worth 10. But some quantities do not fill all the places they use, which is why all place notation systems need a zero. Zeros represent places which are there but do not have anything in them.

Place notation also makes addition and subtraction relatively easy. Each place in a number can be treated in the same way so that learning how to add a large number is as simple as learning how to add one of its places or "carry" numbers when the sum of a place exceeds the maximum value that that place can hold. With Mayan numbers, carrying is done almost the same way as with Arabic numbers.

When you add the numbers 12 and 23, you are adding the values in the individual places of the numbers.

However, when you add two numbers and the sum in an individual place is greater than the amount that place can hold, the part that is greater carries to the next highest place, as in adding 27 to 48:

Knowing when to carry is as simple as knowing the maximum number a place can hold. In our system, that maximum is 9.

Mayan Place Values

In the Mayan system, there are two kinds of elements in each place: dots and bars. A full place looks like this and can be expressed as 19 in our system:

Adding one dot to the place shown above would make it worth 20, which is expressed as a dot with a below it.

Each dot in the new place is worth 20, and since five dots equal one bar, each bar is worth 100 in that place.

The value of a dot in the third place is 400 (20 x 20), and a bar in that place is worth 2,000.

In each successive place, one dot is worth 20 times as much as a dot in the previous place.

Continued page 2

* This article was written for Volume 1, Number 2 (March-April 1989) of   Provoking Thoughts - "The Magazine Devoted to the Thinker in All of Us" (Knowles Dougherty, Publisher and Editor). At the time the author, Steven Fought, was a junior at Strath Haven High School in Wallingford, Pennsylvania.  

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Sarah Seastone Fought
4 January 1997