Maya Mathematics

The Maya lived in the area in Central America that now consists of Yucatan, Guatemala, Belize and southern Mexico (the Chiapas and Tabasco provinces).

This whole area lies south of the tropic of Cancer, and north of the equator, and is about 900 kilometers from north to south and 550 kilometers in the east-west direction. Theirs was a true Stone Age Culture, although the Maya at the time of Spanish contact in the sixteenth century, did know about working with copper and gold. While the Spanish prized gold highly, the Maya venerated jade.

The Maya developed a unique mathematical system that uses dots for units and bars for five units. The numbers can be written vertically or horizontally.

Instead of ten digits like we have today, the Maya used a base number of 20. (Base 20 is vigesimal.)

They discovered and used the zero as well as a vigesimal positioning system, similar to the decimal positioning system used today. Its symbols and their Arabic equivalents are:

Since the Maya numerical system is based on 20 units, when a number higher than 19 has to be written, a vertical positioning system that grows upwards is commonly used.

Thus in order to write 20 they would place a zero in the bottom position with a dot on top of it. The dot in this place means one unit of the second order that is worth 20.

To write 21, the zero would change to a dot and for the subsequent numbers the original 19 number count will follow in the first position. As they in turn reach 19 again, another units is added to the second position.

Because the base of the number system was 20, larger numbers were written down in powers of 20. We do that in our decimal system too: for example 32 is 3 10+2.

In the Maya system, this would be 1 20 + 12, because they used 20 as base.

Numbers were written from bottom to top. Below you can see how the number 32 was written:

It was very easy to add and subtract using this number system, but they did not use fractions. Here's an example of a simple addition:

9449 = 9 + 20 12 + 20² 3+ 20³ 1; 10425 = 5 + 20 1+ 20² 6 + 20³ 1

As you can see, adding is just a matter of adding up dots and bars! Maya merchants often used cocoa beans, which they laid out on the ground, to do these calculations.