Mayan numeration system

The Mayan numeration system evolved around A.D. 300. It is a sophisticated system as you will see below. It uses 3 basic numerals to represent any possible number: a dot for one, a horizontal bar for 5, and a conch shell for zero.

0, 1, and 5 in Mayan numeration
They used the 3 symbols above to represent the numbers from 0 through 19 as shown below:

Mayan chart: 0-19

Numbers bigger than 19 in the Mayan numeration system


For number bigger than 19, a number is written in a vertical position so that it becomes a vertical place value system.

Initially, the base used in the Mayan numeration system was base 20 and their place values were 1, 20, 202,203, ...

Then, they changed their place values to 1, 20, 20 × 18, 202 × 18, 203× 18, ...

Using the base 20, 1, 20, 202,203, ..., we can write 20 as follow:

20 in Mayan numeration

In the ones place we have 0 and in the twenties place we have 1, so the number is 0 × 1 + 1 × 20 = 0 + 20 = 20

Still using a base of 20, we can write 100 as follow:

100 in Mayan numeration

0 × 1 + 5 × 20 = 0 + 20 = 100

Here is how to represent 2007

2007 in Mayan numeration

5 × 202 + 0 × 20 + 7 = 5 × 400 + 0 + 7 = 2000 + 7 = 2007

How do we know which number is in what place value?. This is the complicated part in the Mayan numeration system.

Starting from the bottom, a place value must have a number from the list above (1-19)

Tease your brain with the following number. What is it?

368024554 in Mayan numeration

Look carefully and see how I separated the place values.

368024554 in Mayan numeration

Again, I separated according to numbers that are the list above from 1 through 19.

The number is: 14 + 7 × 20 + 1 × 202 + 3 × 203 + 0 × 204 + 15 × 205 + 5 × 206

The number is 14 + 140 + 1 × 400 + 3 × 8,000 + 0 + 15 × 3,200,000 + 5 × 64,000,000

The number is = 14 + 140 + 400 + 24,000 + 0 + 48,000,000 + 320,000,000 = 368024554

With the base 1, 20, 20 × 18, 202 × 18, 203× 18, ... computation is done the exact same way!

3631 in Mayan numeration

Group as shown below:
3631 in Mayan numeration

The number is 11 × 1 + 1 × 20 + 10 × 20 × 18 = 11 + 20 + 3600 = 3631

No doubt, the Mayan numeration system was sophisticated.

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