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.
They used the 3 symbols above to represent the numbers from 0 through 19 as shown below:
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, 20
^{2},20
^{3}, ...
Then, they changed their place values to 1, 20, 20 × 18, 20
^{2} × 18, 20
^{3}× 18, ...
Using the base 20, 1, 20, 20
^{2},20
^{3}, ..., we can write 20 as follow:
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:
0 × 1 + 5 × 20 = 0 + 20 = 100
Here is how to represent 2007
5 × 20
^{2} + 0 × 20 + 7 = 5 × 400 + 0 + 7 = 2000 + 7 = 2007
How do we know which number is in what place value?. This is complicated part in the Mayan numeration system
Starting from the bottom, a place value must have a number from the list above(119)
Tease your brain with the following number. What is it?
Look carefully and see how I separated the place values
Again, I separated according to numbers that are the list above from 1 through 19
The number is: 14 + 7 × 20 + 1 × 20
^{2} + 3 × 20
^{3} + 0 × 20
^{4} +
15 × 20
^{5} + 5 × 20
^{6}
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, 20
^{2} × 18, 20
^{3}× 18, ... computation is done the exact same way!
Group as shown below:
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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