The Mayan Number System
Between the 3rd and 10th centuries CE in Central America, there
flourished a civilisation known as the Mayan civilisation that made great
intellectual and cultural progress. Among their intellectual achievements
stands their place value system designed independently of those in Asia. In
their place value system, they also made use of a placeholder symbol, for the
modern-day ‘0’, that looked like a seashell.
In
this system, the symbols are placed vertically to represent a number. To write down numbers in this system, there were only three
symbols. A horizontal bar represented the number 5, a dot represented the number
1, and a special symbol (thought to be a shell) represented zero. The Mayan
system may have been the first to make use of zero as a placeholder/number.
Symbols: 
The Mayan culture used a vigesimal number system or base-20 number system, (and, to some extent, base-5), probably originally developed from counting
on fingers and toes. Thus, addition and subtraction were a relatively simple
matter of adding up dots and bars. After the number 19, larger numbers were
written in a kind of vertical place value format using powers of 20: 1, 20, 20 ×
18 = 360, 202 × 18 = 7200, 203 × 18 = 144000, etc.
Solved Examples
Example 1:
Write the following numbers in Mayan Number System.
a. 47 b. 431 c. 8014
Solution:
a. 47 = (2 × 20) + 7
= 
b. 411 = (1 × 360) + (3 × 20) +
11
= 
c. 8014 = (1 × 7200) + (2 × 360)
+ (4 × 20) + 14
= 
Example 2:
Write the following Mayan Numbers in Hindu-Arabic numerals.
a.
b.
c.
Solution:
a.
= (4 × 20) +
6 = 86
b.
= (2 × 360)
+ (2 × 20) + 9 = 769
c.
= (2 × 7200)
+ (1 × 360) + (3 ×
20) + 8 = 22842